Lens Maker Equation Calculator

Lens Maker Equation Calculator | Online Free Tool | Elysia Tools

Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category: Science & Education
Input types: number, select
Output type: text
Sample coverage: 4
API ready: Yes

Overview

The Lens Maker Equation Calculator determines the focal length, optical power in diopters, and converging or diverging behavior of a thin optical lens in air using the standard lens maker's formula 1/f = (n−1)(1/R₁ − 1/R₂).

When to use

Designing or verifying thin optical elements like biconvex, biconcave, plano-convex, or meniscus lenses.
Converting optical surface radii of curvature and glass refractive indices into diopters and focal length.
Solving physics and optics problem sets involving thin lens curvature sign conventions.

How it works

1Enter the refractive index (n) of the lens material relative to air.
2Specify the first radius of curvature (R₁) and second radius of curvature (R₂), entering 0 to represent a flat (plano) surface.
3Select your preferred length unit (millimeters, centimeters, or meters).
4The tool computes the curvature difference, optical power in diopters, focal length in the selected unit and meters, and lens classification.

Use cases

Optics students verifying textbook calculations for symmetric and asymmetric thin lenses.
Optical lab technicians checking diopter power and focal length requirements for stock lenses.
Physics educators demonstrating how changing surface curvature affects real and virtual focal points.

Examples

1. Symmetric Biconvex Glass Lens

Physics Student

Background

Analyzing standard laboratory Crown glass optics for an introductory lab assignment.

Problem

Calculate the focal length and diopter rating of a symmetric biconvex lens with 100 mm curvature radii.

How to use

Set refractiveIndex to 1.5, radius1 to 100, radius2 to -100, and lengthUnit to mm.

{
  "refractiveIndex": 1.5,
  "radius1": 100,
  "radius2": -100,
  "lengthUnit": "mm"
}

Outcome

Yields a focal length of 100 mm (0.1 m), an optical power of +10.0 diopters, and classifies the lens as converging.

2. Plano-Concave Diverging Lens

Optics Lab Assistant

Background

Selecting beam-expansion optics with a flat rear surface to minimize alignment complexity.

Problem

Determine the resulting focal properties of a lens with a concave front radius of -150 mm and a flat back surface.

How to use

Set refractiveIndex to 1.5, radius1 to -150, radius2 to 0, and lengthUnit to mm.

FAQ

How do I specify a flat or plano lens surface?

Enter 0 for either R₁ or R₂; the calculator interprets zero as an infinite radius of curvature.

What sign convention does this calculator use for surface radii?

A radius is positive if its center of curvature lies on the transmission (outgoing) side and negative if it lies on the incident (incoming) side.

What optical medium is assumed around the lens?

The calculation assumes the thin lens is surrounded by air with an ambient refractive index of 1.0.

How is optical power in diopters calculated?

Optical power is calculated as the inverse of the focal length expressed in meters (P = 1/f_meters).

How does the tool distinguish between converging and diverging lenses?

Lenses with a positive focal length (and positive diopters) are classified as converging, while negative values indicate diverging lenses.

{
  "refractiveIndex": 1.5,
  "radius1": -150,
  "radius2": 0,
  "lengthUnit": "mm"
}

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Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Overview

When to use

How it works

Use cases

Examples

1. Symmetric Biconvex Glass Lens

2. Plano-Concave Diverging Lens

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