Optical Power Calculator (Diopters)
Calculate the focal length and optical power of a lens in diopters.
Enter object and image distances to find magnification and lens strength.
Optical power describes how strongly a lens bends light. It is measured in diopters (D), which are simply inverse meters.
Power = 1 / focal length (in meters)
A lens with a 0.5 m focal length has 2 diopters of power. A lens with a 25 cm focal length has 4 diopters.
Sign convention:
- Converging (convex) lens: positive focal length, positive power
- Diverging (concave) lens: negative focal length, negative power
Eye prescriptions use diopters directly. A −2.0 D prescription means a diverging lens correcting myopia (nearsightedness). A +1.5 D means a converging lens correcting hyperopia (farsightedness).
Thin lens equation:
1/f = 1/do + 1/di
Where do = object distance (positive if on the incoming light side), di = image distance (positive if on the outgoing side, meaning real image; negative = virtual image).
Magnification:
m = −di / do
Negative m means the image is inverted. |m| > 1 means the image is larger than the object.
Lenses in contact: when two thin lenses touch, the total power is just the sum:
P_total = P₁ + P₂
An optometrist combining a sphere and cylinder correction exploits this directly.
Enter focal length alone for basic power conversion, or add object and image distances for magnification.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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