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Focal Ratio (f-number) Calculator

Find the f-number of a lens or telescope.

How it is calculated

The f-number is N = f / D, where f is the focal length and D is the diameter of the aperture (the entrance pupil). Both must be in the same unit, usually millimetres, because the units cancel and the result has none. It is shown as f/ followed by the number with two decimals. Aperture must be above zero. A smaller N means a wider opening and more light reaching the sensor; each step of about 1.4 in N halves or doubles the light.

Worked example

A 200 mm lens with an effective aperture diameter of 71.4 mm. Divide focal length by diameter: 200 / 71.4 ≈ 2.80. The focal ratio is f/2.80, which is the usual f/2.8 stop on a camera lens.

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Common mistakes

  • Mixing units, such as a focal length in millimetres and an aperture in centimetres. The ratio is then 10 times off.
  • Entering the lens's maximum f-number or the barrel diameter instead of the real aperture opening.
  • Expecting f/2 and f/4 to differ by a factor of two in light. Light depends on the area, so that gap is two full stops, a factor of four.
  • Using the nominal focal length of a zoom for every setting, when the effective aperture changes with zoom.

About this calculator

The focal ratio (or f-number, written f/N) of a lens or telescope is its focal length divided by the diameter of its aperture: N = focal length / aperture diameter. A lower f-number means a wider relative aperture that gathers more light per unit of sensor area, while a higher f-number means a narrower aperture and greater depth of field.

Photographers use f-numbers on the standard scale (f/1.4, f/2, f/2.8, f/4, f/5.6...) to control exposure and depth of field, where each full stop halves or doubles the light reaching the sensor; astronomers use the same ratio to describe how "fast" a telescope is for imaging faint deep-sky objects — a low f-ratio scope captures dim nebulae in less exposure time.

Photographers choosing lenses and exposure settings, amateur and professional astronomers selecting telescopes for astrophotography, and optics students learning how aperture affects image brightness all use this calculation.

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