Lens Maker Formula
The lens maker formula (also written as lens makers formula or lensmaker formula) relates the focal length of a thin lens to its refractive index and the radii of curvature of its two surfaces. Below you'll find the equation, a short definition, and links to our full guide, derivation, and free calculators.
The Lens Maker Formula (Equation)
1/f = (n − 1)(1/R₁ − 1/R₂)
- f = focal length
- n = refractive index of the lens material
- R₁, R₂ = radii of curvature of the first and second surfaces (use sign convention)
Guides & Derivation
Optics Lens Maker Formula — Complete Guide
Full explanation, sign convention, and worked examples.
Lens Maker Equation
Lens maker equation in depth with examples.
Lens Maker Formula Derivation
Mathematical derivation of the formula.
Focal Length Formula
Focal length formula and lens maker equation.
Radius of Curvature Formula
Rearrange the equation to solve R₁ or R₂.
Thin Lens vs Thick Lens
Compare the approximation against the thickness-corrected formula.
Free Calculators Using the Lens Maker Formula
Focal Length Calculator
Calculate f from n, R₁, and R₂.
Refractive Index Calculator
Calculate n from f, R₁, and R₂.
Index of Refraction Calculator
Alternate phrasing for the same n workflow.
Radius of Curvature Calculator
Choose the right workflow for R₁ or R₂.
Radius R₁ Calculator
Radius of curvature (first surface).
Radius R₂ Calculator
Radius of curvature (second surface).
Thick Lens Calculator
Focal length with thickness correction.
Convex Lens Calculator
Focal length for converging lenses.
Plano-Convex Lens Calculator
Focal length for one-flat-surface convex lenses.
Biconvex Lens Focal Length
Focused page for the symmetric convex case.