How do I calculate focal length for a 1 m × 1 m field of view at 10 m distance?
Asked 4/15/2021
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I want to estimate the focal length needed to frame a 1 m × 1 m subject area from a working distance of 10 m.
Sensor dimensions are:
- diagonal: 6.0 mm
- horizontal: 4.8 mm
- vertical: 3.6 mm
Lens focal length range is 5.1–51 mm.
I’ve seen the relation f = (sensor size × working distance) / field of view, but I’m unsure which sensor dimension to use: diagonal, horizontal, or vertical. Since the target field of view is square, which sensor dimension should I base the calculation on?
Originally by Photography Stack Exchange contributor. Source · Licensed CC BY-SA 4.0
Photography Stack Exchange contributor
5y ago
2 Answers
3
Since your field ov view is square, you only have to worry about the smaller dimension of the sensor, its height.
With H and D: height and distance of object, and h and f: height of sensor and focal length:
D/H = f/h
so
f = h * D/H
So f = 3.6 * 10/1 = 36mm.
Originally by user75947. Source · Licensed CC BY-SA 4.0
user75947
5y ago
0
Generated from our catalog & community — verify before relying on it.
Use the sensor dimension that corresponds to the field-of-view dimension you must guarantee. For a square 1 m × 1 m field of view, use the smaller sensor dimension: the vertical size, 3.6 mm.
By similar triangles:
f / sensor height = working distance / subject height
So:
f = 3.6 mm × 10,000 mm / 1,000 mm = 36 mm
So the required focal length is about 36 mm.
Why not use the diagonal? Because diagonal sensor size corresponds to diagonal field of view, not the horizontal or vertical framing. For a square subject area, using the smaller sensor dimension ensures the full 1 m height fits in frame. Using the horizontal dimension would give a different result because the sensor is not square.
In practice, you may want a little extra margin for framing tolerance, so choosing slightly wider than 36 mm can be sensible.
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