Lens Maker Formula
Calculate any lens parameter with precision
Free online calculator for optics students, engineers, and enthusiasts
Quick Calculator
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Lens Maker Formula
Calculate focal length from lens parameters
Formula
1/f = (n-1)(1/R₁ - 1/R₂)
Typical: 1.5 (glass), 1.33 (water), 1.52 (crown glass)
Positive for convex, negative for concave
Positive for convex, negative for concave
Light Ray Visualization
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Understanding the Formula
Focal Length
meters (m)
The distance from the lens to the focal point where parallel rays converge (or appear to diverge from).
Refractive Index
dimensionless
A measure of how much light slows down when passing through the material compared to vacuum.
First Surface Radius
meters (m)
The radius of curvature of the first lens surface. Positive for convex, negative for concave.
Second Surface Radius
meters (m)
The radius of curvature of the second lens surface. Positive for convex, negative for concave.
Sign Convention
✓ Positive Radius (R > 0)
Convex surface (bulging outward toward the light source)
✗ Negative Radius (R < 0)
Concave surface (curving inward away from the light source)
Example Calculation
Given: n = 1.5, R₁ = 0.1 m, R₂ = -0.1 m
1/f = (1.5 - 1)(1/0.1 - 1/(-0.1))
1/f = 0.5 × (10 - (-10))
1/f = 0.5 × 20 = 10
f = 0.1 m (10 cm)
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Optics Formula
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How to Calculate
Step-by-step focal length calculation guide
Formula Derivation
Mathematical proof of the lens maker formula
Focal Length Formula
Complete guide to focal length formulas
Tutorial
Step-by-step guide to the lens maker formula
Examples
Common lens types with calculations
Glossary
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Materials
Refractive index database