Focal Length Calculator
Use our free online focal length calculator to instantly compute the focal length of any lens. This focal length calculator uses the lens maker's equation to determine focal length from refractive index and surface radii. Perfect for students, educators, and optical engineers who need a reliable focal length calculator for their work.
Use Calculator Now ↓Table of Contents
1. Focal Length Calculator Tool
Our focal length calculator provides instant results for lens focal length calculations. Simply enter the refractive index and radii of curvature below. This focal length calculator automatically applies the lens maker's formula to compute the result.
Focal Length Calculator
Enter refractive index (n), R₁, and R₂ to calculate focal length
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
2. What is Focal Length?
Focal length is the distance from the center of a lens to its focal point, where parallel light rays converge after passing through the lens. Understanding focal length is essential for using any focal length calculator effectively. When you use a focal length calculator, you're determining this critical optical parameter.
A positive focal length (calculated by the focal length calculator) indicates a converging lens that brings light rays together. A negative focal length from the focal length calculator indicates a diverging lens that spreads light rays apart. Our focal length calculator displays both the numerical result and the lens type.
✓ Positive Focal Length
Converging (convex) lens - focuses light to a real point
✗ Negative Focal Length
Diverging (concave) lens - spreads light from a virtual point
3. The Focal Length Formula
The focal length calculator uses the lens maker's equation to compute focal length. This formula, built into our focal length calculator, relates the focal length to the lens material and geometry:
Lens Maker's Equation (Focal Length Calculator Formula)
1/f = (n-1)(1/R₁ - 1/R₂)
Variables
- f = Focal length (meters)
- n = Refractive index
- R₁ = First surface radius
- R₂ = Second surface radius
Calculator Derivation
The focal length calculator rearranges this formula to solve for f directly, giving you instant focal length results.
4. How to Use the Focal Length Calculator
Follow these steps to use our focal length calculator effectively:
Enter refractive index (n)
Input the refractive index of your lens material into the focal length calculator. Common values: glass (1.5), crown glass (1.52), flint glass (1.6).
Enter first radius (R₁)
Input the radius of curvature of the first surface in meters. The focal length calculator accepts positive values for convex surfaces.
Enter second radius (R₂)
Input the radius of curvature of the second surface. For a typical biconvex lens, enter a negative value in the focal length calculator.
Click Calculate
Press the calculate button and the focal length calculator will instantly display your result with lens type indication.
5. Sign Convention for Focal Length Calculator
The focal length calculator uses the standard Cartesian sign convention. Understanding this convention is crucial for getting accurate results from the focal length calculator:
Radius Signs
- R > 0: Center of curvature on right side
- R < 0: Center of curvature on left side
- R = ∞: Flat surface (plano lens)
Common Lens Types
- Biconvex: R₁ > 0, R₂ < 0
- Biconcave: R₁ < 0, R₂ > 0
- Plano-convex: R₁ > 0, R₂ = ∞
6. Focal Length Calculator Examples
Example 1: Biconvex Lens Focal Length Calculator
Input to focal length calculator:
- • Refractive index n = 1.5
- • First surface R₁ = 0.1 m (convex)
- • Second surface R₂ = -0.1 m (convex on right)
Focal length calculator computation:
1/f = (1.5 - 1)(1/0.1 - 1/(-0.1))
1/f = 0.5 × (10 + 10) = 10
Focal length calculator result: f = 0.1 m = 10 cm
Example 2: Plano-Convex Lens Focal Length Calculator
Input to focal length calculator:
- • Refractive index n = 1.6
- • First surface R₁ = 0.2 m (convex)
- • Second surface R₂ = ∞ (flat)
Focal length calculator computation:
1/f = (1.6 - 1)(1/0.2 - 0)
1/f = 0.6 × 5 = 3
Focal length calculator result: f = 0.33 m = 33 cm
7. Applications of the Focal Length Calculator
The focal length calculator is an essential tool for many optical applications. Here's where professionals use a focal length calculator:
Camera Lens Design
Photographers and lens designers use the focal length calculator to determine lens specifications for desired zoom and field of view.
Eyeglass Prescription
Optometrists use focal length calculator principles to prescribe corrective lenses with the right optical power.
Microscope Objectives
The focal length calculator helps design high-magnification microscope lenses for scientific research.
Physics Education
Students use the focal length calculator to verify theoretical calculations and understand optical principles.
8. Focal Length Calculator FAQ
What is a focal length calculator?
A focal length calculator is an online tool that computes the focal length of a lens using the lens maker's equation. Our focal length calculator takes refractive index and radii of curvature as inputs and instantly calculates the focal length.
How accurate is this focal length calculator?
This focal length calculator provides highly accurate results for thin lenses. The focal length calculator uses the standard lens maker's formula, which is valid when lens thickness is much smaller than the radii of curvature.
What units does the focal length calculator use?
The focal length calculator uses meters for all length measurements. Enter radii in meters, and the focal length calculator will output focal length in meters. You can convert the focal length calculator result to other units as needed.
Can I use the focal length calculator for thick lenses?
This focal length calculator is designed for thin lenses. For thick lenses where lens thickness matters, use our Thick Lens Calculator which includes thickness correction in the focal length calculation.