Lens formula calculator

Solve the thin-lens equation 1/f = 1/u + 1/v and magnification m = −v/u.

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Focal length (positive converging)

Object distance (positive real object)

More inputs and assumptions

Input mode

Answer

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Thin lens: 1/f = 1/u + 1/v. Solve image distance v = fu/(u − f), or focal length f = uv/(u + v), using the real-is-positive sign convention.

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Precision and calculation record

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Rounding changes displayed numbers, not the calculation. Text, fractions, matrices and CSV schedules keep their own formatting. Automatic keeps up to 12 significant digits, with money shown to cents where applicable.

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Formula and assumptions

All lengths use one unit. Positive f is converging, positive u is a real object, and positive v is a real image on the opposite side. Ideal thin-lens approximation only.

Automatic precision shows numbers to 12 significant digits. Thousands separators such as 1,000 are accepted; use a dot for decimals.

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Updated 2026-09-26

Using Lens formula calculator

Thin lens: 1/f = 1/u + 1/v. Solve image distance v = fu/(u − f), or focal length f = uv/(u + v), using the real-is-positive sign convention.

All lengths use one unit. Positive f is converging, positive u is a real object, and positive v is a real image on the opposite side. Ideal thin-lens approximation only.

Next: Display viewing angle calculator

A worked example

Example inputs: focal length (positive converging) = 10, object distance (positive real object) = 30. Image distance = 15.

Before you use the result

All lengths use one unit. Positive f is converging, positive u is a real object, and positive v is a real image on the opposite side. Ideal thin-lens approximation only.

Example results for focal length (positive converging)

These examples use Object distance (positive real object): 30; Input mode: Image distance from focal length. They are reference calculations, not recommended settings.

Focal length (positive converging)	Image distance
5	6
10	15
20	60

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