f-stop to Aperture Area Converter

How it is calculated

The f-number N is the focal length divided by the diameter of the aperture opening, so diameter = focal length ÷ N (both in mm). The area of that circle is area = π × (diameter ÷ 2)² in mm². The relative area is 1 ÷ N², which sets f/1.0 to exactly 1, so every other value is a fraction of the light-gathering area at f/1. Both the f-number and the focal length must be above zero. Relative area is shown to five decimals, diameter and area to two. Because area depends on 1/N², one full stop (a change of N by about 1.41×) halves or doubles it; for example f/2.8 to f/4 is about half the area. The diameter is the physical opening (entrance pupil), not the front-element size.

Common mistakes

• Leaving the focal length at a default when switching lenses. The relative area depends only on N, but the diameter and area scale with focal length, so a 50 mm and an 85 mm lens at the same f-number have different physical openings.
• Thinking f/2 has half the light of f/1. The area goes with 1/N², so f/2 gives one quarter of the f/1 area; a full stop halves it, and f/1.4 is the full stop after f/1.
• Entering a focal length in centimetres or in a 35 mm equivalent. The field expects the real focal length in millimetres, and an equivalent value gives a diameter that is too large.
• Taking the diameter as the size of the lens front glass. It is only the effective aperture opening.