How Far Will a Camera Actually See? Focal Length, Sensor Size and Field of View, Worked Out

A supplier says 150°. A competitor says 140°. A third quotes 2.8 mm. These are three different ways of describing the same property, and none of them tells you whether you will be able to read a number plate at the distance you care about. Two numbers are needed before the question can be answered: the lens focal length and the active width of the sensor behind it.

The one formula worth memorising

For a lens focused at a distance much greater than its focal length, the horizontal field of view is:

Sensor width is not a datasheet headline, but it is easy to derive: multiply the horizontal pixel count by the pixel pitch. A 1080P sensor with 1920 pixels at 2.9 µm pitch has an active width of 1920 × 0.0029 mm = 5.57 mm. For most 1/2.8" and 1/2.9" 1080P sensors in vehicle cameras that lands between 5.3 mm and 5.6 mm, which is close enough to use 5.6 mm as a working figure.

A useful check on the method: our JPC-100F forklift camera is built with a 6 mm lens and quoted at 50°, and the formula above returns 50° for a 5.6 mm sensor at 6 mm focal length. Our thermal camera is specified with a 3.6 mm lens at 49° × 37° and a 10 mm lens at 18° × 13°; the same arithmetic applied to its 256 × 192 sensor at 12 µm pitch returns 46° × 36° and 17.5° × 13°. Agreement within a degree or two is the normal outcome — which is exactly what makes the disagreement on wide lenses worth understanding.

Why a 2.8 mm lens is quoted at 110° and calculates to 90°

Rectilinear geometry assumes straight lines in the scene stay straight in the image. Wide lenses do not honour that. A 2.8 mm lens on a 1/2.9" sensor projects a 90° rectilinear view, but the lens design deliberately introduces barrel distortion, bowing straight lines outwards, in exchange for capturing a wider field. The quoted figure — often 110° — includes that distortion, and so does the image. Both numbers are true; they describe different things.

The practical consequence is that quoted angles cannot be compared across suppliers unless you know whether distortion is included. Two cameras quoted at 150° may have visibly different coverage if one of them is closer to rectilinear, and a camera quoted at 110° may cover less ground than one quoted at 90° if the second figure is rectilinear. Where the number matters — in a tender document, for example — ask for the focal length and the sensor size as well, and do the arithmetic yourself.

Sizing a lens for number plate reading

Automatic plate recognition needs a minimum number of pixels across each character. Practice varies, but a planning figure of at least 20 pixels per character cell is a reasonable starting point, with 30 giving comfortable margin. Take a European plate at 520 mm wide with eight character cells across it: 20 pixels per cell means the plate must span at least 160 pixels in the image.

The arithmetic behind the first row: 160 pixels across a 0.52 m plate is roughly 308 pixels per metre, so a 1920-pixel-wide frame can span 6.2 m at the plate’s distance. At a 90° field of view the frame width equals twice the distance, giving about 3 m. A 90° camera, in other words, can identify a plate only at roughly the distance from a loading bay to the back of the vehicle — which is precisely why vendors quoting a 150° or 180° camera for “plate recognition” should be asked what distance they mean.

Where the blind strip comes from

Fitting a wider lens is often proposed as the way to see more, but the near blind area on a side or rear camera is a mounting geometry problem, not a lens problem. The lowest ray a camera can see leaves the lens at its tilt angle plus half its vertical field of view, and hits the ground at:

A camera 2.5 m up with a 6 mm lens tilted 30° downwards has an area it physically cannot see from directly beneath itself out to about 2.5 m along the ground. Anything in that strip — a bollard base, a wheel, a person’s legs — is invisible however good the sensor is. Widening the lens to 2.8 mm reduces the strip to about 1.5 m, and tilting further down reduces it again at the cost of coverage at distance. This is the calculation installers actually need, and it is rarely presented alongside the angle figure it depends on.

The other lens specification: aperture

Focal length decides what the camera can see. The f-number decides how much light reaches the sensor to see it with, and it follows the same inverted logic that confuses people elsewhere in photography: a smaller number is a larger opening. Each step of √2 halves the light — F1.4 admits twice as much as F2.0, and four times as much as F2.8. In a camera that is expected to keep a short exposure at night, aperture and shutter are directly linked: an extra stop of aperture is an extra stop of shutter speed before the image becomes unusable, which translates directly into less motion smear on a moving vehicle.

• Ask for it. Many vehicle camera datasheets omit the aperture entirely, and a supplier who can answer has usually thought about low-light performance rather than only quoting resolution.
• Expect a trade-off. A wide aperture with a wide angle is optically harder to build well, and cheaper in a plastic barrel than a metal one. Where night detail matters, the aperture figure is worth as much attention as the lens angle.
• Remember the depth of field cost. A very wide aperture reduces depth of field, which matters for a camera that must show both the vehicle’s flank and objects some distance away.

Turning the arithmetic into a specification

1. Start from the subject. A number plate at 10 m, a pedestrian’s whole body at 15 m, a wheel and kerb 1 m from the vehicle: each of these is a distance-and-detail requirement, and each resolves to a pixel density.
2. Convert the pixel density into a field of view, using the resolution you intend to buy. 1920 pixels across the frame is the working assumption for 1080P.
3. Convert the field of view into a focal length, using the sensor width. If a supplier cannot give you the sensor size, use 5.6 mm for a 1080P 1/2.9" device and check the result against any angle they quote.
4. Check the mounting geometry separately, using the height, the tilt and the vertical field of view, so that you know what the camera cannot see as well as what it can.
5. Then verify on a sample. Arithmetic narrows the options; a recording at the operating distance, in the operating light, at the operating time of day, settles it.

Most specification mistakes in this category are not made in the choice of camera. They are made by choosing a camera for one duty — wide coverage for manoeuvring — and then expecting it to perform a different one, such as reading a plate at 15 m. Naming the duty and the distance first is what makes the rest of the calculation possible.