Snell's Law Calculator
Enter the two refractive indices and the angle of incidence to get the angle of refraction — and see exactly how light bends as it crosses from one medium into another.
Refraction angle in one step
Enter the refractive indices of both media and the angle of incidence and the calculator returns the angle of refraction, measured from the normal.
Measure from the normal
Both angles are measured from the normal — the line perpendicular to the surface — not from the surface itself.
What is Snell's law?
How light bends between media
Snell's law describes how a ray of light changes direction when it passes from one transparent medium into another — from air into water, or from water into glass. The bending happens because light travels at different speeds in different media, and how strongly each medium slows light is captured by its refractive index. This Snell's law calculator turns three numbers — the refractive index of the medium the light starts in, the refractive index of the medium it enters, and the angle of incidence — into the angle of refraction. It is the relationship behind why a straw looks bent in a glass of water, how lenses focus light, and how prisms split white light into colours.
Enter the refractive index of each medium and the angle of incidence to get the angle of refraction instantly.
Snell's law states that the refractive index of the first medium times the sine of the angle of incidence equals the refractive index of the second medium times the sine of the angle of refraction. Rearranging for the refraction angle gives an inverse sine.
θ₂ = arcsin(n₁ × sin θ₁ / n₂)Here n₁ and θ₁ belong to the medium the light starts in and n₂ and θ₂ to the medium it enters. When light moves into a denser medium (a higher index, like air into water), it bends toward the normal and the refraction angle is smaller than the incidence angle. Moving into a less dense medium, it bends away from the normal instead.
Suppose a ray of light travels from air (n₁ = 1) into water (n₂ = 1.33) at an angle of incidence of 30°.
Take the sine of the incidence angle
sin 30° = 0.5 — the starting point for the ratio.
Apply the index ratio
1 × 0.5 / 1.33 = 0.3759 — this is the sine of the refraction angle.
Take the inverse sine
arcsin(0.3759) = 22.0824° — the angle of refraction. The ray bends toward the normal because water is denser than air.
The angle of refraction tells you the new direction of the ray inside the second medium, measured from the normal. A smaller refraction angle than the incidence angle means the light bent toward the normal — it entered a denser, higher-index medium and slowed down, as when light passes from air into water or glass. A larger refraction angle means it bent away from the normal, entering a less dense medium. The two refractive indices alone set the ratio, so the same pair of media always bends a given incidence angle by the same amount. This is the principle that makes lenses, prisms, optical fibres, and your own eyeglasses work, and it is why objects under water appear shallower and shifted from where they really are.
The formula is exact for ideal media, but two situations need care.
Total internal reflection and measuring from the normal
When light travels into a less dense medium (n₁ greater than n₂) at a steep enough angle, the ratio n₁ × sin θ₁ / n₂ exceeds 1 and there is no refraction angle at all — the light is entirely reflected back, a phenomenon called total internal reflection that makes optical fibres possible. In that case the calculator returns no result. Remember too that both angles are measured from the normal, the line perpendicular to the surface, not from the surface itself.