Numerical Aperture Calculator

About this calculator

This calculator finds a lens's numerical aperture, NA = n·sinθ, where n is the refractive index of the medium the lens is working in (air, oil, water) and θ is the half-angle of the cone of light entering or leaving the lens. NA determines two things at once: resolving power (a higher NA resolves finer detail, following the diffraction-limited resolution formula) and light-gathering ability, and it relates directly to the more familiar f-number used in photography via roughly N ≈ 1/(2·NA) — a higher NA corresponds to a lower f-number and a shallower depth of field.

Microscopists in biology and histology labs use NA ratings to choose objectives capable of resolving the fine structures they need to see; optical and fiber-optic engineers use it to design lenses and fibers that couple light efficiently at a required angle; and photographers use the underlying relationship to understand why wide-aperture (low f-number) lenses gather more light but produce a shallower depth of field. Enter the refractive index and half-angle to get the numerical aperture and equivalent f-number.