Diopter ↔ Focal Length Conversion Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 10/11/2026
Focal length (in meters) is the inverse of optical power in diopters: f = 1 ÷ P. For a -4 diopter correction (a common level of nearsightedness), the focal length is -25 cm.
Explanation
The diopter is the unit of optical power of a lens or corrective glass, defined as the inverse of its focal length expressed in meters: P = 1/f. This relationship means a high-power lens (say, 8 diopters) has a short focal length (12.5 cm), while a low-power lens (0.5 diopter) has a long focal length (2 m): the stronger the correction, the shorter the distance over which light is bent. The sign of the power carries essential information about the type of correction: a positive power corresponds to a converging lens, which corrects farsightedness (difficulty seeing up close) or presbyopia, with a positive focal length (the image actually forms after the lens); a negative power corresponds to a diverging lens, which corrects nearsightedness (difficulty seeing far away), with a negative focal length (the image formed is virtual, on the same side as the object). On a glasses prescription, power is given directly in diopters (written D or δ): for example, "-4.00 D" corresponds to a focal length of -25 cm. This definitional relationship applies identically to any optical lens, not just corrective lenses: camera lenses, magnifying glasses, telescopes — the amount of light actually received by the sensor or eye behind the lens then depends on separate parameters, see our illuminance conversion calculator.
Example: a -4 diopter nearsightedness correction
Inputs
Optical power: -4 diopters.
Calculation
Focal length = 1 ÷ (-4) = -0.25 m = -25 cm.
Result
This corrective lens has a focal length of -25 cm, typical of a moderate nearsightedness correction.
Frequently asked questions
Why is the focal length negative for a nearsightedness correction?
Because a corrective lens for nearsightedness is a diverging lens, which spreads light rays apart rather than focusing them: by optical convention, its focal length is negative, and the image it forms is virtual (it can't be projected onto a screen, unlike the real image formed by a converging lens with positive focal length). This negative sign isn't an error — it's physical information about the type of lens.
How do I read my glasses power on my prescription?
Power is usually given directly in diopters, written "D" or the symbol δ, preceded by a + or - sign. A prescription of "-2.50 D" means a nearsightedness correction of 2.5 diopters, i.e. a focal length of -40 cm; a prescription of "+1.75 D" means a farsightedness or presbyopia correction, i.e. a focal length of about +57 cm.
Does this relationship also apply to contact lenses?
The physical principle is identical, but a contact lens's effective power differs slightly from a glasses lens's power for the same perceived correction, because the contact lens sits directly on the eye while the glasses lens sits a few centimeters in front of it — a length gap that becomes significant for strong corrections (generally beyond ±4 diopters), which is why the prescribed power sometimes differs slightly between the two.