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F-Number, Entrance Pupil Diameter & Area

Relate focal length, f-number and the diameter and area of an ideal circular entrance pupil.

Formula & worked example
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How to use this calculator

Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

A 50 mm focal length at f/2 gives a 25 mm entrance pupil and an area of approximately 490.874 mm².

Pupil diameter = focal length / f-number; circular area = π × diameter² / 4

Worked example

Enter these known values and leave the other values blank.

Focal length: 50 mm
F-number: 2

Entrance pupil diameter: 25 mm
Circular pupil area: 490.9 mm²

Assumptions and limitations

Every quantity must be positive. F-number is a dimensionless focal-length-to-pupil-diameter ratio.
Use the entrance pupil, the apparent aperture seen through the front optics, rather than assuming the physical iris has the same diameter.
The area calculation assumes a circular pupil. It does not calculate exposure, T-stop transmission, vignetting, depth of field or focus-dependent effective aperture.

Common questions

What happens to area when the f-number doubles?

At fixed focal length, pupil diameter halves and circular area becomes one quarter.

Can I solve the f-number from a measured pupil diameter?

Yes. Enter focal length and entrance pupil diameter in their selected units; their ratio gives f-number.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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