Calculate the focal length of a lens based on its material and curvature.
Lens Properties
n
mm
mm
mm
Focal Results
Enter radii and index to calculate focal length
About this calculator
Quick Reference
fFocal length
nRefractive index
R₁/R₂Radii of curvature
Diopter1 / f (in meters)
Overview
The lensmaker's equation relates the focal length of a lens to the refractive index of its material and the radii of curvature of its two surfaces. It is fundamental for designing optical systems like glasses, cameras, and telescopes.
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Pro Tips
For a thin lens, you can ignore the thickness (d=0).
Sign Convention: Convex surfaces have positive R, concave surfaces have negative R.
BK7 glass has a refractive index of approx. 1.517.
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Fun Facts
"Wait, did you know that the same formula applies to your eye? However, your eye changes its 'focal length' by using muscles to actually change the radius of the lens, rather than replacing it!"
"Early telescope lenses were made by hand-grinding glass for weeks to perfectly match the predicted radii of curvature."
"If you put a glass lens underwater, its focal length changes significantly because the refractive index is now relative to water (n≈1.33) instead of air (n≈1.0)."
