Snell's law: solve for index 1

Reviewed by the CalculatorHub team, edited by James Graham. Method from NIST / CODATA. Last verified 2026-06-22.

The Snell's law: solve for index 1 computes snell's law: solve for index 1 from the relation n1 = n2 sin theta2 / sin theta1. It takes 3 inputs (index 2, angle 2 in deg, angle 1 in deg) and returns the index 1. Physics students, lab and workshop technicians, and hobbyist builders and observers who need one quantity in a standard physical relationship worked out from figures they already have, whether those come from an instrument reading, a datasheet, or a published table. Enter your values below and the result updates instantly, and you can share a permalink that pre-fills the exact calculation. Convert every value to one consistent set of units before entering it (lengths and masses on the same scale rather than metres mixed with centimetres, absolute temperatures in kelvin, angles in whatever unit the field asks for), respect the sign conventions that carry meaning, such as direction for velocity, acceleration and force or which side of a lens a distance is measured on, and quote the result to no more precision than your least precise input supports. For example, with index 2 = 2, angle 2 = 30 deg, angle 1 = 30 deg, the index 1 works out to 2, and the worked example further down the page shows every step so you can follow the arithmetic and reproduce it by hand. Units and physical constants follow NIST / CODATA; the relation itself is a standard result of physics, and the figure above each result carries the date it was last verified. Each of these relationships describes an idealised situation, so a result holds only as far as that idealisation does, whether the assumption is a point mass, a uniform field, an ideal component, a single uniform medium, no losses to friction or drag, or a steady rate, and a real measurement can depart from it once conditions stop matching the model.