Understanding Depth of Field, with
Depth of Field Calculator, and Hyperfocal distance

And a better way to blur the background

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The Concept of Depth of Field

The Depth of Field calculator also concerned with blurring the background

The Hyperfocal chart and calculator for your sensor

Blurring Background Without Suffering f/1.8
Standing back with a longer lens can give better background results than f/1.8

Perspective is Not about the lens, but is Only about where the camera stands

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More detail about What Is Depth of Field

Comparison of the numbers of various Sensor Sizes

The Viewing Size of CoC and DOF

So What To Do about Depth of Field?

What is Hyperfocal Distance?

The fraction of DOF in front of subject

Qualifications about Viewing Depth of Field

Lenses are focused at only the ONE distance (determined by the current focus ring rotation), but which we perceive as a zone of distance in which we don't notice any blur yet. A zone of "Good Enough", so to speak. But enlargement for viewing is a factor making it easier to see that blur. Users may not always realize it, but Depth of Field is computed based on what we might see assuming a standard viewing enlargement size of an 8x10 inch print viewed at 10 inches, which you should realize might not always be your own situation. The DOF that we can see depends on the enlargement of the sensor image, because greater enlargement magnifies the blur that we can perceive (and perceiving it is what DOF is about). The next Page 2 here covers that.

The blue object represents the camera lens, and the dark black vertical line at far right is the camera sensor where the scene is focused.

A “point” is the theoretical zero size of a hypothetical point when perfectly focused.
The Blue line is the actual focus point at S1.
The Red line is the out of focus distance of a “point” at S2.
C is the blur circle of the zero size point at S2.
c is the reproduced CoC size on the sensor.
CoC is NOT the size of any scene object, it is about every computed out of focus hypothetical spot of original zero size.
DOF computes the near and far distance limits where c does not exceed the maximum permissible CoC specified for the sensor size, which is judged to be Not perceptible by the eye after a standard 8×10 inch enlargement at the standard viewing distance of 25 cm (10 inches).
More detail at Wikipedia.

The concept of computed Depth of Field: The computed blurred diameter of a "point" that is out of focus in the camera lens is called CoC (Circle of Confusion). A "point" is the theoretical size of a hypothetical speck of size zero when perfectly focused, but any spot computes larger when blurred. However the CoC number that is entered into DOF calculations is chosen as a specific Maximum Allowable Limit of the diameter of a blurred point (computed from sensor size, in preparation for what the eye can see in future enlargement to 8x10 inches). Depth of Field simply computes the distance at which the blur of a out-of-focus point matches this CoC limit, conceptually planned be where any blur becomes just perceivable by eye (in a standard 8x10 inch enlargement). See the CoC diagram (and the next page continues too). Misfocus increases blurred size very gradually, so there is NO precise border line on sharpness. But still, the DOF formula computes the distance very precisely, even if our eye can't detect any difference just barely on either side of that limit.

Just saying, do realize that in the math of Depth of Field calculations, the blur of a "point" at the end of the computed DOF range has reached the full size of this Maximum Allowable CoC limit, but is still reported as being in DOF range and acceptably sharp. And then, just the slightest greater distance is reported as exceeding the CoC limit to be unacceptable, because it is computed to have passed the threshold of perception by the human eye (in the standard 8x10 inch print enlargement). DOF simply reports the distance where the degree of misfocus crosses that CoC limit line, even if such line of difference is pretty vague to our eye. Meaning, sharpness wasn't quite that good just before reaching the limit, and not quite that bad just after. Still, DOF is a good guide of what to expect in terms of focus sharpness. We are usually just guessing distances anyway.

In any given camera, Depth of Field is determined by the combination of three lens factors, and IF with all else the same, then:  

Depth of field Span is total range, the sum of DOF range in front of focus, and DOF range behind focus.

These three lens properties are in the lens image projected onto the sensor, and we adjust those in our camera to control depth of field. However, there are four factors computing Depth of Field, perhaps not always understood.

Sensor Size is a factor too: We can't view the lens image at the sensor, we only see enlargements of it. The sensor size cannot change what the lens does, but sensor size certainly does affect the DOF perceived in the necessary enlargement of it, which affects the corresponding DOF that is computed. Smaller sensors require greater enlargement to compare at the same standard viewing size. Greater enlargement also enlarges the blur, which becomes more easily visible then. So the computed Depth of Field accounts for this expected enlargement from sensor size too (DOF computes what should be perceivable in a standard 8x10 inch enlargement). Circle of Confusion (CoC, next page) represents the enlargement of sensor size, and is the maximum blur limit that calculates the reported DOF span. CoC is directly proportional to sensor diagonal dimension (CoC mm = diagonal mm / 1500, but different divisors can be chosen). CoC is a calculated dimension in the lens image on the sensor, but its maximum size limit is chosen to correspond to the necessary future enlargement of the viewed image (the standard is an 8x10 inch print). The first thing any DOF calculator asks is sensor size (to determine CoC size for calculations). Smaller sensors compute a smaller CoC to intentionally compute less DOF, due to the necessary greater enlargement to view it.

Still, in practice, we do clearly see that using a smaller sensor does result in greater DOF (the opposite of what was just said). But that's only because a smaller sensor "crops" the view, and must use a shorter focal length lens to still capture the same full scene view. That combination in practice normally does see significantly greater DOF. That is only due to the shorter lens which is a larger effect than sensor size. The sensors on compact and phone cameras are so tiny that their lens is necessarily very short (maybe 4 mm), which ensures great depth of field, regardless if they even focus or not. Or even if we could use the Same longer lens on both cameras, the smaller sensor must then stand back farther to be able to capture the same Field of View, and greater distance offers greater DOF span too. These DOF changes are due to the lens focal length or distance actually responsible. But if all else is the same (likely rarely the case), the smaller sensor certainly does compute less DOF. The DOF calculator will easily verify this.

Additional features in this DOF calculator (seen below) that you may not see elsewhere are:

A Depth of Field calculator

also concerned with Blurring the Background

Identify your camera sensor size by entering either actual Sensor Size or Film Size, or Crop Factor, or even Equivalent Focal Length specs. Sensor size can be hard to know, but these can calculate sensor size. Much more arbitrary and less precise, but even CoC can determine sensor size, because CoC relates to the standard enlargement of sensor size. You can see ways to determine your Crop Factor (perhaps even from known Equivalent Focal Length). It's hard to beat precise actual sensor size specifications though.
But in the DOF calculations, always specify the actual real focal length, Never any Equivalent Focal Length.

There are issues when trying to determine the sensor size of compact or phone cameras. Also issues with mixed formats (both video and still photo images from the same camera). These issues are summarized at Issues Determining Sensor Size. If using 16:9 in 3:2 or 4:3 cameras, please see the notes there.

Film or Sensor Size dropdown box in Option 5: The film sizes are known good, but the "1/xx inches digital sensor size" system for compact and cell phone cameras is at best an approximation, because actual size instead depends on the specific camera models chip. Especially the compact and phone sizes like 1/1.8" CCD are vague (actual sensor sizes are instead described as specifications of width and height in mm, and those usual sizes are substituted here). If actual sensor size is not known, I suggest the Crop Factor option may be more accurately known. Crop Factor also needs Aspect Ratio to compute sensor dimensions. Those are rounded values, but still reasonably precise for DOF. The computed sensor size is shown in results.

Fisheye lenses or macro distances are special cases adversely affecting accuracy, NOT included here.

Abbreviations: DOF is Depth of Field, CoC is Circle of Confusion, and FoV is Field of View.

Entering changes:   Most buttons will redraw results automatically. But after changing a text field, it is necessary to either click the Compute button or hit Enter in the text field. The calculator will "blink" once when showing the changed result. The bright Yellow box shows the final sensor size result seen.

Depth of Field Calculator

Five ways to specify Sensor Size
1 Sensor Size x mm
Use Native Aspect
Use Aspect Ratio menu
2 Crop Factor Option 1 Can use, and
Options 2-4 Will use Aspect Ratio menu,
see its suboptions

Aspect Ratio

3 Focal length of this lens
Equivalent focal length used on 35 mm film.
4 CoC, specific and direct, regardless
5 Film or sensor size 
Distance units   Convert Results are same units
Sensor pixels x For CoC size in pixels
CoC DivisorDiagonal / 1442 or 1500 usually
Viewing size dimension x
Standard DOF is 8x10 inches (203x254 mm)

The Hyperfocal Chart below also uses THIS sensor data

ResultsLens ALens B
Focal length mm mm
Subject focus Distance Equivalent of A
From subject,
positive if behind,
  Same for A & B
negative in front
Depth of Field
DOF total span
DOF in front
DOF behind
Blur of CoC
FoV at subject
FoV at

The "d=2.5%" or "d=2.1x" at Hyperfocal means for example that the focus distance is 2.5% or 2.1x hyperfocal. More details of DOF calculator usage are on next page. A chart of hyperfocal distances is below.

CoC is the enlarged blurred diameter of a hypothetical “point” of original zero size (it’s a math thing). CoC is NOT the size of any visible blurred object or area, which is much larger than CoC.

It's a regular DOF calculator too, and if not concerned with comparing two lenses, simply ignore the second lens. Or for two lenses, you can enter a distance for lens B, or another choice, it can compute an equivalent distance (for the B lens, matching the A lens Field of View) from the focal lengths (as described here).

Specifying Sensor Size: (Five options)

The feet/meters selection is which distance units you are using (the DOF and FoV results are these same units). When it is changed, the checked Convert checkbox will convert previous numbers to keep the same distances. Otherwise that feet/meters change will leave distance values numerically unchanged (but feet and meters are different distance values affecting DOF). You can enter 99999 feet for an adequate distance of infinity (19 miles).

CoC Divisor: - CoC is computed from CoC = (sensor diagonal / a constant). The modern constant is a 1500 divisor from the Zeiss formula. Meaning, for 1x full frame sensor (originally 35 mm film size), 1500 divisor computes that CoC as 43.267 / 1500 = 0.0288 mm. Japanese cameras have typically used the CoC value 0.03 mm, which corresponds to a divisor of 1442, which may have been rounding, but 0.03 mm is what we often see now (so the default divisor here is 1442). These differ by 4.17% in computed DOF span, nothing major. Feel free to change the calculator to use 1500 if those results make you more comfortable. Historically, values from 1000 to 1730 have been used in the distant past, but 1442 to 1500 are the modern idea.

Viewing Size: In DOF calculations, the specified CoC limit is computed from the sensor diagonal size. Except we don't view the sensor, instead the CoC concept is designed to be enlarged to viewing size, where we do judge DOF. The perceptible DOF situation absolutely depends on viewing enlargement. The bigger we enlarge it, the easier and better we can detect the blur. So you should know the important DOF concept that the convention is DOF is routinely computed for an enlarged standard 8x10 inch print size (203.2×254 mm) viewed at 10 inches (250 mm). If you have a different viewing size, the DOF calculator has an option to compute for it.

CoC at Viewing Size: Assume a 1x full frame sensor CoC limit is 0.03 mm at sensor size, and that the sensor diagonal is enlarged to the diagonal size of the 8x10 inch print. Then when enlarged this 7.518x for viewing size near 8x10 inches, then it becomes 0.22558 mm (1442) or 0.21685 mm (1500) in the final enlarged 8x10 image (if CoC and diagonals have been computed properly). This constant Enlarged CoC is (CoC x enlargement), but it also reduces to 8x10 diagonal / CoC divisor = 325.2787 / 1442 = 0.22557). Enlargement here is computed from (8x10 diagonal / sensor diagonal). That makes Enlarged CoC = always be the same number, like 0.22558 mm for any sensor size, which is planned for the human eye capabilities to see it in the enlarged print. This limit is about perceiving the presence of a blurred area, nothing that can precisely be measured, or even seen or recognized. Viewing DOF in an image smaller than the standard 8x10 will look better than calculated, and viewing it larger will look worse. This enlarged CoC may compute 5 pixels size on the sensor, and unless resampled, it remains as still 5 enlarged pixels when enlarged to viewing size The idea of this Enlarged CoC limit is that it is a constant designed for the threshold of being perceptible to the human eye. More detail about viewing size adjustments on next page.

The background distance behind subject will here be the same for both lenses, since that's where the subject is standing. A relatively long distance behind is good for blurring the background.

Or if of interest, it can instead compute DOF blur for a foreground point too, in front of the subject. To do that, just enter the distance in Front of the subject as a negative number at Background distance, and it will compute the DOF for that distance in front of the subject. I showed a + in the initial default, only to hopefully help clarify the method. Entering the + is not necessary, it is positive without it (but it is necessary to enter the minus to indicate negative). If minus, the field text names will be reworded as "Foreground" (as applicable), and the Foreground numbers will be correct for that distance.
Example: 8 feet behind a subject at 10 feet is entered as 8, and will be shown as 18 feet Background distance (from camera).
Or 8 feet in front of a subject at 10 feet is entered as -8, and will be shown as 2 feet Foreground distance.

The technical definitions specify that sensor diagonal size determines CoC using a standard divisor (based on standard viewing enlargement size), and that this CoC size is the our computed criteria determining if a point distant from the focus point is "sharp enough" or not sharp enough. The full sensor chip size has a native crop factor, but when we specify a different sensor format in Option 1, 2, 3, or 4 (like using a 4:3 camera for a 16:9 video), this reduces the sensor area used, which slightly changes all of the sensor parameters. The Image Width and Height change, and the Crop Factor and Equivalent Focal Length and CoC, and Depth of Field and Field of View change a little when the sensor format changes away from native format. The calculator calculates Depth of Field using the actual specified sensor format, and shows the values used. This is NOT an issue for Option 5, since it just uses the one fixed sensor size and aspect shape, whatever the film size or sensor size are, and does not use other ratios.

And this is important, so a red warning may be shown if the Aspect Ratio specified does not match the native Crop Factor computed with Option 2, 3 or 4 sensor sizes. This match warning applies to the option's specified Native crop factor (not the smaller mixed format frames). For example, a camera may have a native 4:3 sensor chip, but currently using a 16:9 video format. Both are specified in the Aspect menu, and the warning means that the correct native aspect ratio was likely not selected to match the native crop factor, which seems an easy oversight, not likely intended, but it changes sensor sizes and DOF numbers. Any warning can be ignored if it is actually correct (you could let me know about the facts of that situation if the warning is not shown correctly). It makes the standard assumption that crop factors less than 2x should be 3:2, or larger than 3x should be 4:3 (with exception for 2.7x), which are the normal expected and required values.

If using options 1, 2, 3 and 4, do pay attention to properly specify Aspect Ratio. The aspect menu selection "16:9 in a 4:3 camera" should be clear enough. The crop factor determines sensor Size, and then the native aspect ratio specifies the Shape of it. This in turn specifies the size of the mixed formats contained on it, so it is important to compute the correct native numbers. If any interest, there is a chart that can be shown in the Field of View calculator (using the orange "aspect" button in the calculator, it has the same aspect menu) that can show how these same mixed aspect ratio change sensor area size and shape.

Hyperfocal Distance

Hyperfocal Primer

The Hyperfocal distance is the closest focus distance where Depth of Field range will still reach to infinity. That can be important for landscapes, and also to perhaps include a very near dramatic feature up close to camera. Perhaps a very near colorful flower or an interesting rugged gnarly stump with your scenic in the background. For any given camera, hyperfocal distance is closer with a shorter focal length or a greater f/stop number. It is also affected by sensor size, but the view of a smaller sensor size also normally requires a shorter focal length and a smaller f/stop number.

The usefulness of hyperfocal is this:

  • If focused at infinity, DOF will reach back to the Hyperfocal distance. Of course, there is nothing further than infinity (so to speak), so focusing back between hyperfocal and infinity could use a larger zone of DOF range.
  • If focused at the Hyperfocal distance, the DOF range extends to infinity, and also extends back to Half of hyperfocal. So this is the maximum Depth of Field span possible, but still meaning that sharpness at both near and far extremes are at the acceptable DOF CoC limits (where it is considered to become unacceptable). However perceived DoF can vary, it is Not a precise limit. The focused distance is of course always the sharpest point.
  • Knowledge of hyperfocal is often pretty useful to maximize DOF involving infinity, especially if using a shorter wide angle lens stopped well down (like to f/16 or f/22) to provide this extreme DOF range. It can be amazing.

    • Cell phone cameras have an extremely short lens (the normal lens is almost 5 mm focal length), and does not focus so they are preset to focus at hyperfocal distance for maybe f/2.8, so about everything is in focus. In bright sun (for a stopped down lens aperture), then perhaps back to about one foot or two. The cell phone camera offers no manual control, but hyperfocal focus is how this is achieved.
    • Compact cameras both focus and zoom, so hyperfocal offers choices for great DOF.
    • Larger cameras, such as DSLR class, have a larger sensor to make DOF a little harder, which makes focusing at hyperfocal be very useful in those special situations. Any focus further than hyperfocal will make DOF reach infinity. But focus at infinity prevents DOF closer than hyperfocal.

    But if there are no objects so very close (like back at half of hyperfocal), then focusing out a little farther than hyperfocal might fit your situation better (to be a little sharper there, and at infinity). These are of course vague guesses since the marked lens distance scale has so very few numbers on it. The DOF calculator can compute that DOF range estimate, or the chart below shows hyperfocal clearly, but setting that value on the lens is guesswork. And if it's a zoom lens or one with internal focusing (these change internal elements as they zoom or focus), so you might want to check its marked numbers at some measured distances. Small Hyperfocal numbers (like 5 or 10 feet) should be easier. In the old days, we "bracketed" photos with different exposure tries, hoping one was right. Similarly try some different distance settings on the lens, and some awesome results can be achieved.

  • But always remember, a lens focuses at only the one distance. That focused point will always be the sharpest focus (which might be very important at times, or sometimes you need the entire zone). Depth of Field defines a plus and minus distance zone around the focus point as the "acceptable" zone of out-of-focus blur, providing an approximate "often good enough" sharpness zone, as defined by CoC limits (size of Circle of Confusion). Sharpness is considered unacceptable when that limit is reached, however it is gradual, there is no visible boundary there. Hyperfocal focus offers a maximum DOF zone (reaching infinity), which certainly can be a big help, but maybe don't expect extreme miracles every time. The one actual focus point will always be the sharpest focus.

The Redraw button below will compute the chart's hyperfocal distances for various focal lengths and apertures, for the current sensor size and settings selected above. The chart will show all aperture cases for that selected sensor size.

Knowing just a few of these numbers for your lens will find occasions when it can be handy (using a shorter focal length at stopped down aperture will be most dramatic at reaching both near and far). If you want a printed chart (suitable for letter or A4 paper) in your camera bag for such situations, here's a printable PDF of hyperfocal for f/1 to f/64, which includes charts for five sensor sizes (crop factors 1, 1.5, 1.6, 2, 2.71), for both Feet and Meters (ten charts). Print and keep the one page of interest for your sensor size and distance units. A cell phone or even a compact camera (normal focal length) lens is so short that some apertures will likely have depth of field from a a couple of feet to infinity. But hyperfocal is a real plus for larger cameras.

Including an interesting close and sharp foreground object can have dramatic effect on landscapes. A stopped-down wide angle lens can do this. Try this in the calculator, for example with the default 23.5x15.6 mm sensor (1,5x crop factor), and 18 mm lens at f/16, hyperfocal is 3.456 feet. Then try focus distance at the 3.5 foot hyperfocal. See? DOF is 1.73 feet to infinity. Three significant digits helps calculator precision, and it is touchy. So for nitpickers, round up slightly, to 3.5 here, call it "at least hyperfocal will reach infinity". Note however (don't misunderstand), if you look at the image at all closely, focusing at 3.5 feet is Not the same thing as focusing at infinity. But this is the maximum permissible range of focus error allowed by the Circle of Confusion definition of Depth of Field. That's the same meaning in the hyperfocal chart too. That can be pretty awesome to know when you need it.

The calculator shows Hyperfocal distance adding info like (D=2.5%), meaning that the specified subject focus Distance is 2.5% of hyperfocal. Note that if the DOF span reaches to infinity, the DOF range behind focus is infinite, so then the percentage DOF in front of focus will compute 0%, even if it is a significant distance in feet or meters. If Hyperfocal is new to you, you may like to know more about it, see next page.

This Hyperfocal calculator also uses the sensor
in the left DOF calculator box values, above

The yellow shading in the chart indicates where hyperfocal is arbitrarily closer than 14 feet or 4.267 meters which is same as half of hyperfocal being less than 7 feet (1.13 meters), which with a short lens can be dramatically close, an extreme DOF span to infinity. The 7 feet was just my notion of close, but another thought also was that at least 7 feet is always a good suggestion for any lens as a sufficient distance for the best portrait perspective of the human face.

The minimal sparse marking on the lens focus distance dials don’t directly set a focus distance to an exact value, like 9 or 18 feet. But approximating it should be still be useful. Maybe step off the short distance and manually focus on that spot.

Most camera normal lenses at short focal length and well-stopped down aperture will be near hyperfocal and can provide astonishing depth of field.

Most shorter lenses are in the chart, but if desired, you can add up to six other focal lengths to the screen chart here (NOT included in the printed copy, but you can make notes on it). The added field is ignored if blank or a duplicate, or if Not a Number. If the chart is too wide for your screen, the widest apertures can be omitted, which are not likely of great interest for hyperfocal.

Fisheye lenses or macro distances are special cases adversely affecting accuracy of DOF or Field or View calculations. And not all focal lengths are used by all sensor sizes.

Sensor size and the feet/meter choice is from
the left DOF calculator box values, above

Add       mm lenses

Show apertures from   to  
Show Third stops (can be very wide)  

These options are Not included in the printable chart.

Hyperfocal Distance Chart

This chart IS the hyperfocal distances for the sensor size, focal length and f/number shown.

Example: In the chart, if with the DOF calculators initial default 23.5x15.6 mm sensor choice (Nikon DX, APS-C, 1.5x crop factor), an 18 mm lens set to f/22 and focused at this hyperfocal at 2.46 feet, will have a Depth of Field span from half at 1.23 feet to infinity (sharpest focus is at the focused point). That's an extremely large span of DOF, and the hyperfocal chart is how you can achieve such results. Including an interesting near object at only a few feet can create a dramatic landscape. Yes, the diffraction at f/22 is probably a slight degrade, but in comparison, the DOF increase can be overwhelmingly awesome. You'll have to try it to see this, so you can decide which is important (DOF normally always easily wins).

Caution: As impressive as that may sound, and while hyperfocal is a strong and often very useful concept, it may not always be the best choice that it might seem. Hyperfocal calculates the maximum Depth of Field limits (normal DOF spans), determined by the Maximum Acceptable CoC, or the maximum blur at both ends of the DOF span. The sharpest point is always the actual focus distance.

So with this same 18 mm lens example at f/22 (on your crop 1.53x APS-C sensor), hyperfocal comes out as 2.46 feet. Then focusing at 2.46 feet will reach back to 1.23 feet, but which is not the same as focusing at 1.23 feet nor at infinity. Still perfect if that's your goal, but those extremes may only be fair results. DOF extremes are not maximally sharp (that’s where the blur reaches the maximally acceptable CoC limits), but the minimal blur there is still considered acceptably sharp, usually, if not too critical. Which distance is most important to your picture?

So if in this case, if you don't really need as close as 1.23 feet, then for example, maybe focusing this landscape at f/22 at 100 feet instead of 2.46 feet still reaches back fairly far. The DOF calculator then shows the DOF span of this lens to be 2.35 feet to infinity then, only a foot less but not great difference up very close, but which can improve the results at infinity. Computing background at 99999 feet (which is 19 miles), the blur at infinity is only 0.024x CoC (1/40th of the acceptable 1x CoC blur limit at infinity if focused at 2.46 feet), and is improved at 100 feet too. If you do focus at any point beyond the hyperfocal distance, the DOF span will always reach infinity easier. So use your head a little, as there are choices, and cautions, but a page of hyperfocal chart for your sensor size can be very useful.

A Better Way to Blur the Background
Maximizing Background Blur Without Suffering f/1.8

Two of the Depth of Field (DOF) factors are focal length and subject distance. We can use them both for the goal (of bypassing 50 mm f/1.8 issues). My notion of a portrait at f/1.8 is that it will have extremely limited DOF, and also optical aberrations are especially bad at f/1.8. IMO, f/1.8 is usually about the worst choice to make the best picture, and is the last thing I want if I can prevent it. The 50 mm lens at f/1.8 has almost no DOF span, noticeable vignetting, and noticeable optical defects unless maybe you spend $3000 on it. This is a well known subject, and if you might be unaware, here's a good look at this subject of wide lens aberrations. Such wide apertures are simply not the optical best. Formal portrait studios choose to work at maybe f/8 or more (because their goal is that the picture will sell well). We do like the sharpness of depth of field, and we can choose to work a better way. Pros know the advantages of a longer lens for this purpose (including hiding the background in an outdoor portrait).

Equivalent Distance for Same FoV

Distances here can be feet or meters

Focal Length A mm, Distance: 

Focal Length B mm,

"The Same Depth of Field for Same Size Image"

This rule of thumb is an old well known adage. It means if at the same f/stop and same sensor size, adjusting the camera distance of different lenses to all show the same subject size in the frame (which is simply the same Field of View) will also have the same Depth of Field (at the focused distance). This is speaking of at the subject (the background FOV and DOF will still vary with focal length). It means that for the same sensor size, when lenses of different focal lengths are using the same f/stop, and are adjusted to stand at "equivalent distances" which have the same subject size, then in those adjusted cases, all lenses of different focal lengths have the Same Field of View and same Depth of Field span (at the subject)

This "sameness" is NOT speaking of the background. If it is even several feet distant, the longer lens will have a smaller view of the background (which you can move slightly to choose), getting rid of most of it, and what is remaining will have worse depth of field, which both are the goal here. This is illustrated in the Summary Chart next below.

The "same FoV and same DOF at subject" is pretty much true, but it is more true when the lens focus distance is less than 1/4 of its hyperfocal (see Google). Which seems realistically true of portrait situations. That is speaking of the same FoV and DOF at the subject (not at the background), which is same subject size, but Not necessarily the "same image", because perspective depends on the distance where the camera stands (and perspective can be horrible when standing too close). And FWIW, for focus arbitrarily at 7 feet for the shorter lens, the 1/4 rule extends about two stops to the left in the hyperfocal chart above, about two stops wider aperture than the yellow half of hyperfocal limit. Two stops more open doubles hyperfocal distance.

The lenses (on same camera, using same f/stop) do have the same Depth of Field at the subject, if subject distance is adjusted for same Field of View there (which I'm calling "equivalent distances"). But the more distant background is a very different situation then, longer lens have a much smaller view of that background, which is also blurred more with the longer lens. And then the longer lens has advantage of being able to stop down a little more, winning with more DOF at the subject, and still winning with more blur at the background (if background is not too close behind subject).

But if the goal is to Not blur the background (as in Landscapes), then stopping down more helps (with a larger f/stop Number). Stopping down much increases diffraction (costing some sharpness), but when needed, the Depth of Field gain normally can be a much greater benefit than the smaller loss hurts. Don't be afraid to use f/22 or the maximum f/stop when and if it is really needed, which yes, is extreme, but it can solve big problems, which is why the lens offers it. Or a shorter focal length will also increase Depth of Field (but that also increases the Field of View, which makes objects in it smaller, but which may still be OK). See the hyperfocal section above.

Summary examples for Crop Factor camera
Background is feet ( m) Behind subject

Demonstration of Two Important Concepts

If at equivalent distance with longer lens:
All are the same FoV at the subject
DOF Span can become greater (a plus)
Background blur can become greater (a plus?)
FoV at background becomes much smaller (a plus?)

But if Checked here, all four lenses will use
then creating the same DOF span at same size subject,
with same field size, but changed background DOF.
Toggle this checkbox On and Off to see what changes.

Summary Chart of Numeric Examples

If the goal is to blur the background, this chart shows the evidence of a better way. It should clarify the concepts. The chart selects starting equivalent distances (increasing as above concept) to create the same portrait 2x3 foot Field of View (FoV) at each subject, rotated to vertical. Each crop here is compared as 3:2 aspect ratio. So to retain the same 2x3 foot view, the 2x crop which is normally 4:3 is also shown as 3:2 (with same diagonal). The focal lengths for the two smallest sensors (largest crop factors) are divided by 2 as being more suitable for their small size. If interested in infinity, entering 99999 feet is about 19 miles. The main DOF calculator above can show all these same values for any two focal lengths, for any sensor or other subject distances or in meter units.

This calculator always uses CoC divisor = 1442, and standard viewing size of 8x10 inches.

The term 32x CoC means that the blur diameter of an “infinitesimal point” at the background is 32 times larger than the maximum limit CoC diameter that is used to determine the maximum acceptable extents of the DOF range (where blur is 1x CoC). This is Not the size of a blurred object, but the blur of a tiniest point on it. The DOF calculator above will also show this diameter in pixels.

If the background is closer than about 15 feet from subject (speaking of DSLR size sensors), the 50 mm f/1.8 lens may blur the background as well as the longer lenses, but the longer lenses will still have superior depth of field at the subject. That's a Big Deal. Farther than about 15 feet, and the longer lens wins in every way (including even a smaller Field of View of the more blurred background, which removes most of it). It is certainly something to think about.

If the bottom checkbox is Checked, all lenses will use the same aperture for comparison. Then when the same f/stop, then DOF at all focal lengths each at equivalent distances will be (very closely) the same DOF span at the subject, but background blur still increases with longer focal length (if the background is not too close). The longer lens can also generally still choose to stop down a bit more for DOF improvement at the subject.

We often tend to routinely focus on the nearest point on the front side of a subject, but then only about half of the DOF span is Behind the point of focus, so the other half is mostly wasted for portraits (in front where often there isn't anything but air). It's something to think about. Focusing on the far eye is not a bad plan for portraits, hopefully to slightly improve centering the DOF span. But the obvious point is, when another couple of inches of DOF is so critical, the longer lens standing back is a very advantageous better method, also allowing stopping down a bit more to increase subject sharpness, but still blurring the background as much, or usually more, if background is sufficiently distant. Eliminating the f/1.8 problem is a big plus in several ways.

A 50 mm lens is too short for proper perspective on a close portrait anyway, certainly if on full frame (1x crop factor). You could better choose 100 mm f/2.8, which still offers all of the several advantages over 50 mm f/1.8. And 200 mm can work great too (speaking of a DSLR size sensor). Regardless of sensor size, we should always stand back a bit for better portrait perspective. It should be obvious that this is a really big deal to know. For portraits, there are a few strong advantages normally offered by standing back with the longer lens.

In this Summary chart, we said this Field of View (FoV) at the subject would be the same in any of the situations (arbitrarily chosen to be 3x2 feet, which oriented vertical would be just about right for head and shoulders). We simply ignored that 50 mm on full frame would be too close when at 3x2 feet (but you certainly should not ignore it). But the background field at 40 feet of the 50 mm lens is over 21x32 feet size. 21 feet of stuff you want blurred away. However, the Field of View of the 200 mm lens is only 6.8 feet wide at 40 feet (behind the subject). So most of the objectionable stuff you want to blur is simply missing, simply gone, removed in the best possible way. And better, you can surely simply move the camera a slight step or two to one side to choose to align the best (least objectionable) 6.8 feet of background decently enough, probably even if it were not blurred. But in fact, it is also more blurred at 200 mm. The 200 mm f/4 is probably blurred more than 50 mm f/1.8 (depending on adequate background distance), so the 200 f/4 subject DOF span is more than twice larger, and there is much less of the background even showing. And depending on distance, usually the smaller background that is visible is blurred even more. If this is the goal, then consider using the best tool. Also don't forget about proper portrait perspective.

What's not to like? 100 mm can do most of this too, but speaking of 200 mm (and DSLR class sensors), more than twice as much DOF range at the subject (than 50 mm), yet with greater blur on the background, and only about 1/3 of that background width even showing, which all seem like a big pluses. The only downside is we need the longer lens, and to have room to stand back. Flash power of tiny internal flashes would be an issue at extremes.

There are many numerical combinations where the longer lens is simply better in a few ways. And even with a close background, there's still a property or two worth consideration. If you also find f/1.8 distasteful, there is this better way.

Perspective is NOT at all about the Lens.
It's Only about Where you Stand to Use it

Perspective is Only about the View that the camera Sees from Where It Stands. Zooming in does not affect perspective, but the camera standing nearer certainly does. Perspective is NOT about depth of field or sharpness, but is only about relative Size and relative Position of objects in the view, due to their camera distance.

Perspective is a very strong portrait consideration. A common perspective problem for beginner portraits is from standing too close to the subject. It's certainly a problem with selfies held at arms length. The camera being too close can ruin a portrait.

You've seen online examples of the same portrait taken with various focal lengths showing the perspective differences. Their point seems to be that short lenses cause bad perspective effects (enlarged noses, etc), and seemingly shows perspective is improved greatly by using longer lenses. Which is true enough in its way, but you should realize that the whole point that they do NOT mention is that the camera distance was of course changed dramatically in each shot to show the same subject size in all, but then necessarily with the different perspective that they create and show. Perspective is NOT lens distortion. Perspective only depends on the view the camera actually sees at the distance from where the camera is standing. That actually seems self-evident.

Saying, don't think that focal length affects perspective. It does not. Any lens simply shows what it sees from where it stands. Zoom all you want, focal length changes the view size, but NOT the perspective. Standing too close is what affects perspective badly. Each of those multiple pictures necessarily were taken at the different distance specifically chosen for the focal length, so that the subject Field of View stays the same in all (equivalent distances as described above). The longer lens is better because the subject framing requires that we must stand back at a more proper portrait distance. The idea with any lens and any portrait is suggesting about 6 or 7 feet subject distance is necessary for portraits, and 10 feet is fail safe. Then use whatever lens that can show what you want to see there. 4 or 5 feet is insufficient for human face perspective. Sure, you can get a picture closer, but it may not be flattering.

The Best Perspective Rule for Portraits

The camera should be back at least about 6.5 feet or 2 m (and a bit more is really good insurance), and then use any lens focal length that gives the view you want, by zooming in as desired. This is true for tight head shots, head & shoulders, waist length, full length standing, or groups. It's about the proper perspective for human faces.

For a full frame 1x crop camera at 10 feet, that's about 120 mm zoom for a 2x3 foot view, and flash at f/8 gives near a 12 inch Depth of Field depth, front to back (which is a second reason for the distance).
For a 1.5x or 1.6x crop camera, that's about a 75mm zoom, and is a bit more DoF.
The 3x2 foot field is maybe 58 mm zoom for a 2x crop Four/Thirds camera.
Or 44mm zoom for a 2.73x crop One Inch camera, and 16 inches DoF range.

If you've been in a commercial portrait studio, you probably remember the camera placed well back from the subject, and perspective is the reason. The portrait camera should stand well back and zoom in as desired.

From the same location, changing the lens focal length cannot change the perspective. Any lens can only show whatever perspective that can be seen from standing where it is. However, yes, the lens focal length certainly does influence where you would choose to stand to use it, and then location distance does affect perspective.

The focal length does affect magnification, and thus framing/cropping, but those "same portrait with different lenses" examples seen always fail to mention that the perspective result is only because the camera distances were adjusted to keep the same Field of View for the different focal lengths. The camera distance is the important factor of perspective (and the camera view angle is of course becomes important too.) Meaning, back up a bit, don't stand too close. Many longer lens work fine, simply use whatever zoom focal length that can show the view you want to see from standing where you should choose to use it. Do choose distance wisely, and stand back a bit. Zoom in all you want, which does not affect perspective, but do stand back a bit, which does improve portrait perspective.

Perspective: In photography, perspective is the depth and spatial relationship of objects, i.e., the perceived size and spacing appearance of near vs. far objects. Simply the way it looks from where you are standing. Perspective of both subject and background objects depends Only on the distance where you stand, because any lens can only see whatever view is seen when standing there. The lens might zoom and enlarge the image, but it cannot otherwise change the actual view that you see when standing there, with lens or not. The longer lens has advantages (crops an enlarged view), desirable for portraits, to force us to always stand back a bit for proper perspective, a Minimum distance of at least 6 or 7 feet (2 meters) for better perspective in portraits. And longer and a bit farther can be even greater advantage. This same Minimum distance is valid for any lens and any portrait you choose, from a tight head shot to full length standing, or even a group shot. Stand back a bit, same Minimum.

Standing back a bit is a primary rule of portraits, for the purpose to improve the perspective (to not enlarge the nose, etc). But there is more, an overwhelming advantage is even better yet: Using the longer lens, the background is also zoomed into, and only a much smaller area of it is even still visible, which can be a tremendous advantage if wanting to eliminate the background distraction. And what little is left of it is even more blurred focus (assuming that is to be a plus here). A simple sideways step or two with the camera can choose the best part of it. This standing back at greater distance is little problem to do outdoors, and focal length possibly need not be that extreme. If both could use the same f/1.8 then, the depth of field at the subject is the Same, only 3.57 inches DOF span in a APS size DSLR... so is f/1.8 really what you want to use?) DOF does not exactly describe the sharpest zone, instead it defines the limits where maximum blur becomes unacceptable. But equivalent distances don't have to use the same aperture, a 150 mm lens at 18 feet can stop down a bit, say to f/3.5, which is same picture with twice the DOF span of 50 mm f/1.8 at 6 feet. That's still not much, but it's sure a lot better, where it counts.

Maybe I'm a purist, but IMO, a "portrait lens" certainly does not mean f/1.8. Portrait lens means a longer lens to force standing back for proper portrait perspective. No one specific focal length, sensor size affects it too, but just whatever your proper distance requires for the view you want. Newbies may get other notions, but a f/1.8 lens would be a laughable thing in a portrait studio. f/1.8 is certainly Not about the best capture of the face. To me, f/1.8 is about low light levels, but today, improved high ISO does that better. f/1.8 can blur backgrounds, but it's extreme, and a little brutal, and we're describing an obviously better method in the section above. A portrait studio (with the goal hoping to sell the photo) prefers depth of field, and will be using around f/8, or maybe more, and will provide the proper sufficient light this needs (easy with flash). A "portrait lens" for "head and shoulders" means 65 to 90 mm for 1.6x or 1.5x crop APS, or 105 to 135 mm for full size 35 mm frame. That longer length forces us to stand back for better perspective, to NOT enlarge noses, etc. The 50 mm lens standing back properly might do full length well, but is simply too short and close (not the best try) for tighter portraits. My own choice is 110 to 120 mm (full frame) at 9 or 10 feet, typically at f/8 (nearly 12 inches of Depth of Field span). A cardinal rule of "Portrait" includes standing back for proper portrait perspective, a Minimum of at least 6 or 7 feet (a couple of meters), or better 8 or 10 feet. Which is very important. We guys are often too dumb to notice or realize it, but the wives will tell us they don't like their too-close portraits. Backing up a little more and then zooming in as desired is always a good plan.

Much more about DOF continued on next page.

The third page has photo examples of the calculators two initial default cases (in A and B).

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