Compute focal length from thickness and curvatures quickly. Include refractive indices, media, and units easily. Export results for reports, labs, and design checks today.
These sample values demonstrate typical glass in air.
| Case | R1 (mm) | R2 (mm) | d (mm) | n | n0 | EFL (mm) | Power (1/m) |
|---|---|---|---|---|---|---|---|
| Biconvex | 50.00 | -50.00 | 10.00 | 1.500 | 1.000 | 51.724 | 19.333333 |
| Plano-convex | 60.00 | ∞ | 8.00 | 1.520 | 1.000 | 115.385 | 8.666667 |
| Meniscus | 80.00 | 40.00 | 6.00 | 1.620 | 1.000 | -136.891 | -7.305093 |
This calculator uses the thick-lens lensmaker form with a consistent sign convention. Define nrel = n / n0.
Sign convention: Use a positive radius when the center of curvature lies to the right, in the direction light travels. Distances are positive to the right.
A thick lens has two curved surfaces separated by a real thickness, so its focal behavior depends on both curvatures, the center thickness, and the refractive indices of the lens and the surrounding medium. Unlike a thin lens, the principal planes shift, so vertex-to-focus distances can differ from the effective focal length. For paraxial rays, the calculator assumes small angles; it does not model aberrations, aspheric surfaces, or gradient-index profiles. It is ideal for first-pass sizing and sanity checking before detailed ray tracing later.
Radii are often 10–500 mm in small optics, while thickness may be 1–30 mm. Common crown glasses sit near n=1.50–1.53, flint glasses near n=1.60–1.75, and plastics around n=1.49. The surrounding medium is usually air (n0≈1.000) or water (n0≈1.333).
This page uses a “center to the right is positive” convention with light traveling left to right. A biconvex lens typically uses R1>0 and R2<0. If signs are flipped, the computed power can change sign, turning a converging design into a diverging one.
You get effective focal length (EFL), optical power (1/m), front focal length (FFL), back focal length (BFL), and principal plane offsets H1 and H2. The matrix method reports these values consistently, even when thickness is not negligible compared with focal length.
With R1=+50 mm, R2=−50 mm, d=10 mm, n=1.50 in air, EFL is about 50.8 mm and power is about 19.7 1/m. If thickness increases to 20 mm with the same radii and index, EFL becomes slightly longer, showing how thickness reduces power for the same curvatures.
Thick-lens modeling is important for camera lenses, magnifiers, LED collimators, and any element where d is more than roughly 5% of the focal length. It is also useful for immersion setups, because changing n0 alters power and shifts principal planes.
After calculating, download CSV for spreadsheets or PDF for lab notes and design reviews. The export captures inputs, EFL, power, focal distances, and principal plane locations in your chosen unit, making it easier to compare multiple lenses or track revisions over time reliably.
EFL is the focal length measured from the principal planes. BFL is the distance from the second surface vertex to the rear focal point. In thick lenses, those points are not the same location.
Enter the curved surface with the correct sign. For the flat surface, use a very large radius magnitude to approximate infinity. Keep light direction consistent, so “center to the right” stays positive.
Optical power depends on refractive index contrast. Increasing the surrounding index reduces contrast, so power drops and focal length increases. Immersion can also shift principal planes and alter FFL and BFL.
Yes. Choose inches in the unit selector and enter R1, R2, and thickness in inches. Outputs in the results section will be shown in the same unit, while power stays in 1/m.
Very small radii, near-zero curvature, or inconsistent signs can push C toward zero in the matrix, making focal length extremely large or undefined. Check units, avoid R=0, and confirm your geometry.
No. It is a paraxial model for first-order properties like focal length and principal plane shifts. Use full ray tracing for spherical aberration, coma, astigmatism, field curvature, and distortion.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.