Focal Length Calculator

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.

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.