Angle of Refraction Calculator

Written by Great Medico

Updated September 25, 2026 •2 min read

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Refraction is easy to picture and just as easy to miscalculate when angles or refractive indices are mixed up. Angle of Refraction Calculator turns the interface relation into a compact check of angle of refraction while keeping the optical assumptions visible.

What this calculator does

The Angle of Refraction Calculator centers on angle of refraction using the fields that are actually present here: Medium 1, Refractive index 1 (n₁), Medium 2, Refractive index 2 (n₂), Angle of incidence (θ₁). Rather than treating every box as an independent input, use the equation below to identify the driving quantities and read the remaining fields as derived or supporting values when appropriate.

How to use it

Enter n₁ and n₂, then provide either the incidence angle or the refraction angle. If both angle boxes contain values, the current calculation gives priority to θ₁ as the driving angle. Keep the angle unit selector consistent.

How the calculation works

Snell’s law links the two media through n₁ sin θ₁ = n₂ sin θ₂. When θ₁ is supplied, the page evaluates θ₂ = asin[(n₁/n₂) sin θ₁]; if θ₂ is the supplied angle, it rearranges the same relationship for θ₁. A real refracted angle exists only while the sine argument stays between −1 and 1.

Example

Take light going from air-like n₁ = 1.00 into glass-like n₂ = 1.50 at θ₁ = 30°. The ratio is (1/1.5) × sin 30° = 0.3333, so θ₂ ≈ 19.47°. The ray bends toward the normal because it enters the higher-index medium.

How to interpret the result

For Angle of Refraction Calculator, read angle of refraction in the context of the equation above. Read the result as an interface angle predicted by Snell’s law for the entered refractive indices. The strongest sanity check is direction: entering a higher-index second medium should normally bend the ray toward the normal, while a lower-index second medium can bend it away and may reach total internal reflection.

Limitations and notes

The medium selectors on this page do not currently supply preset refractive-index values; enter n₁ and n₂ explicitly. The equation also assumes isotropic media and a well-defined interface. If the calculated sine exceeds 1 in magnitude, the page correctly treats the case as total internal reflection rather than inventing a refraction angle.