Lens Power (Diopter) Calculator
Calculate lens power in diopters from focal length, or find focal length from a diopter value.
Covers eyeglasses, contact lenses, and optical instruments.
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.