How do I calculate the focal length needed to frame a subject of a given size at a given distance?
Asked 12/31/2014
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2 answers
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I’m choosing a first prime lens for a Blackmagic Pocket Cinema Camera and want a simple way to estimate focal length from subject size, distance, and sensor size.
Example: if I know the camera’s sensor height is 7.02 mm, the subject is about 36 in tall in frame, and the camera is 77 in from the subject, can I calculate the focal length as:
focal length = sensor height × (distance ÷ subject height)
So in this case: 7.02 mm × (77 in ÷ 36 in) ≈ 15 mm
Is that correct, and is this a reasonable plug-and-chug method for similar framing calculations?
Originally by user35614. Source · Licensed CC BY-SA 4.0
user35614
11y ago
2 Answers
1
What you did looks correct, you are using a form of h=f*tan(theta) which is used a lot in optical design. Usually one would use half the vertical sensor size (7.02/2 = 3.51) and half the height of the object(91/2 = 45.5), but in this case it doesn't matter.
It is important to note that this equation assumes some things, mostly that the axis of the lens is pointed at the person's shoulder area in the "desired result" frame that you gave, though the result holds if you depart from that a little bit.
Originally by user35709. Source · Licensed CC BY-SA 4.0
user35709
11y ago
0
Generated from our catalog & community — verify before relying on it.
Yes — for a simple framing estimate, your result is correct: about 15 mm.
A useful approximation is:
focal length = sensor dimension × (distance to subject ÷ subject size in frame)
Use matching dimensions:
- sensor height if you’re calculating vertical framing
- sensor width for horizontal framing
- keep subject size and distance in the same units
With your numbers: 7.02 mm × (77 ÷ 36) ≈ 15 mm
That means a 15 mm lens should roughly frame a 36-inch-tall subject at 77 inches away so it fills the sensor height.
This is essentially the same geometry as the field-of-view relationship. A more formal version often uses half the sensor size and half the subject size, but it gives the same result here.
Main assumption: the lens is aimed roughly at the middle of the subject area you want to frame. If you tilt the camera a lot or compose far off-center, the estimate becomes less exact.
So yes: for practical lens selection, this is a valid plug-and-chug method.
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