# How to calculate the correct focal length needed for a subject of a given size and distance?

I need to purchase my first ever lens. So far I've only used lenses that were built into a camera. This specific lens is for the BlackMagic Deign Pocket Cinema Camera (a video only camera, but one that uses photography lenses). I would prefer this to be a prime lens.

I have tried to find the exact way to calculate the focal length of the lens I need but I have not been able to find a good resource to make this simple enough for my limited optics knowledge. Can you please explain a simple way to calculate the focal length of a lens given the following inputs as an example: I would prefer a simplified mathematical explanation so that I may use it to make similar determinations in the future using a "plug and chug" method.

I have found this answer. Using that method, I came up with:

``````Required lens focal length = 7.02mm sensor height x (77in / 36in) = 15mm
``````

Is that correct?

• Suppose you want to frame an object of size `a` at distance `l`. Then, roughly, `a/l = s/f` where `s` is the sensor size and `f` is the focal length. – Szabolcs Dec 31 '14 at 22:21
• @Szabolcs Thanks! So does 36/77 = 7.02/f sound right? Solving for f I get 15.015mm. – user35614 Dec 31 '14 at 22:40