# How do I correctly convert from aperture diameter into f-stops?

I'd like to know whether it's possible to convert the radius of the focal point into f-stops properly. The following equation illustrates that the diameter is dependent on the f-stop:

$$\text{Aperture diameter [m]} = \frac{\text{focal length [mm]}}{\text{f-number}} \times \frac{\text{1 [m]}}{\text{1000 [mm]}}$$

Q: Is there a way to convert the radius (or diamteter) value into f-stops based on the lens and sensor dimensions only?

Sensor dimensions don't matter.

F-stop is shorthand for "fractional" and what it's a fraction of is the lens focal length and the diameter of the iris and the real calculation is simply the lens focal length $$\f\$$ divided by aperture diameter $$\D\$$ (that is, $$\{f\,/\,D}\$$).

50 mm lens with an iris 25 mm across is at f/2.

So in your case, if you know the radius then it's simply $$\text{f-number} = \frac{\text{focal length}}{2\,\times\,\text{radius}}$$

Note regarding measurements: Scientific pursuits are usually done in metric, so most things with lenses are measured in mm and therefore the diameter is mm. (The fraction remains the same since it's just a number and the mm cancels out in the division.) Lenses in the early part of last century were sometimes measured in inches, and because the units carry through in the calculations the answer would also be in inches.

• The actual diameter of the iris is irrelevant. It is the diameter of the entrance pupil that matters. Jun 25, 2016 at 21:09
• Michael is technically right, of course. Since the original question was a bit confused on what exactly an f-stop was I decided to keep the answer minimalist because terms like "entrance pupil" would confuse more than help. Jun 27, 2016 at 5:41

F-number equals the focal length of the lens divided by the diameter of the entrance pupil. Since both measurements are linear dimensions when the same units of measurement are used for both the focal length and the diameter of the entrance pupil then they cancel each other out without any further conversion. If the measurement units are dissimilar then either one of the measurements must be converted to match the unit of measurement of the other dimension or both units must be converted to a same third unit.

The entrance pupil is most easily understood as the apparent size of the aperture diaphragm as measured when observed from the outside of the front of the lens. Thus the entrance pupil is not necessarily the same diameter as the actual physical aperture inside the lens, but is rather the diameter on the lens' front element for which light falling on the front element is allowed to pass through the lens. The lens elements between the actual iris and the front of the lens typically magnify the size of the entrance pupil.

• Thanks Michael! In my case I can't determine the entrance pupil since it's a 3d camera as part of a 3d render engine, so all values are more or less aproximated anyway. The radius as mentioned unfortunately is all what I know...
– p2or
Jun 27, 2016 at 19:01