Optical Power Calculator
Convert a lens's focal length in centimetres to optical power in diopters instantly. Use it to understand eyeglass prescriptions, compare lenses, or solve optics problems.
About this calculator
Optical power (P) measures how strongly a lens converges or diverges light, and is defined as the reciprocal of the focal length expressed in metres. Because this calculator accepts focal length in centimetres, the formula becomes: P = 100 / focalLength (cm), which is equivalent to P = 1 / focalLength (m). The unit of optical power is the dioptre (D). A positive power (converging lens) brings parallel rays to a focus, while a negative power (diverging lens) spreads them apart. Optometrists use dioptres directly in prescriptions because powers of lenses in contact are simply additive: P_total = P₁ + P₂ + … This additive property makes dioptres far more practical than focal lengths when combining lenses in eyeglasses or multi-element optical systems.
How to use
Your reading glasses have a focal length of 25 cm. Step 1 — Enter 25 in the Focal Length field (cm). Step 2 — The calculator computes: P = 100 / 25 = 4.0 D. Your lenses have an optical power of +4.0 dioptres. Now try a diverging lens with a focal length of −50 cm: P = 100 / (−50) = −2.0 D. A negative sign confirms the lens is diverging — consistent with a myopia correction prescription.
Frequently asked questions
What does a diopter value mean in an eyeglass prescription?
A dioptre value tells you how strongly the lens bends light to compensate for your eye's refractive error. A prescription of +2.0 D means you need a converging lens with a 50 cm focal length to help a farsighted (hyperopic) eye focus on near objects. A prescription of −3.5 D means a diverging lens with about a 28.6 cm focal length is needed to correct nearsightedness (myopia). The larger the absolute dioptre value, the stronger the correction required and the thicker the lens tends to be.
Why is optical power measured in diopters instead of focal length?
Focal length is inversely related to lens strength, making it awkward to combine lenses arithmetically — you cannot simply add focal lengths. Dioptres solve this by expressing power as 1/f (in metres), so placing two thin lenses in contact gives a total power that is just the sum of their individual powers. This additive property enormously simplifies the design of multi-element systems like eyeglasses with sphere and cylinder corrections, contact lenses, and compound microscopes. Opticians and ophthalmologists universally use dioptres for this reason.
How do I convert between focal length in millimetres and optical power in diopters?
Camera lenses are typically specified in millimetres, so you first convert to metres by dividing by 1000, then take the reciprocal. For example, a 50 mm camera lens has a focal length of 0.05 m, giving P = 1 / 0.05 = 20 D — a very powerful converging lens compared to typical eyeglass lenses. This highlights how strong camera lenses actually are optically; eyeglass prescriptions rarely exceed ±10 D, while a standard 50 mm prime lens is 20 D. If you are using this calculator, simply enter the focal length in centimetres (50 mm = 5 cm) and you will get 100 / 5 = 20 D directly.