Example Data Table
Examples assume n1 = 1.000 and n2 = 1.500. Convex uses positive sign. Concave uses negative sign.
| Radius | Unit | Surface | n1 | n2 | Diopters (D) | Focal Length (m) |
|---|---|---|---|---|---|---|
| 50 | mm | Convex | 1.000 | 1.500 | +10.0000 | +0.1000 |
| 100 | mm | Convex | 1.000 | 1.500 | +5.0000 | +0.2000 |
| 200 | mm | Convex | 1.000 | 1.500 | +2.5000 | +0.4000 |
| 100 | mm | Concave | 1.000 | 1.500 | -5.0000 | -0.2000 |
| 0.25 | m | Convex | 1.000 | 1.530 | +2.1200 | +0.4717 |
Tip: If n2 equals n1, diopters become zero.
Formula Used
This calculator uses the paraxial surface-power relationship for a spherical interface:
- D is surface power in diopters (1/m).
- n1 is the refractive index before the surface (often air).
- n2 is the refractive index after the surface (lens material).
- R is the radius of curvature in meters.
Sign convention used here: convex surfaces are positive; concave surfaces are negative.
How to Use This Calculator
- Enter the radius of curvature and select its unit.
- Choose the surface type to apply the correct sign.
- Set refractive indices for the two media (n1 and n2).
- Select decimal places and whether to show a plus sign.
- Press Calculate to view diopters and focal length.
- Use CSV or PDF buttons to export the results table.
Note: This tool reports surface power, not full lens power.
Radius to Diopter Guide
1) What diopters represent
Diopters (D) measure optical power as inverse meters (1/m). A surface with +5.00 D bends light more strongly than +2.00 D. When power is positive, rays converge; when negative, rays diverge, producing a virtual focus on the incident side.
2) The radius–power link
For a single spherical interface, power grows as radius shrinks. With n2 − n1 = 0.50, a 100 mm radius (0.10 m) produces about +5.00 D. Halving the radius to 50 mm doubles the power to about +10.00 D.
3) Units and conversion data
The formula expects meters. Use these quick conversions: 1 mm = 0.001 m, 1 cm = 0.01 m, and 1 m = 1 m. A common optics radius like 200 mm equals 0.200 m and, with Δn = 0.50, gives about +2.50 D. If you measure in inches, multiply by 0.0254; for example 4 in ≈ 0.1016 m, close to 100 mm.
4) Choosing refractive indices
Refractive index depends on medium and wavelength. Typical values: air ≈ 1.000, water ≈ 1.333, many plastics ≈ 1.49–1.59, and crown glass ≈ 1.50–1.52. Increasing n2 while holding radius constant increases Δn and therefore diopters. Many catalogs quote nD at 589 nm; using the same wavelength value keeps comparisons consistent across materials.
5) Sign convention and surface shape
This calculator uses a practical convention: convex surfaces are positive radius and concave surfaces are negative radius. With the same magnitude radius and indices, changing convex to concave flips the sign of D. That helps you model diverging surfaces quickly.
6) Focal length as a cross-check
Surface power can be inverted to an equivalent focal length: f = 1/D. For +5.00 D, f ≈ +0.20 m (20 cm). For −5.00 D, f ≈ −0.20 m, indicating a virtual focus. This sanity check is useful when reviewing designs.
7) Typical ranges in practice
Many gentle curved interfaces fall between about 0.50 D and 10 D. For Δn = 0.50, that corresponds to radii from roughly 1.0 m down to 0.05 m (50 mm). Example: Δn = 0.50 and R = 0.08 m gives 6.25 D, while R = 0.16 m gives 3.125 D. Very small radii can create high power but are harder to manufacture and align.
8) Surface power vs full lens power
A complete thin-lens estimate usually combines two surface powers and lens thickness effects. This tool reports a single surface interface power, which is perfect for comparing curvature changes, checking a mold radius, or validating a step in a larger lens-power workflow. Index changes can shift power noticeably.
FAQs
1) What is a diopter?
A diopter is optical power measured in 1/m. A surface with 2 D has an equivalent focal length of 0.5 m, while 5 D corresponds to 0.2 m.
2) Why must radius be in meters?
Diopters are defined as inverse meters. Converting radius to meters keeps the units consistent so the computed power matches standard optical conventions.
3) What should I use for n1 and n2?
Use n1 for the incident medium (often air ≈ 1.000) and n2 for the second medium (glass or plastic). If you know the material grade, use its specified index.
4) What happens if n2 equals n1?
Then Δn becomes zero, so the interface has zero surface power. Light does not bend at the boundary in the paraxial approximation.
5) Why does convex show positive power?
With the sign rule used here, convex radius is positive. If n2 is greater than n1, (n2 − n1)/R becomes positive, indicating a converging interface.
6) Is this the same as a lens prescription?
Not exactly. Prescriptions describe overall lens power, usually combining two surfaces and thickness effects. This calculator reports one surface interface power, which is a building block.
7) Can I use this for contact lenses?
Yes for quick curvature-to-power comparisons, especially when the surrounding medium is not air. Enter appropriate indices (for tears or saline) to better approximate the interface behavior.