# Lens Maker’s Equation Calculator

URL: https://speedycalculator.com/calculators/physics/lensmakers-equation/
Last updated: 2026-10-30

> The lens maker's equation calculator finds a lens's focal length from the radii of curvature of its two surfaces, its thickness and its refractive index.

## Inputs

- Radius of curvature R₁ (mm, cm, m, in, µm)
- Radius of curvature R₂ (mm, cm, m, in, µm)
- Lens thickness d (mm, cm, m, in, µm)
- Refractive index n

## Results

- Focal length f
- Optical power

## Formula

```
1/f = (n − 1)·[1/R₁ − 1/R₂ + (n − 1)·d / (n·R₁·R₂)]
```

## Explanation

The lens maker's equation tells optical designers how to shape glass to get a desired focal length. Convex surfaces facing the light have positive radius; a symmetric biconvex lens has R₁ = −R₂.

### How to use the Lens Maker's Equation Calculator

- **Radius of curvature R₁**
- **Radius of curvature R₂**
- **Lens thickness d**
- **Refractive index n**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Enter both radii with sign (positive when the centre of curvature is beyond the surface), the centre thickness and the index of the glass. Use a very large radius for a flat surface.

### Inputs explained

FieldWhat to enterRadius of curvature R₁Units: mm, cm, m, in, µmRadius of curvature R₂Units: mm, cm, m, in, µmLens thickness dUnits: mm, cm, m, in, µmRefractive index nA number

### What each result means

- **Focal length f** = 1÷(([Refractive index n] - 1)×(1÷[Radius of curvature R₁] - 1÷[Radius of curvature R₂] + ([Refractive index n] - 1)×[Lens thickness d]÷([Refractive index n]×[Radius of curvature R₁]×[Radius of curvature R₂])))
- **Optical power** = 1÷[Focal length f]

### Example values

How the main result changes when **Radius of curvature R₁** changes and everything else stays at the example values above:

Radius of curvature R₁ (mm)Focal length f (mm)5065.24047583.743110097.5804125108.3193150116.8956200129.7357

## Worked example

Inputs — Radius of curvature R₁: 100 mm; Radius of curvature R₂: -100 mm; Lens thickness d: 5 mm; Refractive index n: 1.5168.

Results — **Focal length f = 97.58041 mm**; Optical power = 10.248 D.

## Key terms

- **Radius of curvature**: Radius of the sphere a lens surface is part of.

## FAQ

**What is the sign convention?**
R is positive if the centre of curvature is on the outgoing side of the surface.

**What does a negative focal length mean?**
A diverging lens.

**Can I ignore thickness?**
For thin lenses yes; the last term then vanishes.

**How does n affect f?**
Higher index glass gives a shorter focal length for the same shape.


## Sources

- [OpenStax – University Physics Volume 3](https://openstax.org/details/books/university-physics-volume-3)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)