Want to Blur the Background?
Comparing Depth of Field of Two Lenses

There is a Depth of Field (DOF) calculator below (about mid page), but which was not really done for general purpose. It does do that too, but there's already a very good one at DofMaster, so there was no need for another doing the same thing. And I shirk at the work to provide sensor size and Circle of Confusion (CoC) for every camera model known to man. :)

So the DOF calculator below is a little different, in that it also adds a few new features.

This is quite difficult for a compact camera. The sensor is so small that their lens is necessarily very short, which ensures a great depth of field. Setting a wide aperture may not be a choice, but choosing more dim lighting can help. The best chance to blur the background some with a compact camera is to zoom in greatly, and then stand back as necessary, but stand as close as that zoom can allow (not closer than about 5 feet for a portrait). Choose a background that is very much more distant, hopefully a few hundred feet.

Maximizing Background Blur Without Suffering f/1.8

We should realize that both focal length and subject distance are Depth of Field (DOF) factors. We can use them both for our goal. My notion of a portrait at f/1.8 is that there will of course be DOF problems, usually about the hardest possible way to make a good picture, and the last thing I want if I can prevent it. Notions may vary, but studio portraits likely work at f/8 or f/11 (again, the usual goal is that the work will sell). Studio flashes are made big to allow those apertures. We like the sharpness of depth of field.

Equivalent distance for same FOV

Focal Length A mm, Distance:

Focal Length B mm, Equivalent: 

(distances can be feet or meters)

The defaults shown in the DOF calculator below initially compares a 50 mm f/1.8 portrait at 6 feet with a 200 mm f/4 at 24 feet, both using a DX APS DSLR camera. It assumes the background we want blurred is 40 feet behind the subject (try other distances too, the longer lens usually wins). Pros would more likely use maybe a 200 mm at f/4 for this purpose (of hiding the background). Or 100 mm at f/2.8 can be better too. The 200 mm is 200/50 = 4x longer than 50 mm, therefore the two subject fields of view are the same size if the 200 mm lens stands back at 6x4 = 24 feet.

And if both lens with distances adjusted to be the same field of view at the subject are also at the same aperture, then they have the Same DOF range too (at the subject) - the adage about the "same image has same DOF", etc. (at the subject, it does). But where we stand does affect the perspective, and the background is certainly NOT the same then... in the long lens, most of the wide background is zoomed out and gone missing, but what's left is even more blurred focus (assuming that is a plus here). This standing back at greater distance is little problem to do outdoors, and it 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, both 0.29 feet of DOF (which is only 3.5 inches - from nose to hair may be more than that). DOF does not describe the sharpest necessarily, instead it defines the maximum blur that we can accept. But we don't have to use the same aperture, the 200 mm lens at 24 feet can use say f/4, which has 0.66 feet of DOF (8 inches). That's still not much, but it's sure a lot better, more than twice as much DOF. But it is even more blur at the background.

Qualification: This adage is a rule of thumb that the "same image" (meaning "same size subject image") at same f/stop will have the same depth of field. It is true when the shorter lens subject distance is less than about 1/5 of its Hyperfocal distance (then DOF is same within 4%, and normally well less). At reasonable subject distances, this is generally quite true except wide angle lenses need shorter subject distance. There are multiple parameters affecting the result, but try it, you'll find a lot you like. Proper portrait perspective is generally considered to need a longer lens anyway. FWIW, regardless of lens focal length, a subject distance less than 6 or 7 feet is simply too short for proper portrait perspective. 8 or 10 feet is even better. Stand back a bit, don't get the camera up in their face.

And the overwhelming advantage is even much better yet: We said this Field of View (FOV) at the subject would be the same in either situation (about 2.9x1.9 feet, about right for head and shoulders). But the background field at 40 feet of the 50 mm lens is 22 feet wide. 22 feet of stuff you want blurred away. However, the field of view of the 200 mm lens is only 8 feet wide at 40 feet (behind the subject). So most of the objectionable junk you want to blur is simply missing, simply gone, removed in the best possible way. And better, you can surely move the camera slightly to one side to choose to align the best 8 feet of background decently enough, probably even if it were not blurred. But in fact, it is blurred at 200 mm. Probably blurred more (perhaps a bit less if background is near), but 1) the subject DOF is so much better, and 2) there is much less of the background even showing. And 3) usually the background that is visible is blurred even more.

So again, it's like this. Two lenses, one longer and standing back at equivalent distance to have the same field of view at the subject. If at the same f/stop, then they have the same depth of field at the subject. Assuming the background is not real close behind subject: The long lens is further from the background, so the background is still blurred quite well. A very big deal is that long lens also has a much smaller view of that background, so we can move a slight step sideways to choose a nice small spot to show, one which does not distract. And another very big deal, then the longer lens can be stopped down a couple of stops more to improve the subject DOF considerably. This does reduce the background blurriness some, but it's still more blurred than the short lens. What's not to like? The only downside is we need to bring the longer lens, and have room to stand back.

It should be obvious that this is a really big deal to know. There are three properties offered by the longer lens: Greater DOF at subject, a much smaller area of background to select and be seen, and greater blur on the background. There are many numerical combinations where the longer lens is simply better. And a few more where a property or two is still worth consideration. If you also find f/1.8 distasteful, there is this better way.

So the calculator below computes the sensor CoC at both subject and background distances, to make this point.

A Depth of Field calculator
concerned with CoC at the Background

Here we go. Identify your camera sensor size by entering either actual Sensor Size or Film Size or Crop Factor or even a final CoC value. Any of those can calculate sensor size. CoC also determines a sensor size, because CoC is about the standard enlargement of sensor size. Full frame 35 mm cameras often use 0.03 mm for CoC, and APS cameras often use 0.02 mm. A compact camera or smart phone might have CoC = 0.004 to 0.007 (much more enlargement is necessary). This is from CoC = Sensor Diagonal / 1442 (these are standard definitions, but are somewhat arbitrary too). Sensor size can be hard to know, but it can be computed from Crop Factor. You can see how to determine your Crop Factor.
It's hard to beat precise actual sensor size specifications though.

Film or Sensor Size dropdown box: I have NOT researched every possible cameras sensor size (virtually none). The film sizes there are known good, but the digital sensor sizes are approximations, ballpark, because actuals can instead depend on the specific camera models chip. Especially the compact and phone sizes like 1/1.8" CCD are possibly vague (actual sensor sizes are instead described as specifications of XxY mm). The approximated sensor size used is shown in results. The film sizes are known good, but other than for film, I suggest the Crop Factor option may be more accurate (if actual sensor size is not known).

Megapixels is unimportant here, only used to compute image size (pixels). It does NOT affect Depth of Field or Field of View. Megapixels is only for you to see and confirm that computed sensor size is about correct, which does affect CoC and FOV. Many camera numbers are approximations, so a size difference of several pixels is probable and not a big deal, if not too far off.
Aspect Ratio computes image dimension in pixels, image diagonal, and also Field of View (except direct Sensor Size or Film Size instead uses actual sensor shape for Aspect ratio).

Depth of Field Calculator

  Four ways to specify Sensor Size
Sensor Size WxH x mm
Film or Sensor size
Crop Factor of sensor size
Circle of Confusion mm for sensor
CoC DivisorDiagonal / Default 1442
Distance Units ConvertResult is
same units
Largest print dimension
10 inches is standard DOF
Aspect Ratio Optional, for
Field of View
Megapixels mpOptional, for
image size

Lens A

Lens B

Focal length mm mm
Subject distance
Background distance behind subject
DOF at Subject
DOF in front
DOF total span
Background distance
BG CoC: X times CoC
FOV at subject
FOV at background

It will be appreciated if you would please report (Here) any problems with the calculator, or with any aspect of this or any page.

If you see results of NaN, it's an error meaning an input is Not A Number (periods are OK, but don't use commas).

DOF is Depth of Field, CoC is Circle of Confusion, FOV is Field of View, and BG is background.

The next page has photo examples of these initial default cases.

When feet/meters 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 distances).

BG CoC is the computed CoC at the BackGround distance. It is shown as "X times CoC", meaning X times size of that acceptable CoC entered (probably diagonal / divisor mm). It is a relative scale of blurring. The DOF concept implies that if the background were exactly at the computed far limit of DOF, the blur diameter there would be exactly equal to CoC (1X CoC). A larger multiple is a multiplied greater blur.

Largest Print Dimension is about the relative enlargement of your viewed image. An example is the "largest dimension" of 8x10 is 10. When we enlarge the viewed image, we enlarge the CoC too, so it's easier to see the blur then, which becomes no longer a suitable indictor. The DOF concept is all about the CoC we can perceive, when enlarged from the sensor size we use. If we are going to enlarge our view, then we need to start with a smaller CoC. Standard DOF calculations assume viewing a standard 8x10 print size from 10 inches, which is the 10 inch default here (254 mm). This feature is to describe a different image size that you may view, to account for the effect of your enlargement on the Depth of Field calculation.

CoC is computed as (sensor diagonal mm / 1442), default unless CoC or Divisor is directly specified.

However, note that you can specify any CoC limit directly. Yes, it will then compute and show a sensor diagonal size based on (CoC x Divisor), but that sensor size is just for reference, and is not further used. It does Not affect DOF now, since CoC has already been specified directly. The DOF formula computes with only CoC, focal length, f/stop, and focus distance. Sensor size is not in the DOF formula, except that it should have of course defined CoC. So, bottom line, you need to know what you're doing if you specify CoC directly. Just because you saw someplace use 0.03 CoC, this does NOT mean that is a proper number for your camera and its sensor size.

If comparing results with other calculators numbers, make sure the CoC and/or Sensor Size used is the same value. The DOF numbers here agree perfectly with DofMaster, Canon Europe, Bob Atkins, PhotoPills when we use CoC Divisor 1442 to match their fixed 0.03 and 0.02 mm CoC for FX and DX. However one major site does show different results. I don't know why it doesn't agree with anyone, it doesn't say what they're doing, but something seems off there.

My notion is that the CoC 1442 divisor was a film era number, and 1500 is considered more modern now, as a slightly tighter limit in sharpness (Wikipedia and others think that now). I used 1500 here at first, however, 1442 still seems clearly the norm on the internet, so I went with the flow. CoC is a little arbitrary, and you can use either above. There's not much difference, being 0.03 or 0.029 mm CoC for full frame 35mm, perhaps a 4% change in DOF calculations. Other factors like focal length and distance seem a larger issue.

Rounding: Note that numerically, real world APS sensors are slightly smaller than 24x16 mm, and their crop factors are actually slightly larger than 1.5 or 1.6. Just for example, the Nikon D5300 DSLR camera manual provides specifications:

Nikon D5300
6000x4000 pixels
24.2 million pixels
1.5 crop factor
23.5 x 15.6 sensor
Photo results show the 6000x4000 pixels is correct, which is 6000x4000 = 24.0 megapixels (there are extra pixels involved in calibrations, but not part of the image area). If the sensor is 23.5 mm wide, then the crop factor is 36/23.5 = 1.532 (normally we compare diagonals, but these are same 3:2 aspect ratio). Canon would be a similar situation. If CoC or Crop Factor or megapixels are typical rounded values, they can slightly skew calculated results in a small way, but the concept should still be very clear.

Depth of Field calculators are not accurate for macro situations. Macro calculations are inaccurate because we don't know extended focal length, and maybe not f/stop reduction, and probably not the location of the front nodal point of the lens to know distance. At the close focus point, these are large factors. Accuracy depends on knowing the numbers. Macro instead computes DOF from measured magnification. Macro 1:1 means the object image is the same size on the sensor as the object in real life, true regardless of sensor size. Distances of at least a few feet will be most accurate in any lens calculation.

What is Depth of Field and Circle of Confusion?

Circle of Confusion (CoC) is theoretically zero diameter (a point) at the focus point. But this blur circle grows larger when not in focus, and the DOF range is calculated to not exceed the standard limit (sensor diagonal/1442) of acceptable CoC. CoC (and therefore Depth of Field) definitely also depends on the current enlarged viewing size, which is magnification of the DOF blur. We should know that standard CoC is considered to view as acceptable sharpness in the standard 8x10 inch enlarged print viewed at 10 inches.

Depth of Field (DOF) is certainly not ONLY about aperture. DOF is an extremely important basic of photography, however IMO, exact DOF calculators may not be great practical use, other than to get a rough idea. But we certainly do need to know the concept. We need to know this, it should be second nature to you.

DOF is increased by
DOF is decreased by

** The three lens properties above cause the CoC (blurred diameter) in the sensor image. Then the DOF that we perceive relates to how large we enlarge that CoC to view it. We do think of cameras with smaller sensors giving greater DOF, which might appear to be the opposite of just said above. And they certainly do that, a little cell phone may not even adjust focus, yet it is in adequate focus about everywhere. But that is only because the field of view of a tiny sensor is drastically cropped (compared to a larger sensor). Therefore it must use a very short lens to achieve the same normal wider view (Crop Factor). That shorter lens certainly does increase DOF drastically. But even if we could use the Same lens (and ignore the crop), then the smaller sensor image still must be enlarged more (to view at same size), which reduces DOF. In the math, a larger sensor computes a larger acceptable CoC limit, which increases DOF.

For portraits at around 8 or 10 feet, I think a good tip is to focus on the near eye, after ensuring ample DOF, like f/8. IMO, f/1.8 is never the best try, and this article is about an alternative. For full frame portraits, I like about 120 mm at around 10 feet. For DX or APS crop cameras, that would be about 80 mm around 10 feet. Ten feet is very good portrait perspective, and at f/8, that's about a 2x3 foot FOV with around a one foot zone of DOF (again, of course speaking about the standard 8x10 inch print viewed at 10 inches).

Qualifications about Viewing Depth of Field

Depth of Field is NOT an exact number. Depth of Field is computed based on the Circle of Confusion (CoC), which is the arbitrary criteria defining the maximum acceptable blur circle (to be small, not quite perceptible) due to being out of focus. CoC is the diameter of the smallest possible theoretical point after it is defocused to be seen as a larger blur circle (because it focuses in front of, or behind, the sensor plane - then causing a larger out of focus circle on that plane). CoC is the maximum permissible diameter of this blur circle, arbitrarily still judged to be imperceptible in our vision (also assuming a standard viewing enlargement). If the blurred circle is too small for us to perceive it, then we imagine it's not blurred.

Carl Friedrich Gauss 1777-1855 was a most brilliant mathematician (in a class with Newton) who did many amazing great things, one of which was to formulate optical theory (1840) that is still used today. He founded the renown optics factory in 1846, which in 1945 came to be in Jena, East Germany. Coc is computed from the film or sensor diagonal dimension. Gauss thought the eye's criteria of visibility of focus blur ought to be a CoC of (frame diagonal divided by 1730, in mm, which computes 0.025 mm today for 35mm film). But today, CoC of diagonal divided by 1442 is common universal (0.03 mm for 35mm film). But it's still an arbitrary guess about blur, about what our eyes see after enlargement. Blur diameter cannot be precisely defined... kinda depends. And so a CoC limit is somewhat arbitrary, there's been a few choices. CoC is just a rough guess attempting to measure focus blur, which makes DOF numbers be a vague thing.

The DOF standard of viewing calculations is in an enlargement of an 8x10 inch print (near A4 size) when viewed at 10 inches (25 cm). Viewing the enlargement size is an important factor in what we see, and in CoC and the Depth of Field calculations. This viewing enlargement factor makes small sensor diagonal be an important factor of DOF. It's the reason smaller sensors have a smaller CoC, and larger sensors have a larger CoC (sensor size requires enlargement of CoC). But standard DOF calculations assume a standard 8x10 inch print is viewed. So this affects viewing a smaller print or a larger print:

Computing on the diagonal attempts to equalize for different sensor or print shapes, but many vague assumptions are included. You should include a safety factor, especially for large prints, one extra f/stop for safety.

DOF is an angular size concept, and the math is all very precise, EXCEPT for the main factor of CoC, which is rather vague and arbitrary. So there are no hard answers about Depth of Field. And since Depth of Field GRADUALLY changes with distance, there is of course no sharp line at the computed limit. There will be virtually no difference seen slightly either side of the computed limit. Numerical Depth of Field is at very best, an extremely rough guide.

Depth of Field is a fundamentally important principle of photography. However using it is MUCH LESS ABOUT any computed numbers, and VERY MUCH MORE ABOUT understanding how to use the factors that increase or decrease it (f/stop, distance, focal length, and sensor size). Normal situations are not much concern, but sometimes we're aware we want a lot of depth of field, or don't want much of it, and we should know how to control that, to do what we can.

Continued - Part Two, Examples

Copyright © 2016-2017 by Wayne Fulton - All rights are reserved.

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