Snell's Law Calculator

Snell's law relates the angles on each side of a boundary between two media: n1 x sin(theta1) = n2 x sin(theta2). Here n1 and n2 are the refractive indices and theta1 and theta2 are the angles measured from the normal, the line perpendicular to the surface. This calculator rearranges it to solve theta2 from your n1, n2 and theta1.

It measures how much a medium slows light relative to a vacuum, which is exactly 1. A vacuum is 1, air is roughly 1.0003 and usually rounded to 1.00, water is about 1.33 and ordinary crown glass is near 1.50. A higher index bends light more strongly and slows it further.

A critical angle only exists when light moves from a denser medium into a rarer one, that is when n1 is greater than n2. The tool computes it as asin(n2 / n1). Water to air gives asin(1.0 / 1.33), about 48.7535 degrees. When n1 is less than or equal to n2 the result card shows none, because refraction always succeeds.

When the incident angle exceeds the critical angle, Snell's law would need sin(theta2) greater than 1, which is impossible, so no light refracts out and all of it reflects back inside the denser medium. The tool detects this and shows a Total internal reflection notice instead of a refracted angle. This effect is what guides light along fiber optic cables.

Going from air (about 1.00) into glass (about 1.50) means n1 is less than n2, so light always crosses the boundary and bends toward the normal. A critical angle needs the reverse arrangement, a denser starting medium, so the tool correctly reports none for that direction.

Enter the angle of incidence, measured between the incoming ray and the surface normal rather than the surface itself. A ray hitting the surface straight on is 0 degrees, and a grazing ray approaches 90 degrees. The calculator accepts any value from 0 to 90 degrees.

The on-page form solves the refracted angle from an angle of incidence. The underlying engine can also solve the incident angle when an angle of refraction is supplied to the API, but the form is set up for the common forward direction. Swap the n1 and n2 values to model the reverse boundary if you need it.

The engine works in double precision and rounds the internal result to six decimal places, and the display keeps six significant figures. Real accuracy is limited by your index values, which vary slightly with the light's wavelength and the material's temperature, so treat published indices as typical rather than exact.

No. The calculation runs entirely in your browser with plain arithmetic, so your indices and angles never leave your device and there is no account or server call involved.