Fundamentals

Calculating field of view: which angle covers how much width

11 September 20262 min readcctvfinder

Most planning does not fail on the camera. It fails on one number nobody worked out: how wide the image actually is at the target. Everything else hangs on it, and it takes one line to calculate.

The one formula

The field of view opens out from the camera like a triangle. How wide that triangle is at a given distance is answered by the tangent.

Image width = 2 × distance × tan(field of view ÷ 2)
Pixel density = sensor width in pixels ÷ image width

What matters is which distance you put in. Not the distance on the site plan, but the slant distance from the camera to the test target. A camera at 3.5 metres looking at head height is further away than the plan suggests.

The width in metres

Calculated with a camera at 3.5 metres and a test target at 1.6 metres, the head height of a standing person.

Distance	20°	40°	60°	90°	110°
10 m	3.6 m	7.4 m	11.8 m	20.4 m	29.1 m
20 m	7.1 m	14.6 m	23.2 m	40.2 m	57.4 m
30 m	10.6 m	21.9 m	34.7 m	60.1 m	85.9 m
50 m	17.6 m	36.4 m	57.8 m	100.1 m	142.9 m

A 110-degree lens at 30 metres covers 86 metres of width. That sounds like a lot of surveillance, and it is the most common planning mistake: the 1920 pixels of a Full HD camera have to spread across those 86 metres.

What arrives in pixels per metre

The same cases in Full HD. For comparison: the standard asks for 125 pixels per metre to Recognise and 250 to Identify.

Distance	20°	40°	60°	90°	110°
10 m	535	259	163	94	66
20 m	271	131	83	48	33
30 m	181	88	55	32	22
50 m	109	53	33	19	13

Read the table across and then down. Across: at the same distance, halving the field of view roughly doubles the pixel density. Down: with the same lens, doubling the distance halves it again.

The field of view is the strongest lever you have. It costs nothing but width.

Four places to turn

Choose a narrower lens. Strongest effect, costs covered width.
Move the camera closer. Just as strong, costs cable run.
Raise the resolution. Works in a straight line, costs money, bandwidth and storage.
Lower the requirement. Sometimes Observe is enough for the yard and Identify only at the gate.

The fourth line is the one that gets checked least often. A camera meant to identify everywhere gets expensive. Two cameras with clearly separated jobs are often cheaper than one that attempts both.

In cctvfinder you see all four at once: set distance, height, field of view and resolution, and next to them stands the level that comes out.