About the Snell's Law Calculator
When light passes from one clear material into another, such as from air into water, it changes direction. Snell's law gives the new angle from the refractive index of each material and the angle at which the light arrives, measured from the line at right angles to the surface. This calculator also tells you the critical angle and whether the light is totally reflected instead of passing through. Type the two materials and the angle of incidence and the angle of refraction appears at once, with a few related figures underneath, and you can copy the result with one tap. The sums run in your browser, so nothing you enter is uploaded.
Updated October 2026
How to use the Snell's Law Calculator
- 1Enter the two materials and the angle of incidence.
- 2Pick the units or options from the menus if the angle of refraction tool offers them.
- 3Read the angle of refraction in the large result box.
- 4Look at the extra rows for related figures.
- 5Press Copy result to keep the answer.
When you need the angle of refraction
Opticians, photographers and students use the law to explain lenses, prisms, rainbows, the apparent bending of a straw in a glass and the sparkle of diamonds. Fibre optic cables rely on total internal reflection to keep light inside the glass.
A higher refractive index means light travels more slowly in the material and bends more strongly towards the normal. Diamond, with an index of 2.42, has a critical angle of only 24 degrees, which is why light is trapped and bounces around inside it.
How the angle of refraction is worked out
n1 × sin(θ1) = n2 × sin(θ2). So the refracted angle is arcsin(n1 × sin θ1 ÷ n2). The critical angle, when n1 > n2, is arcsin(n2 ÷ n1). Light entering water (n = 1.333) from air at 30 degrees bends towards the normal to 22.03 degrees. Going from glass (n = 1.5) to air at 60 degrees, the light cannot leave: the critical angle is 41.81 degrees, so it is totally reflected. For water to air the critical angle is 48.61 degrees.
Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.
- Six materials plus custom
- Critical angle
- Total internal reflection flagged
Mistakes to avoid with angle of refraction
Angles are measured from the normal, the line at right angles to the surface, not from the surface itself. The angle of incidence must be below 90 degrees. The refractive index depends a little on the colour of the light, which is why prisms split white light.
On phone and computer
On a phone, type into the boxes one after another and read the angle of refraction underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the angle of refraction move. The snell's law calculator works the same on both. Bending light is one half of optics. See what a lens does with the Lens Equation Calculator, check angles with the Trigonometry Calculator, and find the wavelength with the Wavelength Calculator.
Features
- Angles from the normal
- Higher index bends more
- Colour changes the index slightly
- Clear messages when the angle of refraction inputs make no sense
- Copy the result with one tap
- Private: nothing is uploaded
Frequently asked questions
How do I calculate angle of refraction?
n1 × sin(θ1) = n2 × sin(θ2). So the refracted angle is arcsin(n1 × sin θ1 ÷ n2). The critical angle, when n1 > n2, is arcsin(n2 ÷ n1). Light entering water (n = 1.333) from air at 30 degrees bends towards the normal to 22.03 degrees. Going from glass (n = 1.5) to air at 60 degrees, the light cannot leave: the critical angle is 41.81 degrees, so it is totally reflected. For water to air the critical angle is 48.61 degrees.
What is the formula for angle of refraction?
n1 × sin(θ1) = n2 × sin(θ2). So the refracted angle is arcsin(n1 × sin θ1 ÷ n2). The critical angle, when n1 > n2, is arcsin(n2 ÷ n1). The snell's law calculator applies it exactly and rounds only the displayed answer to six significant figures.
What is total internal reflection?
When light in a denser material meets a thinner one at an angle above the critical angle, all of it is reflected back.
What is the refractive index of air?
About 1.0003, very close to the value of 1 for a vacuum.
Why does a straw look bent in water?
Light from the part under water bends as it leaves the water, so your eye sees the straw in a different place.
Is this snell's law calculator free and private?
Yes. It is free, needs no account and runs in your browser, so the numbers you type are not uploaded or stored.