Lens Focal Length Calculator
Compute the focal length of any thick or thin lens from its refractive index, surface curvatures, and center thickness using the lensmaker's equation. Essential for optical designers, physics students, and DIY telescope builders.
About this calculator
The lensmaker's equation relates a lens's physical geometry to its optical power. For a thick lens immersed in air the full formula is: 1/f = (n − 1) × [(1/R₁) − (1/R₂) + (n − 1) × t / (n × R₁ × R₂)], where n is the refractive index of the lens material, R₁ is the radius of curvature of the first surface, R₂ is the radius of the second surface, and t is the center thickness. A positive radius means the surface curves away from incoming light; sign conventions follow the standard Cartesian system. For a thin lens (t ≈ 0) the thickness term vanishes, simplifying to 1/f = (n − 1)(1/R₁ − 1/R₂). A shorter focal length means a more powerful, more strongly curved lens. This calculator handles both converging (f > 0) and diverging (f < 0) lenses automatically.
How to use
Suppose you are grinding a biconvex glass lens with n = 1.5, R₁ = +10 cm, R₂ = −10 cm, and center thickness t = 0.5 cm. Plug into the formula: 1/f = (1.5 − 1) × [(1/10) − (1/−10) + (1.5 − 1) × 0.5 / (1.5 × 10 × −10)]. Step 1: (0.5) × [0.1 + 0.1] = 0.5 × 0.2 = 0.1. Step 2: thickness term = 0.5 × 0.5 / (1.5 × −100) = 0.25 / −150 ≈ −0.00167. Step 3: 1/f = 0.1 − 0.00167 ≈ 0.0983, so f ≈ 10.17 cm. Enter the same values here to confirm instantly.
Frequently asked questions
What does a negative focal length mean in the lensmaker's equation?
A negative focal length indicates a diverging lens — one that spreads parallel light rays outward rather than focusing them to a point. Concave lenses and plano-concave lenses typically produce negative focal lengths. In optical design, diverging lenses are used to correct nearsightedness and to expand laser beams. The sign of f follows directly from the signs you assign to R₁ and R₂ using the Cartesian sign convention.
How does lens thickness affect the calculated focal length?
For thin lenses the thickness term (n − 1)t / (n × R₁ × R₂) is negligible, but for thick lenses — such as those used in high-power microscope objectives or camera lenses — it introduces a measurable correction. Thicker glass shifts the principal planes further apart, effectively shortening the back focal distance relative to the thin-lens approximation. Ignoring thickness when it is significant can lead to focusing errors of several percent. This calculator includes the full thick-lens formula so the result remains accurate regardless of t.
What refractive index value should I use for common lens materials?
Crown glass (BK7) has n ≈ 1.52, flint glass ranges from 1.60 to 1.90, fused silica is about 1.46, and acrylic (PMMA) is roughly 1.49. These values are wavelength-dependent — a phenomenon called dispersion — so for precision work you should use the refractive index at your specific wavelength of interest (e.g., n_d at 589 nm for visible light). Many optical glass datasheets list Sellmeier coefficients that let you calculate n at any wavelength.