ONE FORMULA, ONE ANSWER
Snell Refraction Angle Calculator
Check a refracted ray angle measured from the interface normal. Choose input units and calculate one value within the stated conditions.
Inputs
Calculations run in this browser. Scientific notation such as 1.2e-3 is supported. Do not group thousands.
Result
Refraction angle from the normal θ₂
Enter values and select Calculate.
θ₂ = asin((n₁/n₂) sin θ₁)
Assumptions
Use n₁,n₂>0 and an incident angle from 0 to 90°. Assume nonabsorbing isotropic media. If the inverse-sine argument exceeds one, the result is total internal reflection with no propagating refraction angle.
Displayed values are floating-point approximations. Measurement uncertainty and design safety factors are not calculated.
Formula references and credits
NaNa Lab created the code, descriptions, icons and preview images. Text, figures and code from the linked references have not been reproduced.
Physical constants: NIST / CODATA 2022. The values of μ₀ and ε₀ are measured recommendations, not exact defining constants. Values and precision notes are in the source record.
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