Diopter Calculator — Optical Power & Focal Length
A diopter (D) is the SI unit of optical power — the reciprocal of focal length in metres. Enter optical power or focal length and instantly see both, whether the lens converges or diverges, and the image distance for an object at the standard 25 cm near point.
D (diopters)
m
Diopters (D) = 1 / focal length in metres
- 1
Focal length (m)
1 ÷ 2 D = 0.5f = 1 / P — the focal length is the reciprocal of optical power in metres. - 2
Optical power (D)
1 ÷ 0.5 m = 2
How does this calculator work?
Diopter (D) = 1 / focal-length (m). Enter either value to get the other. Positive diopters = converging (convex) lens; negative = diverging (concave). The calculator also applies the thin-lens equation to find the image distance for an object at the 25 cm near point.
Formula
How this is calculated
Optical power in diopters is simply the reciprocal of the focal length measured in metres: P = 1/f. A lens with a focal length of 0.5 m has a power of 2 D; a 0.25 m lens has 4 D. Positive power means the lens converges light (convex lens, used for hyperopia/far-sightedness corrections); negative power means it diverges light (concave, used for myopia/near-sightedness).
The thin-lens equation 1/v − 1/u = P (where u is the object distance and v the image distance, both in metres using the real-is-positive sign convention) lets you find where the image forms. This calculator evaluates it for an object placed at the standard near-point distance of 25 cm (u = −0.25 m), the reference used in optometry. A positive image distance means a real image forms on the far side of the lens; a negative value means a virtual image behind the object side.
This calculator covers single thin lenses only. Real optical systems (eyes, camera lenses, telescopes) consist of multiple elements; combined power is approximately P₁ + P₂ for thin lenses in contact but requires more complex ray-transfer matrices for separated elements.
Frequently asked questions
A diopter measures the optical power of a lens or curved mirror — it equals 1 divided by the focal length in metres. A 2 D lens focuses parallel light to a point 0.5 m away; a −3 D lens diverges parallel light as if it came from a virtual focus 0.33 m behind the lens.
Diopters are convenient for prescriptions because lenses in contact add: a −2 D correction combined with the eye's own error gives a net result directly. The prescription also includes cylinder and axis for astigmatism, which this calculator does not cover.
Divide 100 by the focal length in centimetres: P = 100 / f_cm. For example, a 25 cm focal length = 4 D. Equivalently, convert to metres first and take the reciprocal.
TG we-Calculate Editorial Team. (2026). Diopter Calculator — Optical Power & Focal Length [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/diopter-calculator
TG we-Calculate Editorial Team. "Diopter Calculator — Optical Power & Focal Length." TG we-Calculate. 2026. https://we-calculate.com/calculator/diopter-calculator.
TG we-Calculate Editorial Team, "Diopter Calculator — Optical Power & Focal Length," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/diopter-calculator
@misc{wecalculate_diopter_calculator, title = {Diopter Calculator — Optical Power & Focal Length}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/diopter-calculator}}, year = {2026}, note = {TG we-Calculate} }
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