Aperture Area Calculator

Find a lens or optical aperture's diameter and area from focal length and f-number, using D = focal length / f-number and A = π(D/2)².

Quick Facts

Diameter formula
D = focal length ÷ f-number
This is the standard optics definition of f-number: N = f/D.
Area formula
A = π × (D/2)²
Area scales with diameter squared, so one full stop (e.g. f/2 to f/2.8) roughly halves the aperture area.

Your Results

Calculated
Aperture diameter
-
D = focal length ÷ f-number
Aperture radius
-
D ÷ 2
Aperture area (mm²)
-
A = π × radius²
Aperture area (cm²)
-
Same area, alternate unit

Ready

Enter focal length and f-number, then press Calculate.

About the Aperture Area Calculator

An optical aperture is the opening — typically circular, controlled by an iris diaphragm in a camera lens or telescope — that limits how much light passes through the system. Its size is usually described two ways: as a physical diameter (in millimeters) or, for photographic and optical systems, as a relative aperture or f-number, written f/N. This calculator converts between the two and reports the resulting area.

The formulas

The f-number is defined as the focal length of the lens divided by the diameter of its entrance pupil: N = f / D. Rearranged, the aperture diameter is:

  • Diameter: D = focal length ÷ f-number
  • Radius: r = D ÷ 2
  • Area (circular aperture): A = π × r² = π × (D/2)²

Because area depends on the diameter squared, aperture area is inversely proportional to the square of the f-number: A ∝ 1/N². This is why a standard full f-stop — a factor of √2 in the f-number, such as f/2.8 to f/4 — always changes the light-gathering area by a factor of exactly 2.

Working with units

  • Focal length and f-number are unitless ratios of length, so the diameter comes out in whatever unit the focal length was entered in — this calculator uses millimeters (mm), the standard for lens specifications.
  • Area is reported in both square millimeters (mm²) and square centimeters (cm²); 1 cm² = 100 mm².
  • A smaller f-number means a larger opening (more light); a larger f-number means a smaller opening (less light) — the scale is inverse.

Knowing the limits

This formula treats the aperture as a perfect circle and ignores vignetting, the entrance-pupil magnification of the lens elements in front of the stop, and diffraction effects that become significant at very small apertures (high f-numbers). For a quick, standard estimate of light-gathering area from focal length and f-number, the formula above is the one used throughout photography and optics.

Frequently Asked Questions

What is the formula for aperture area?
Aperture area is A = π × (D/2)², where D is the aperture diameter. For a camera lens or telescope, D is usually derived from the f-number: D = focal length ÷ f-number. Combining both gives A = π/4 × (focal length ÷ f-number)².
How does the f-number relate to aperture diameter?
The f-number (or relative aperture), written f/N, is defined as N = focal length ÷ diameter. A lower f-number means a physically larger opening relative to the focal length; a higher f-number means a smaller opening. A 50 mm lens at f/1.8 has a roughly 27.8 mm aperture, while the same lens at f/8 has a roughly 6.25 mm aperture.
Why does one f-stop change the area by a factor of 2?
The standard f-stop scale (f/1.4, f/2, f/2.8, f/4, f/5.6...) increases the f-number by a factor of the square root of 2 at each step. Since area is proportional to 1/N², squaring that √2 factor gives exactly 2 — so each full stop halves or doubles the aperture area and the light reaching the sensor or film.
Does this formula work for non-circular apertures?
No — A = π(D/2)² assumes a circular opening, which is standard for camera lenses and most telescopes. A rectangular or slit aperture (as used in some diffraction experiments) needs area = width × height instead, and does not have a single "diameter."

Related calculators