Field of View Calculator: Angle of View and Frame Size

Updated

How to work out a lens's horizontal, vertical and diagonal angle of view on any sensor, how much of the scene the frame covers at a distance, and how to work back from the frame you want to the lens or the camera position.

14 min readIntermediate
  • Field of View
  • Angle of View
  • Lens Choice
  • Framing
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What field of view depends on

Field of view comes in two forms. The angle of view is how many degrees of the scene the lens takes in, across the frame, up it and corner to corner. The coverage is what that angle means at a real distance: how many meters of wall, set or landscape fit across the frame where the subject stands.

For an ordinary (rectilinear) lens focused at a distance, the angle depends on just two things: the focal length and the size of the area the camera records. It does not depend on the stop, the brand of lens or the size of its image circle. A bigger image circle lets a lens cover a bigger sensor without dark corners, but a 35mm lens is a 35mm lens on any camera that it covers.

The angle of view formula

With the lens focused at infinity, the recorded area sits one focal length behind the lens. Half the sensor width and the focal length form a right triangle, so half the angle is the arctangent of their ratio. Double it for the full angle.

Angle of View
Angle = 2 × arctan(d ÷ (2 × f))

Put in the recorded width for the horizontal angle, the height for the vertical angle and the diagonal for the diagonal angle. Stills lens makers usually quote the diagonal angle on 36 × 24mm; on set, frames are matched on the horizontal angle.

Where

d
Width, height or diagonal of the recorded area(mm)
f
Focal length(mm)

Example: 35mm lens on Super 35 (24.89 × 18.66mm, 31.11mm diagonal)

Calculation:
H = 2 × arctan(24.89 ÷ 70) | V = 2 × arctan(18.66 ÷ 70) | D = 2 × arctan(31.11 ÷ 70)
Result:
39.1° horizontal, 29.9° vertical, 47.9° diagonal

Super 35 here is the 35mm full camera aperture, 24.89 × 18.66mm, which is also CineMath's Super 35 preset. Digital "Super 35" sensors vary by a few millimeters either way, so use your camera's own figure when you have it. The free field of view calculator gives all three angles for any lens and recorded area in your browser.

Angles by focal length and format

The same focal length gives a narrower view on a smaller sensor. The table gives horizontal and vertical angles for full frame (36 × 24mm), Super 35 (24.89 × 18.66mm) and Micro Four Thirds (17.3 × 13mm).

Focal lengthFull frame H × VSuper 35 H × VMicro Four Thirds H × V
18mm90.0° × 67.4°69.3° × 54.8°51.3° × 39.7°
25mm71.5° × 51.3°52.9° × 40.9°38.2° × 29.1°
35mm54.4° × 37.8°39.1° × 29.9°27.8° × 21.0°
50mm39.6° × 27.0°28.0° × 21.1°19.6° × 14.8°
75mm27.0° × 18.2°18.8° × 14.2°13.2° × 9.9°
100mm20.4° × 13.7°14.2° × 10.7°9.9° × 7.4°
135mm15.2° × 10.2°10.5° × 7.9°7.3° × 5.5°

Horizontal × vertical angle of view, lens focused at infinity.

Read along a diagonal of the table and the angles nearly line up: 50mm on full frame (39.6°), 35mm on Super 35 (39.1°) and 25mm on Micro Four Thirds (38.2°) see almost the same width of scene. That ratio between sensor widths is the crop factor, and crop factor and focal length equivalence covers how to use it to match a shot across cameras, and what it does not carry over.

Frame size at a distance

Coverage is the more useful number on a scout: how wide and tall the frame is at the subject. By the same similar triangles it is simply the distance scaled by sensor size over focal length.

Frame Width (or Height) at a Distance
Coverage = Distance × d ÷ f

Use the recorded width for frame width and the recorded height for frame height. The answer is in the same unit as the distance, so meters in give meters out and feet in give feet out. It is the same as 2 × Distance × tan(angle ÷ 2).

Where

Distance
Lens to the subject plane(m or ft)
d
Recorded width or height(mm)
f
Focal length(mm)

Example: 25mm on Super 35, subject 3m away

Calculation:
3 × 24.89 ÷ 25 = 2.99m wide | 3 × 18.66 ÷ 25 = 2.24m tall
Result:
The frame is about 3.0 × 2.2m at the subject

The free field of view calculator gives the frame width and height at any distance, in feet or meters.

Coverage on Super 35 (24.89 × 18.66mm)

Focal lengthAt 1mAt 2mAt 3mAt 5mAt 10m
18mm1.38 × 1.042.77 × 2.074.15 × 3.116.91 × 5.1813.83 × 10.37
25mm1.00 × 0.751.99 × 1.492.99 × 2.244.98 × 3.739.96 × 7.46
35mm0.71 × 0.531.42 × 1.072.13 × 1.603.56 × 2.677.11 × 5.33
50mm0.50 × 0.371.00 × 0.751.49 × 1.122.49 × 1.874.98 × 3.73
85mm0.29 × 0.220.59 × 0.440.88 × 0.661.46 × 1.102.93 × 2.20

Frame width × height in meters at the subject, lens focused there. A 16:9 recording on the same width keeps the widths and loses some height.

Lens or distance for the frame you want

The coverage formula rearranges two ways. On a scout you usually know two of the three numbers: how far back the room lets you go and how wide the frame must be, or which lens you want and how big the subject should be.

Focal Length for a Frame Size
f = d × Distance ÷ Coverage

The focal length that makes the frame exactly the size you want at that distance. Pick the nearest lens you have, then check the real coverage with the formula above.

Where

d
Recorded width (or height, if you are framing on height)(mm)
Distance
Lens to subject(m)
Coverage
Frame width (or height) you want at the subject(m)

Example: A 3m-wide frame from 4m away, Super 35

Calculation:
24.89 × 4 ÷ 3 = 33.2mm. With a 32mm: 4 × 24.89 ÷ 32 = 3.11m; with a 35mm: 2.84m
Result:
A 32mm gives a touch more than 3m; a 35mm cuts it to 2.84m
Camera Distance for a Frame Size
Distance = Coverage × f ÷ d

How far back to put the camera so a subject of known size fills the frame with a given lens.

Where

Coverage
Frame height (or width) you want at the subject(m)
f
Focal length(mm)
d
Recorded height (or width)(mm)

Example: A frame 1m tall on a 50mm, full frame recording 16:9 (36 × 20.25mm)

Calculation:
1.0 × 50 ÷ 20.25 = 2.47m
Result:
Put the lens about 2.5m from the subject

Camera distance by lens and frame height (full frame, 16:9)

Shot sizes are a matter of taste, so the table uses frame height at the subject rather than names: about 0.35m is a tight close-up on a face, about 1m takes a seated person from the waist up, and about 2.2m takes a standing adult head to toe with a little room. The recorded area is the full 36mm width of a full-frame sensor at 16:9, which is 20.25mm tall.

Focal lengthFrame 0.35m tallFrame 1m tallFrame 2.2m tall
25mm0.43m (1.4 ft)1.23m (4.1 ft)2.72m (8.9 ft)
35mm0.60m (2.0 ft)1.73m (5.7 ft)3.80m (12.5 ft)
50mm0.86m (2.8 ft)2.47m (8.1 ft)5.43m (17.8 ft)
85mm1.47m (4.8 ft)4.20m (13.8 ft)9.23m (30.3 ft)
135mm2.33m (7.7 ft)6.67m (21.9 ft)14.67m (48.1 ft)

Lens-to-subject distance. Under about 1m, focusing changes the angle enough to matter: see the next section.

The same frame from a longer lens means a longer distance, and that changes perspective: the background looks larger behind the subject and noses look smaller. Perspective comes only from where the camera stands, so choose the distance for the look first, then the lens that fills the frame from there.

Case study

Interview in a small office

  • Corporate interview
  • Intermediate
  • Worked example

Scenario

A two-camera interview in an office 5m deep. The subject sits 1m from the back wall, so the A camera can be at most about 3.5m from them once the operator and stand fit behind it. The A camera records 16:9 on full frame (36 × 20.25mm).

Challenge

The director wants a medium close-up, about 0.6m of frame height, and does not want the subject's features flattened or stretched. Which lens gives that framing from a comfortable distance?

Solution

  1. Pick a working distance that leaves the operator room: 2.5m
  2. Work out the focal length for 0.6m of frame height at 2.5m
  3. Round to a lens in the kit and check the real framing
  4. Check the widest framing the room allows for a wide safety shot

The numbers

  • f = 20.25 × 2.5 ÷ 0.6 = 84.4mm, so an 85mm
  • Check: 2.5 × 20.25 ÷ 85 = 0.60m tall, 2.5 × 36 ÷ 85 = 1.06m wide
  • Wide from the back of the room on a 35mm: 3.5 × 36 ÷ 35 = 3.6m wide, 2.0m tall

Result

An 85mm at 2.5m gives the medium close-up with a natural perspective; a 35mm from the back of the room takes in a 3.6m-wide slice of the office for the wide.

Key takeaways

  • Choose the camera distance for perspective, then the lens for the framing
  • Frame on height when the delivery is 16:9 and the subject is a person
  • Check the rounded lens against the frame you wanted

Where the simple formula drifts

The formula assumes a distortion-free lens focused at infinity. That is close enough for most planning, but three things move the real frame away from it.

Focusing closer narrows the view

A simple lens focuses by moving away from the sensor. At a focus distance s, the image forms f × s ÷ (s − f) behind the lens instead of f, and that longer distance is what sets the angle. The effect is small at a few meters and grows quickly near close focus.

Focus distanceEffective distance to sensorHorizontal angleChange in frame width
Infinity50.0mm39.6°0%
5m50.5mm39.2°−1%
2m51.3mm38.7°−2.5%
1m52.6mm37.8°−5%
0.45m56.3mm35.5°−11%

A 50mm lens on full frame (36mm wide), thin-lens model. Lenses that focus by moving internal groups can breathe more, less or the other way; check the frame at the real focus distance.

This is the root of focus breathing: as the focus puller racks, the frame size shifts. Lenses that focus by moving internal groups change their effective focal length as they focus, so the real amount varies from one design to the next, and some cinema lenses are built to keep it small. The table shows the size of the effect for a lens that moves as a single unit; for close work, trust the monitor.

Distortion and fisheyes

The arctangent formula describes a rectilinear lens, which keeps straight lines straight. Wide lenses with barrel distortion take in a little more at the edges than it predicts, and fisheye lenses follow a different projection altogether, so their published angle (often 180° diagonal) cannot be put through this formula. CineMath's Field of View calculator warns when the horizontal angle reaches 170°, where a rectilinear lens stops being practical and the coverage figures run toward infinity.

Anamorphic squeeze

An anamorphic lens squeezes a wider horizontal view onto the same sensor width. Its horizontal angle is 2 × arctan(width × squeeze ÷ (2 × f)), while the vertical angle stays that of the spherical focal length. A 50mm 2× anamorphic sees the width of a 25mm and the height of a 50mm. The full treatment, with the recording modes that suit each squeeze, is in open gate vs 16:9 vs anamorphic.

Questions

How do you calculate field of view?

Use angle = 2 × arctan(d ÷ (2 × f)), where d is the recorded width, height or diagonal and f is the focal length, both in millimeters. A 35mm lens on Super 35 (24.89 × 18.66mm) sees 39.1° across, 29.9° up and 47.9° on the diagonal.

How wide is the frame at a given distance?

Multiply the distance by the recorded width and divide by the focal length. A 25mm on Super 35 (24.89mm wide), 3m from the subject, covers 3 × 24.89 ÷ 25 = 2.99m across. Use the recorded height instead for the frame height: 2.24m here.

Do lens makers quote the horizontal or the diagonal angle of view?

Stills lens makers usually quote the diagonal angle on a 36 × 24mm frame, while camera departments match shots on the horizontal angle. A 50mm on full frame is 46.8° on the diagonal but 39.6° across, so check which one a spec sheet gives.

Does focusing closer change the field of view?

Yes. A lens that focuses by moving forward sits further from the sensor at close focus, which narrows the view. For a 50mm on full frame the horizontal angle drops from 39.6° at infinity to 37.8° at 1m and 35.5° at 0.45m, a frame about 5% and 11% smaller. Lenses that focus by moving internal groups behave differently, which is why focus breathing varies between designs.

What focal length do I need for a shot?

Multiply the recorded width by the camera distance and divide by the frame width you want. For a 3m-wide frame from 4m away on Super 35, 24.89 × 4 ÷ 3 = 33.2mm: a 32mm gives slightly more than 3m and a 35mm slightly less.

Field of view in CineMath

CineMath's Field of View calculator runs the formulas in this guide. Enter the focal length, the distance to the subject and the sensor width and height, and it gives the horizontal and vertical angles, the diagonal angle under its details, and the frame width and height at that distance, with the formula and your numbers shown beneath.

  • Focal length presets from 14 to 135mm; distance presets from 1 to 50m
  • Sensor width presets of 36, 24.89, 23.6, 22.3, 17.3 and 13.2mm, and height presets to match, or type the recorded area of your camera's mode from the sensor size chart
  • Distances in feet when the app is set to Imperial units
  • An Anamorphic switch with 1.25, 1.33, 1.5, 1.8 and 2.0× squeeze presets or a custom factor

Like the formulas above, the calculator uses the focal length as marked, which is exact at infinity focus, so at close distances its coverage runs slightly large. To carry a framing from one camera to another, use Focal Length Match; to see what stays sharp in the frame you have planned, go on to Depth of Field; the depth of field guide shows how the format changes it.

The free web version runs the same formulas in your browser, with sensor presets, an anamorphic squeeze and distances in feet or meters.

Calculators for this guide