PhysicsCalcs
Optics

Diopter Calculator

Convert between focal length and diopters, combine lenses, calculate reading additions, and classify lens power.

Interactive calculator

Diopter Calculator

Convert between focal length and diopters, combine thin or separated lenses, calculate reading additions, and classify lens power.

Try an example

Your result will appear here.

Choose a calculation mode, fill in the known values, and click Calculate.

Quick Guide

  • Choose: focal → diopters, diopters → focal, combined lenses, multi-lens, reading addition, or separated lenses.
  • Use presets for common prescriptions and camera lenses.
  • Click Calculate for results with classification.

Table of Contents

Key Takeaways

  • A diopter (D) = 1/f(m) measures optical power — the ability of a lens to converge or diverge light.
  • Positive diopters = converging (convex) lens; negative = diverging (concave).
  • Thin lenses in contact: total power = sum of individual powers.
  • Separated lenses: D_total = D₁ + D₂ − d·D₁·D₂ accounts for the gap.
  • The reading addition (ADD) is always positive and provides extra focusing power for near vision.

What Is a Diopter?

A diopter is the SI-derived unit of optical power. It equals the reciprocal of the focal length measured in metres. Optometrists use diopters to write prescriptions, photographers relate them to focal length, and physicists use them when combining lens systems.

Key Formulas

D=1fD = \frac{1}{f}
Dtotal=D1+D2−d⋅D1⋅D2D_{\text{total}} = D_1 + D_2 - d \cdot D_1 \cdot D_2

For thin lenses in contact (d = 0), the formula simplifies to D_total = D₁ + D₂.

Vision Correction

Power RangeClassificationTypical Use
< ±1 DVery weakMild correction, cosmetic lenses
±1 to ±3 DWeakCommon everyday glasses
±3 to ±6 DModerateModerate myopia/hyperopia
±6 to ±10 DStrongHigh prescriptions
> ±10 DVery strongMagnifiers, thick lenses

How to Use

  1. Select a conversion or combination mode.
  2. Enter lens powers or focal lengths. Negative values for diverging lenses.
  3. Click Calculate for power, focal length, and classification.

Examples

50 mm camera lens

D = 1/0.050 = 20 D (strong converging lens)

Myopia correction −3.00 D

f = 1/(−3) = −0.333 m = −333 mm (diverging virtual focus)

FAQ

What is a diopter?›

A diopter (D) is the unit of optical power equal to the reciprocal of the focal length in metres: D = 1/f. A +2 D lens has a focal length of 0.5 m (50 cm). Higher absolute diopter values mean stronger lenses.

What do negative diopters mean?›

Negative diopters indicate a diverging (concave) lens, used to correct myopia (nearsightedness). The negative sign means the focal point is virtual — on the same side as the incoming light.

How are diopters added?›

For thin lenses placed in direct contact, their diopter values simply add: D_total = D₁ + D₂. For separated lenses, the formula includes a correction term: D_total = D₁ + D₂ − d·D₁·D₂, where d is the separation in metres.

What is the ADD in a prescription?›

ADD (reading addition) is the extra plus power added to the distance prescription for near vision. It compensates for presbyopia and typically ranges from +0.75 to +3.00 D.

How does focal length relate to magnification?›

For a simple magnifier held at the near point (25 cm), magnification ≈ D/4 or (25 cm)/f. A +10 D lens (f = 10 cm) gives roughly 2.5× magnification.

Sources

  1. Hecht – Optics (6th ed.) — Thin Lenses
  2. AAO – Ophthalmic Optics
  3. HyperPhysics – Thin Lens Combinations
Manish Kumar

Author & technical reviewer

Manish Kumar

PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.

Learn more about Manish