Lens Power (Diopter) Calculator
Calculate lens power in diopters from focal length, or find focal length from diopter value.
Covers eyeglasses and optics.
Lens Power measured in diopters (D) describes how strongly a lens converges or diverges light. It is the reciprocal of the focal length in meters.
Formula:
Power (D) = 1 / Focal Length (m)
Or equivalently:
Focal Length (m) = 1 / Power (D)
Sign Convention:
- Positive (+) diopters: Converging (convex) lens — used for farsightedness (hyperopia) and magnifying glasses.
- Negative (−) diopters: Diverging (concave) lens — used for nearsightedness (myopia).
Common Diopter Values:
| Prescription | Meaning | Focal Length |
|---|---|---|
| +1.00 D | Mild farsightedness | 1.0 m (100 cm) |
| +2.50 D | Moderate farsightedness / reading glasses | 0.4 m (40 cm) |
| -1.00 D | Mild nearsightedness | 1.0 m |
| -3.00 D | Moderate nearsightedness | 0.33 m (33 cm) |
| -6.00 D | High nearsightedness | 0.17 m (17 cm) |
| +10.00 D | Strong magnifier | 0.1 m (10 cm) |
Combined Lens Power:
When multiple thin lenses are placed together (touching):
Total Power = P₁ + P₂ + P₃ + ...
For example, reading glasses of +1.50 D combined with a +1.00 D lens = +2.50 D total.
Magnification of a Simple Magnifier:
Magnification = Power (D) / 4 + 1
(Assuming 25 cm standard near point)
A +10 D magnifying glass provides approximately 3.5× magnification.
Practical Example: An eyeglass prescription of -2.50 D means:
- Focal length = 1 / 2.50 = 0.40 m = 40 cm = 15.7 inches
- The lens is concave (diverging) to correct nearsightedness
- Without glasses, distant objects appear blurry beyond about 40 cm
Lens Maker’s Equation (for advanced users):
1/f = (n-1) × [1/R₁ - 1/R₂]
Where n is the refractive index and R₁, R₂ are the radii of curvature.
Tips:
- Eyeglass prescriptions include sphere (SPH), cylinder (CYL for astigmatism), and axis values.
- This calculator handles the sphere component only.
- Higher diopter lenses are thicker and heavier — high-index lens materials can reduce thickness.
- Over-the-counter reading glasses typically range from +1.00 to +3.50 D.