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Focal Length Calculator

Find the focal length of a thin lens.

Result

11.11 cm
9.00 D

How it is calculated

The thin-lens equation is 1/f = 1/dₒ + 1/dᵢ, which the tool solves as f = dₒ × dᵢ ÷ (dₒ + dᵢ). dₒ is the distance from the object to the lens and dᵢ the distance from the lens to the image, both entered in centimetres, so f comes out in centimetres. The optical power is P = 100 ÷ f in dioptres (D), because the power uses the focal length in metres. Both distances must be above zero. This means the tool covers only a real image formed on the far side of the lens: a virtual image, such as a magnifying glass or a diverging (concave) lens would give, would need a negative image distance, and such an input returns no result. Thickness of the lens and lens aberrations are ignored.

Worked example

An object stands 25 cm from a converging lens and a sharp image appears on a screen 20 cm behind it. f = (25 × 20) ÷ (25 + 20) = 500 ÷ 45 ≈ 11.11 cm. In metres that is 0.1111 m, so the power is 100 ÷ 11.11 = 9.00 D. As a check, 1/25 + 1/20 = 0.04 + 0.05 = 0.09 per cm, and 1 ÷ 0.09 is the same 11.11 cm.

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Common mistakes

  • Mixing units, for instance the object distance in metres and the image distance in centimetres. Both must be in cm.
  • Entering a negative image distance for a virtual image. The tool only accepts positive distances and returns nothing otherwise.
  • Reading the power in dioptres from a focal length in centimetres without converting. The tool already does this, so do not divide again.
  • Entering the distance from the object to the image rather than the distance from each to the lens.
  • Using the sum of the reciprocals as the focal length. 1/dₒ + 1/dᵢ equals 1/f, so you must invert the result to get f.

Sources

About this calculator

The thin lens equation, 1/f = 1/dₒ + 1/dᵢ, relates a lens's focal length f to the object distance dₒ and image distance dᵢ. A lens's optical power in diopters is simply P = 1/f (with f in metres) — a common unit on eyeglass prescriptions and camera/telescope specs.

Opticians and optometrists use this relationship (and optical power) when prescribing corrective lenses; photographers and cinematographers rely on focal length to understand field of view and depth of field for a given lens; and telescope and microscope builders use it to design optical systems, positioning lenses and mirrors to achieve a target magnification.

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Comments (1)

  • Editorial team

    Both distances go in as positive numbers, which models a real image such as a projected one. A lens with an object at 30 cm and a sharp image at 60 cm has a focal length of 20.00 cm, or 5.00 dioptres. Virtual images are not handled here. Tell us if you need a negative-distance case supported.

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