Power of Lens Calculator
Convert between focal length and diopters using P = 1/f. Understand lens power in optometry, eyeglass prescriptions, and optical design.
Use Calculator Now ↓P = 1/f Calculator
Formula
P = 1/f
P in diopters (D), f in meters (m)
Understanding Lens Power
Diopters (D) measure the optical power of a lens. Power is defined as P = 1/f, where f is the focal length in meters. A lens with f = 0.5 m has power +2.0 D; a lens with f = −0.25 m has power −4.0 D.
P = 1/f
Positive P → converging (convex) lens; Negative P → diverging (concave) lens
Relationship to Lens Maker Formula
The power of a lens is directly related to the lens maker formula. For a thin lens:
P = (n − 1)(1/R₁ − 1/R₂)
Since 1/f = (n−1)(1/R₁ − 1/R₂), we have P = 1/f. Power combines refractive index and curvature into a single number.
Learn the Lens Maker Equation →Practical Applications
Eyeglass prescriptions
Optometrists prescribe lens power in diopters. −2.0 D corrects mild myopia.
Optometry
Diopters standardize lens strength for vision correction and contact lenses.
Optical design
Engineers use power for camera lenses, telescopes, and microscope objectives.
Combined Lens Power
For thin lenses in contact, powers add:
Ptotal = P₁ + P₂
Example: A +2.0 D and a +3.0 D lens in contact give 5.0 D total. For separated lenses, use the effective power formula.
Lens Combination Calculator →Common Prescription Values
| Condition | Typical Power | Focal Length |
|---|---|---|
| Mild myopia | −0.5 to −2.0 D | −50 cm to −1 m |
| Moderate myopia | −2.0 to −6.0 D | −17 cm to −50 cm |
| Severe myopia | > −6.0 D | < −17 cm |
| Mild hyperopia | +0.5 to +2.0 D | 50 cm to 2 m |
| Moderate hyperopia | +2.0 to +5.0 D | 20 cm to 50 cm |
| Reading glasses | +1.0 to +3.0 D | 33 cm to 1 m |
Frequently Asked Questions
What is the formula for power of a lens?
The power of a lens is P = 1/f, where P is the power in diopters (D) and f is the focal length in meters. A lens with a focal length of 0.5 m has a power of +2.0 D. Positive power means converging, negative means diverging.
How do I convert diopters to focal length?
To convert diopters to focal length: f = 1/P. For example, a +3.0 D lens has a focal length of 1/3 = 0.333 meters (33.3 cm). A −2.5 D lens has a focal length of 1/(−2.5) = −0.4 meters (−40 cm).
What does a negative lens power mean?
Negative lens power indicates a diverging (concave) lens. It spreads light rays apart and is used to correct myopia (nearsightedness). For example, a prescription of −3.0 D means a concave lens with a focal length of −33.3 cm.
Why is focal length in meters for diopters?
The diopter is defined as 1/meter. Using meters keeps the formula simple: P = 1/f. If f is in cm, you must convert: P = 100/f (cm).