Focal Length Calculator – Lensmaker's Equation

Calculate the focal length of a lens using the lensmaker's equation. Enter refractive index and radii of curvature.

Lens Type

Refractive Index (n)

Radius R₁ (m)

Radius R₂ (m)

Use positive for convex surface, negative for concave

How to Calculate Lens Focal Length

Select Lens Type

Choose from biconvex, biconcave, plano-convex/concave, or meniscus lens configurations.

Enter Lens Parameters

Input the refractive index and radii of curvature for both lens surfaces.

Get Focal Length Results

Receive the focal length in meters and optical power in diopters instantly.

Key Features of This Lens Calculator

Lensmaker's Equation

Uses the complete lensmaker's formula: 1/f = (n-1)(1/R₁ - 1/R₂) for accurate calculations.

Multiple Lens Types

Supports converging (biconvex) and diverging (biconcave) lenses with proper sign conventions.

Optical Power Calculation

Automatically converts focal length to diopters (D = 1/f) for optometry applications.

Sign Convention Guide

Clear instructions on positive/negative radius values for convex and concave surfaces.

Common Lens Materials and Refractive Indices

Material	Refractive Index (n)	Common Uses
Crown Glass	1.52	Standard eyeglasses, camera lenses
Flint Glass	1.62-1.75	High-index eyeglasses
Polycarbonate	1.59	Safety glasses, sports eyewear
CR-39 Plastic	1.50	Standard plastic lenses
Sapphire	1.77	Specialty optics, watches

Frequently Asked Questions

What is the lensmaker's equation?

The lensmaker's equation relates focal length to the lens material and shape: 1/f = (n-1)(1/R₁ - 1/R₂), where n is refractive index and R₁, R₂ are the radii of curvature of both surfaces.

What does a negative focal length mean?

A negative focal length indicates a diverging (concave) lens that spreads light rays apart. Positive focal length means a converging (convex) lens that focuses light to a point.

How do I know if R₁ and R₂ are positive or negative?

By convention: if the center of curvature is on the opposite side from incoming light, the radius is positive. For a biconvex lens, R₁ is positive and R₂ is negative.

What is optical power in diopters?

Optical power (P) in diopters equals 1/f where f is in meters. A 0.5m focal length lens has 2 diopters of power. Optometrists use diopters to prescribe corrective lenses.

Can this calculator handle thick lenses?

This calculator uses the thin lens approximation, which is accurate when lens thickness is much smaller than the radii of curvature. For thick lenses, additional corrections are needed.

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