Critical Angle Calculator

It is the angle of incidence, measured from the normal, at which light grazes along the boundary between two media. Above this angle none of the light refracts across and all of it reflects back inside the denser medium. This calculator returns it from the two refractive indices you enter.

It uses the standard result from Snell's law, theta_c = asin(n2 / n1), where n1 is the denser medium and n2 is the rarer one. The angle is computed in radians and then converted to degrees, and both figures are shown rounded to six significant digits.

Total internal reflection only occurs when light moves from a slower, denser medium into a faster, rarer one. If n1 is equal to or smaller than n2 the ratio n2 / n1 is at least one, its arcsine is undefined or 90 degrees, and no true critical angle exists. The tool shows a notice in that case instead of a number.

It is the effect where light hitting a boundary beyond the critical angle bounces entirely back rather than passing through. Optical fibers trap light this way to carry signals over long distances, and it is also why a diamond sparkles and why the underside of a water surface can act like a mirror.

It gives the critical angle in degrees on one card and in radians on the other, so you can drop the value straight into a physics problem or a trigonometry function without converting it yourself.

Air is close to 1.00, water is about 1.33, common crown glass is near 1.50, and diamond is roughly 2.42. A larger n1 gives a smaller critical angle, which is why diamond, at about 24 degrees, traps light so readily and looks brilliant.

No. Refractive index depends slightly on wavelength, an effect called dispersion, but the tool treats each index as a single fixed number. For precise work at a specific color, look up the index for that wavelength and enter it directly.

No. The whole calculation runs in your browser with plain JavaScript and nothing is uploaded to a server, so the indices you try stay on your device.

You can use it to find the core to cladding critical angle, which is a good starting estimate. Full fiber design also involves the numerical aperture and acceptance angle, so treat this as one step rather than a complete optical model.