Optical Power Diopter Calculator
Optical power (measured in diopters, D) is the reciprocal of focal length in meters: P = 1/f (m). A converging lens has positive power; a diverging lens has negative power. Diopters are convenient because thin lenses in contact have their powers simply added: P_total = P1 + P2. This calculator converts between focal length (in mm or cm) and diopters, and also computes the combined power of up to two lenses in contact. Enter focal lengths with appropriate sign: positive for converging, negative for diverging.
Diopter formula
P = 1/f (meters)
Ptotal = P1 + P2 (lenses in contact)
fmm = 1000 / Pdiopters
Where f is focal length in meters, P is power in diopters (D = m-1). Converging lenses: P > 0, f > 0. Diverging lenses: P < 0, f < 0.
Common optical power values
- Normal reading glasses: approximately +1.0 D to +3.5 D.
- Typical myopia correction: -1.0 D to -8.0 D (most common range).
- Strong hyperopia correction: up to +10 D or more in some cases.
- Camera telephoto lens (f = 400 mm): P = 2.5 D.
- Camera wide-angle lens (f = 24 mm): P = approximately 41.7 D.
- Compound microscope objective (f = 3.3 mm): P = approximately 303 D.
Optical power (diopters): frequently asked questions
What is optical power in diopters?
Optical power P = 1/f, where f is the focal length measured in meters. The unit is diopters (D or m^-1). A converging lens with f = 0.25 m has power P = +4.0 D. A diverging lens with f = -0.5 m has power P = -2.0 D. Diopters are additive for thin lenses in contact.
How are diopters used in eyeglass prescriptions?
Eyeglass prescriptions specify sphere and cylinder power in diopters. A prescription of -2.50 D sphere means a diverging lens correcting myopia (nearsightedness). A +1.75 D sphere corrects hyperopia (farsightedness). The add power for reading glasses (bifocals) is always positive and typically ranges from +0.75 D to +3.50 D.
How do you combine two lenses in contact?
For two thin lenses in contact, the combined power is P_total = P1 + P2. The combined focal length is 1/f_total = 1/f1 + 1/f2. For example, a +3.0 D lens with a -1.0 D lens gives +2.0 D total power (f = 0.5 m). This approximation works when the lens separation is negligible compared to the focal lengths.
What is the human eye's optical power?
The unaccommodated (relaxed) human eye has a total optical power of about 59 D. The cornea contributes about 43 D and the lens about 16 to 24 D. When fully accommodated (focused on a near object), the eye increases its power by up to about 8 to 14 D in young people. This range decreases with age (presbyopia).
What is the vergence of light?
Vergence is the optical power associated with the convergence or divergence of a light beam. It equals 1/distance from the current focus point (in meters). Converging beams have positive vergence; diverging beams have negative vergence. A lens adds its power to the incoming vergence to produce the outgoing vergence.
Official sources
- OpenStax University Physics Volume 3, Chapter 2: Geometric Optics. openstax.org.
- ISO 10343:1994, Ophthalmic instruments: Ophthalmometers. iso.org.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.