Physics

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Lensmaker's Equation Calculator.

Calculate thin-lens focal length from indices and signed surface radii.

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Set your values

Results update as you type.

Focal length: 0.1 m

Focal length

0.000000m
Optical power: 10 D

Optical power

0.000000D

Results update automatically as you type.

Use Cases

Design a lens for a specific focal length

Use this calculator to determine the required surface radii for a lens made of a given material (refractive index) surrounded by a specific medium, to achieve a desired focal length.

Example: Find the radii for a glass lens (n=1.5) in air (n=1) to have a focal length of 0.2 m.

Analyze an existing lens

Given the refractive indices and measured surface radii of a lens, compute its focal length to understand its optical power and behavior.

Example: A lens with radii 0.1 m and -0.15 m, n_lens=1.6, n_medium=1.33 (water) – what is its focal length?

Frequently Asked Questions

What does the Lensmaker's Equation Calculator do?
This calculator computes the focal length of a thin lens using the Lensmaker's equation. You provide the lens refractive index, the medium refractive index, and the signed radii of curvature for the two lens surfaces (in meters). The calculator then applies the formula to give you the focal length.
How do I interpret the signed radii?
The sign of each radius follows the Cartesian sign convention. A positive radius means the surface's center of curvature is on the same side as the incoming light (usually to the right), while a negative radius means it is on the opposite side. This affects whether the lens is converging or diverging.
What units should I use for the radii?
The radii must be entered in meters. The calculator will output the focal length in meters as well. Ensure both radii are in meters to get a correct result.

Tips & Common Mistakes

Tips

  • Remember to use the correct sign for each radius: positive if the center of curvature is on the same side as the incoming light, negative otherwise.
  • Ensure the lens refractive index and medium refractive index are entered as dimensionless numbers (e.g., 1.5 for glass, 1.0 for air).
  • Double-check that both radii are in meters; if you have measurements in centimeters or millimeters, convert them to meters before entering.
  • For a symmetric biconvex lens, the first radius is positive and the second is negative (or vice versa) depending on orientation; the calculator handles the signs automatically.

Common Mistakes to Avoid

  • Using the wrong sign for the radii, which can lead to an incorrect focal length or even a diverging lens result.
  • Forgetting to convert radii to meters – entering centimeters or millimeters will give a focal length in the wrong unit.
  • Confusing the lens refractive index with the medium refractive index – swapping them will produce a different focal length.

Last updated: August 13, 2026