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Field of View Calculator (FoV)
of a Camera and Lens


Image from Wikipedia

This calculator computes the Field of View seen by your camera and lens. Field of View is an angle which depends on the focal length and sensor size, but it also computes dimensional Field of View sizes (width, height, or diagonal fields) at some specific distance, like at the subject distance, and another, like at a background distance. We don't often care about precise field size, but suppose you plan a portrait to include a 2x3 foot subject area. You know you need to stand back six or eight feet for proper portrait perspective. What focal length is that field size and distance going to require? (Option 6, and it depends on your sensor size). And the background may be six feet farther back yet, then how large is it? This calculator can plan or verify your choice. More usage descriptions are below the calculator.

There's also a large chart of Field of View (angular, in degrees) for many lens focal lengths and a few popular sensors on the next page. Another page is a FoV math section if interested. The Depth of Field calculator here also shows Field of View at both subject and at background. Or somewhat related (same math), another calculator can compute distance or size of an object in a photo.

Notes Especially about Compact or Phone Cameras or Video format

This calculation requires accurate sensor size and focal length. Calculators simply MUST be told accurate numbers, else otherwise, garbage in, garbage out. That means YOU have to know those numbers. These values may be very difficult to determine for phones and compact cameras and camcorders, but larger cameras likely show specification values better. You can specify crop factor as a way to compute actual sensor size. Or Option 4 can compute Crop Factor from the lens Equivalent Focal Length specifications for that camera sensor. The image's Exif data normally reports focal length. Use the actual real lens focal length with the actual sensor size. If you don't know focal length, the Exif data in the image file can show it (focal length changes with zoom).

The image Exif data may show what you need to know to obtain all the required information about your cell phone or compact camera to operate this calculator. This otherwise can be a rather difficult task (especially for video formats), and there are still ifs and buts. If you don't know sensor size, Option 4 can be just the ticket for phones and compacts, but if unsure about what it wants, please see this summary of Issues determining Sensor Size which might help.

The biggest risks to FoV accuracy are in not actually knowing the specific sensor size or accurate focal length, also your vague guess about the distance likely may not be precise. DSLR specifications seem easily determined, and their specifications generally specify all the lens and sensor numbers, accurately, even if rounded a bit. But Compact and especially cell phone camera specifications don't bother to tell us much, so you may not find the necessary numbers for this calculator. Some newest phone models do contain two cameras (for wide and telephoto, which use two different sensors — Not necessarily the same sensor size or crop factor). But hints are offered that should determine some usable numbers.

Field of View Calculator

Field of View CalculatorField DimensionAngle of View
Focal Length  mm

Field Distance units

Any units for Distance, feet or meters. Dimension results are the same units

Width
Dimension
Width
Degrees
Height
Dimension
Height
Degrees
Diagonal DimensionDiagonal Degrees
Optionally show field size at a 2nd distance from camera (perhaps at background?)2nd distance: units
1 Native Sensor Size, Width

Native Sensor Size, Height

mm

mm

Option 1 Aspect ratio uses

3 Sensor Crop Factor

Options 3 & 4, also see Aspect Ratio sub-options

4 Focal length of this lens

Equivalent focal length on 35 mm film or 1x sensor
mm

mm

5 Film and
Sensor Size Description
Mostly this is Film Size. For CCD sensors, it will show the approximate WxH mm dimensions
6
6 & 8
Using Sensor Size in Option

of Same units
 in the

Width
Height
Diagonal

 dimension

7 Field Distance
is optional
Find Focal Length for a Field of View Angle of
    degrees

    radians
8 x   using
Feet
Meters
9 Compute Sensor Size from the measured dimensions of
Field Width × Field Height (same units) actually measured AT the distance and focal length specified above

The Angle of Field of View is independent of the field distance, but the angle is computed from sensor size and focal length. The Field Distance is not limited to be only the subject or focus distance. Here it means the distance to the point where you want field size calculated. It might be the background distance for example (which then would show the Field of View at the background distance). A 2nd distance can be entered for convenience, but it is the same result as simply changing the first distance.

When you specify a different format (like 16:9 video) on your 3:2 or 4:3 camera sensor, this changes the effective sensor size from the format's original native value, and changes the Field of View too. The calculator can show this.

If using options 1 to 4, do pay attention to properly specify Aspect Ratio. The crop factor determines sensor Size, and then native aspect ratio specifies the Shape of it. This in turn specifies the size of any mixed formats contained within it, so it is important to compute the correct numbers. Mixed format is a complication, but it is necessary to know the sensor area used.

Clicking the orange button near Option 4 uses the Crop Factor currently in Option 3 to show more detail in a chart about these changes (showing all of the aspect choices in this calculator). May not always be a big difference, but a format change affects the calculated numbers. So if you are using a 3:2 or 4:3 or 16:9 camera, then please select their correct native Aspect Ratio option (for options 3 or 4). Aspect ratio is automatic in Options 1 or 5, the sensor or film size is whatever it is.

This mixed format size change is important, so a red warning may be shown if the Aspect Ratio specified does not match the native Crop Factor computed in Option 3 or 4 (native Aspect Ratio in Option 1 or 5 is computed from actual sensor size). The warning means that an aspect ratio with the correct base aspect ratio (the native sensor size) was likely not selected, which seems an easy oversight, not likely intended, but mistakes change active sensor size and the DOF numbers. Verify, but the warning can be ignored if it's actually correct (you could let me know about the facts of that situation). But meaning, if you select a 16:9 movie aspect ratio in a 4:3 camera, this correct aspect ratio selection specifies both, as "16:9 in 4:3 camera". The warning makes the standard assumption that native crop factors less than 2x should be 3:2, or equal or larger than 2x should be 4:3 (with exception for 2.7x), which are the normal expected and required camera values. Actually, I use 1.9x as that warning boundary.

Rounding: Four or five significant digits may be shown, but inputs of focal length or distance or sensor size or aspect ratio values are rounded values, not that precise (the math is accurate, but camera specifications round things). In math, the final answer can only contain as many significant digits as the least precise value. Only couple of significant digits is not very precise, but should be somewhat close. Still multiplying a 5 mm sensor width into a 30 foot field width multiplies any error too. Excessive digits are shown just in case those results are reentered to recompute back to original values, avoiding additional round-off (for example in Option 9). That's just my whim to aid verifying all results are accurate.

But for example, if you might claim the calculator does not compute your precisely measured field dimensions, then use them in Option 9 to compute your computed sensor size. It is simple geometry, except distance is normally a guessed value, and focal lengths are approximated rounded values. And also, the focal length marked on the lens is when focused at infinity. It generally becomes longer at close focus distances, except internal focusing can change focal length to other values. And zoom lenses report focal length in steps, not with full precision. Magnification of field size from sensor size can also compute actual focal length. But these rounded issues are generally not much problem for routine Field of View work. Knowing the accurate distance to the field is usually the main problem.

Accepted Ft' In"
InputValue
8.58.5
8' 6"8.5
8, 68.5
8 6.58.542
8' 6.5"8.542

Units of either feet or meters work, but clicking the Green Ft' In" button (below the Distance field above) will assume distance is Feet, and will show Dimension results in "Feet and Inches" format. You can click the Green button again to toggle this option off or on.

The Four distance fields above with green borders (the top Distance, and one in Option 6, and two in Option 9) will always accept distance input in either distance format. The chart at right shows accepted Ft' and In" formats (and always works in these green borders, whether if in Ft" In" mode or Not). Feet or inches can be decimal fractions, or inches can be present or not, and the ' or " marks can be present or not. Meaning, in these four fields, two values with a space between will be interpreted as feet and inches. Any single value is feet or meters, as you intend as your choice, but any second value is assumed to be added as inches added to feet, regardless of any ' or " on it (the ' " , or space here are just non-numeric field separators). So you can always enter feet either way, just as decimal feet without the inches, such as 8.5 feet, still same format as meters. Do use a simple clear method, and I'd suggest that entering fractional 8.5 feet style is always pretty clear. You can verify how the distance result was interpreted, as seen on the Magnification line of the results.

The term Native (about sensor dimensions, aspect ratio, or crop factor) is used to mean the actual full size of the original chip area (before cropping to other smaller formats like 16:9 for example). The original size might not be exactly a nominal 3:2 or 4:3 aspect ratio, which is probably very minor, but the calculator accepts any size.


Select an Option, and click the Compute button (for all Option numbers). Options 1-5 are four ways to specify sensor size. Options 6 to 8 compute special requirements using the sensor size currently specified in options 1-5.

Aspect Ratio (for options 3 and 4) Options 1 and 5 would already know native Aspect Ratio, but any special features (like 16:9 video format) require more (see Aspect Ratio options). If the red warning triggers, it will be good to double check your settings that Aspect Ratio and Crop Factor do not disagree. Crop Factor is size, and Aspect Ratio is shape, but there are conventions matching them. Generally DSLR are 3:2 in larger sensors (crop factor less than 2, except Four Thirds cameras are 2.7x), and phone and compact cameras are 4:3 in smaller sensors (larger crop factors), but some cameras may provide additional aspect options. One Inch (4:3 2x) and Four Thirds (3:2 2.7x) models both typically provide a menu allowing 1:1, 3:2, 4:3, and 16:9. See the end of the summary of Issues determining Sensor Size for more about mixed formats (video and still photos from same sensor).

Options 6-8 still use the sensor size currently described in Options 1-5.

The blue Flip button (near Option 6) will toggle to swap finding either Focal Length or Distance from the other, with the specified image size in option 6 and 8, to compute either one from the other. This Flip recomputes, but flipping will not show any change unless you change a corresponding number. Angles in Option 7 are not affected by this Flip.

There are issues when trying to determine the sensor size of compact or phone cameras, and also with mixed formats (both video and still photo images from the same camera). Video 16:9 may use the assumed full sensor width, or it may not in some cameras. See this summary of Issues determining Sensor Size for more, if any issues.

Scaling Field of View

Greater focal length magnifies, and smaller sensor size crops.

Using different focal lengths on the same sensor size scales the Field of View inversely proportionate. If 2x focal length, the field dimensions are 1/2 size, but the objects therein are 2x size on the sensor. This is the concept of "zooming".

However, the Angle of View is Not linear. 2x focal length is NOT half angle (with more extreme difference for larger angles). The field size varies with the trigonometry tangent function of the half angle. Wide angles become huge fields, however angles less than 10 degrees can still be considered approximately linear (this is the "small angle approximation" used in math).

Using the same focal length on different sensor sizes scales the field frame size proportionately (half of sensor dimensions is half of field frame dimensions), but the objects therein are the same size. This is the notion of "cropped sensors".

Magnification

Reproduction Magnification is a related property here. Greater lens magnification reduces Field of View, which calculation becomes inaccurate if magnification exceeds about 0.1 (i.e., if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus any closer. But this FoV calculation is not accurate for macro distances. Macro purposes find it much easier to use Magnification for calculations instead of focal length, that being:

The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths.

Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm (that 24 mm Height is 0.94488 inches), then:

The field corresponding to 0.01 size reproduction is 100 times larger, or 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers.

Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same).

Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then:

When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1.

Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor.

Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses).

Binocular and telescope magnification numbers are a different system, being "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept.

If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size, so that's an extreme size reduction, and not likely a meaningful number. Then 10x binoculars will show it enlarged to apparent 5 degree size. Some astronomers in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses number there.

But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor.

In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance).

Lens magnification is Not affected by sensor size, the lens does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle.


Actually knowing the precise accurate sensor size is the key to Field of View accuracy.

Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors.

And there is also a FoV Math section for FoV.

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Copyright © 2014-2022 by Wayne Fulton - All rights are reserved.

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