Camera Field of View Calculator

Background.

This calculator tells you what a lens actually sees. Give it a sensor format, a focal length and a distance, and it returns the three angles of view — horizontal, vertical and diagonal — together with the width, the height and the area of scene the frame spans at that distance. It is the answer to "will the whole group fit from here?", "how many cameras cover this car park?" and "what does 24 mm look like on my body?".

Angle of view comes from one relation, applied three times. At infinity focus a sensor dimension x subtends α = 2·arctan(x ÷ 2f) at the lens, so the width, the height and the diagonal each give their own angle. That is the convention every lens manufacturer publishes to, which is what makes these numbers checkable: type in 50 mm on full frame and you get 39.6° horizontally, 27.0° vertically and 46.8° diagonally, which is exactly what a 50 mm datasheet says. It also explains a common confusion. Datasheets almost always quote the diagonal figure, because it is the biggest of the three, so a lens advertised as "84°" is not 84° across the frame — that one is a 24 mm, and its horizontal angle is 74°.

The coverage figures use the exact finite-distance relation rather than the angle. For a subject at distance u the thin-lens magnification is f ÷ (u − f), so the frame spans W = w(u − f)/f. At five metres with a 50 mm on full frame that is 3.56 m across and 2.38 m tall — 8.47 square metres of scene. Note that width divided by height always comes out at the sensor aspect ratio, which is a useful sanity check on any field-of-view calculation.

The sensor is the input people most often get wrong, and it changes everything. The same 50 mm lens covers 39.6° on full frame, 26.4° on Nikon DX and 19.6° on Micro Four Thirds. That is not the lens changing — the lens projects exactly the same image circle whatever is behind it — it is a smaller sensor recording a smaller rectangle out of the middle of it. Enter the focal length engraved on the barrel, not the 35 mm equivalent, because the sensor dropdown already handles the format.

Two limits are worth stating before you rely on the numbers. First, the angles assume infinity focus, which is the published convention; at a finite distance the true angular coverage is wider by the factor (u − f)/u, about one percent at the defaults here and dominant in close-up work. Once your magnification passes roughly 0.1 you want the lens magnification calculator instead. Second, everything here assumes rectilinear projection — straight lines staying straight. Fisheye lenses use a deliberately different projection, which is how they reach 180° when the arctan relation says a rectilinear lens never can, so feeding a fisheye focal length in here will understate what it sees by a wide margin.

Below the widget you will find the derivation, a worked 50 mm example computed by hand, why Micro Four Thirds and full frame agree on the diagonal but not on the horizontal, and how to use the coverage output for site planning.

What is camera field of view calculator?

Field of view is how much of the world a camera records, and it can be stated two ways. Angularly, it is the angle subtended at the lens by the frame: α = 2·arctan(x ÷ 2f), where x is a sensor dimension and f the focal length, evaluated at infinity focus. Because a frame has a width, a height and a diagonal, there are three such angles and they are all correct — a 50 mm lens on the 35 mm format is 39.6° horizontally, 27.0° vertically and 46.8° diagonally. Linearly, field of view is the size of the patch of scene the frame spans at a stated distance, which follows from the thin-lens magnification m = f/(u − f): the frame covers X = x(u − f)/f. The two descriptions are consistent to within the finite-focus factor (u − f)/u, because the published angle is defined at infinity while the coverage is evaluated at a real distance. Field of view depends on exactly two things, the sensor dimension and the focal length, and on nothing else — not on aperture, not on megapixels, not on whether the camera is a stills or a video body, though a video mode that crops the sensor changes the effective sensor dimension and therefore the answer. All of this assumes rectilinear projection. Fisheye lenses use equidistant, equisolid-angle or orthographic projections, for which this relation does not hold at all.

How to use this calculator.

1. 01Pick your sensor format. If your camera is not listed — a phone, a drone, a surveillance or machine-vision camera — choose Custom and enter the imaging-area dimensions in millimetres from the datasheet. Do not try to infer them from a "1/2.8-type" style designation, which is a tube-era convention rather than a measurement.
2. 02Enter the focal length engraved on the lens in millimetres, never the 35 mm equivalent. The sensor selection already accounts for the format; entering an equivalent would apply the crop factor a second time.
3. 03Enter the distance to the part of the scene you care about, in metres. The three angles do not depend on it, but the coverage figures do. Convert feet by multiplying by 0.3048.
4. 04Read the horizontal angle first for framing decisions and the vertical angle when height is the constraint — fitting a whole building, a full-length figure or a ceiling.
5. 05Compare against lens datasheets using the diagonal angle, not the horizontal one. Manufacturers quote the diagonal because it is the largest number, and mixing the two is the usual cause of a calculator appearing to disagree with a specification.
6. 06Use the coverage width, height and area for planning: how much wall a camera sees, how many frames a panorama needs, how much ground a survey pass covers. Remember to allow overlap — mapping flights typically need 60 to 80 % forward overlap, so the usable new area per frame is far less than the figure shown.
7. 07Sanity-check the result by dividing the covered width by the covered height. It must equal your sensor's aspect ratio: 1.5 for a 3:2 frame, 1.333 for 4:3. If it does not, one of the sensor dimensions was entered wrongly.

The formula.

The angular half of the calculation is one line of trigonometry. At infinity focus the sensor sits one focal length behind the rear principal plane, so half a sensor dimension, x ÷ 2, subtends arctan(x ÷ 2f). Doubling gives the full angle:

α = 2 · arctan(x / 2f)

Run it on the width, the height and the diagonal and you get the three published angles. For a 50 mm on the 36 × 24 mm frame:

horizontal 2·arctan(36/100) = 39.598° vertical 2·arctan(24/100) = 26.991° diagonal 2·arctan(43.2666/100) = 46.793°

One structural consequence is worth noticing: arctan is bounded by 90°, so α is bounded by 180° and reaches it only as f approaches zero. No rectilinear lens can ever cover 180°, and the corner stretching gets punishing well before that — which is why fisheyes exist and why they need a different projection entirely.

The linear half comes from the thin-lens equation. With the object at distance u from the front principal plane, 1/f = 1/u + 1/v gives v = uf/(u − f), and the transverse magnification is m = v/u = f/(u − f). A sensor dimension x therefore records an object dimension

X = x / m = x (u − f) / f

At 5 m with a 50 mm on full frame, (u − f)/f = 4950/50 = 99, so the frame covers 36 × 99 = 3564 mm across and 24 × 99 = 2376 mm high — 3.564 m by 2.376 m, an area of 8.468 m². The ratio 3.564 ÷ 2.376 is exactly 1.5, the 3:2 aspect ratio, as it must be.

Why not just use the angle and write W = 2u·tan(α/2)? Because that mixes an infinity-focus angle with a finite-focus distance and is therefore slightly wrong. The two differ by exactly (u − f)/u: at 5 m with a 50 mm that is 0.99, a 1 % overstatement, invisible in practice. At u = 10f it is 0.9, a 10 % overstatement, which is not invisible. This page uses the exact relation for the coverage and the published convention for the angles, and states that they are not the same model.

Sensor size enters only as x, and it is the dominant term in practice. The same 50 mm gives 39.6° on full frame, 26.4° on Nikon DX (23.5 mm wide) and 19.6° on Micro Four Thirds (17.3 mm wide). The lens has not changed at all — it projects the identical image circle — but a smaller sensor records a smaller rectangle from the centre of it.

One last subtlety that explains a lot of apparent disagreements between calculators. Comparing formats with different aspect ratios, only one angle can match at a time. Micro Four Thirds at 25 mm gives a diagonal angle of 46.806° against full frame at 50 mm giving 46.793° — near-identical, as the 2× crop factor promises, because crop factor is defined on the diagonal. But their horizontal angles differ by 1.4° and their vertical angles by 2.2°, because 4:3 is a genuinely different shape from 3:2. Equivalence is a diagonal property, and it does not survive being applied to a single axis.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Nasse, H. H. (2010). 'Depth of Field and Bokeh.' Carl Zeiss Camera Lens Division. Source for the object-side magnification relation M ≈ Dist/f' underlying the coverage formula, and for the principle that a smaller sensor records a smaller part of the same image circle rather than changing the lens: 'the lens does not know how much of its image circle we are capturing with our sensor.'
2. [2]Canon Inc. EOS R6 Product Manual, Specifications — Image Sensor. Gives the full-frame sensor size as 'Approx. 35.9×23.9 mm', the measured dimension behind the nominal 36 × 24 mm frame used for the full-frame preset and its 39.6° / 27.0° / 46.8° angles at 50 mm.
3. [3]Nikon Corporation. D7500 Online Manual, Technical Notes — Specifications. Gives the Nikon DX imaging area as '23.5 × 15.7 mm CMOS sensor' and states that DX lenses are 'equivalent to approx. 1.5×' the 35 mm-format angle of view.
4. [4]Canon Inc. EOS R7 Product Manual, Specifications. Gives the Canon APS-C sensor as 'Approx. 22.3 × 14.8 mm' and the angle-of-view conversion as 'Approx. 1.6 times the focal length indicated on the lens'.
5. [5]OM Digital Solutions. OM SYSTEM OM-1 Mark II Specifications. Lists the imaging area as 'Aspect ratio & area 4:3 / 17.3 x 13.0 mm' — the 4:3 shape behind the horizontal and vertical angle differences described on this page — and 'Focal length: 40mm (35mm equivalent: 80mm)'.
6. [6]FUJIFILM Corporation. GFX100 II Specifications. Lists the image sensor as '43.8mm×32.9mm', the dimensions used for the medium-format preset.
7. [7]Ray, S. F. (2002). Applied Photographic Optics: Lenses and Optical Systems for Photography, Film, Video, Electronic and Digital Imaging, 3rd ed. Focal Press. Standard reference for the object-field relation X = x(u − f)/f, for the finite-focus correction (u − f)/u to the published infinity-focus angle of view, and for the non-rectilinear projections used by fisheye lenses.