Index of Refraction Calculator
Calculate the refractive index of any optical medium. Choose from two methods: compute n directly from the speed of light in the medium (n = c/v), or apply Snell's law to find the unknown refractive index from the angles of incidence and refraction.
Calculation method
m/s
Ratio of the speed of light in vacuum to the speed of light in the medium
- 1
n = c ÷ v
299,792,458 ÷ 225,000,000 = 1.3324Speed of light in vacuum divided by speed in medium
How does this calculator work?
The index of refraction n = c/v (c = 299,792,458 m/s). Higher n → slower light, shorter wavelength, greater bending. Use Snell's law (n₁ sin θ₁ = n₂ sin θ₂) to find n from angles. Common values: air ≈ 1.0, water ≈ 1.33, glass ≈ 1.5, diamond ≈ 2.42.
Formula
How this is calculated
The index of refraction (also called refractive index) of a medium is defined as n = c / v, where c = 299,792,458 m/s is the speed of light in vacuum and v is the speed of light in the medium. Because electromagnetic waves travel more slowly in any material than in vacuum, n is always ≥ 1 for real materials (vacuum: n = 1 exactly; air: ≈ 1.0003; water: ≈ 1.33; ordinary glass: ≈ 1.5; diamond: ≈ 2.42). A higher n means light travels more slowly and bends more when entering the medium.
The second mode uses Snell's law: n₁ sin θ₁ = n₂ sin θ₂, where θ₁ is the angle of incidence (measured from the surface normal in medium 1) and θ₂ is the angle of refraction (in medium 2). Knowing n₁, θ₁ and θ₂ lets you solve for n₂ = n₁ sin θ₁ / sin θ₂. This is exactly how many laboratory measurements of refractive index are performed — shine light at a known angle, measure where it bends.
The wavelength of light in the medium is λ = λ₀ / n, where λ₀ is the vacuum wavelength. So a higher refractive index compresses the wavelength proportionally. Note that the refractive index varies with wavelength (dispersion), so the value depends on the colour of light; the figures above are typical values for visible light near 589 nm (sodium yellow line).
Frequently asked questions
Vacuum: 1.000 (exact). Air: ≈ 1.0003 (often approximated as 1.000). Water: ≈ 1.333 at 20°C. Ordinary crown glass: ≈ 1.52. Diamond: ≈ 2.42. These values are for visible light near 589 nm and vary slightly with wavelength (dispersion).
When light travels from a denser medium (higher n) to a less dense medium (lower n) at an angle of incidence greater than the critical angle θ_c = arcsin(n₂/n₁), it cannot refract out — it is completely reflected. This is total internal reflection. Optical fibers rely on this principle to guide light.
In a material, photons are absorbed and re-emitted by atoms, effectively slowing the wave front. The denser the optical medium, the more interactions occur per unit length. The refractive index n = c/v directly encodes this slowdown: n = 2 means light travels at half the vacuum speed.
Also known as
TG we-Calculate Editorial Team. (2026). Index of Refraction Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/index-of-refraction-calculator
TG we-Calculate Editorial Team. "Index of Refraction Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/index-of-refraction-calculator.
TG we-Calculate Editorial Team, "Index of Refraction Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/index-of-refraction-calculator
@misc{wecalculate_index_of_refraction_calculator, title = {Index of Refraction Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/index-of-refraction-calculator}}, year = {2026}, note = {TG we-Calculate} }
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