Snell's Law
Refraction angle and critical angle with a ray diagram
About this calculator
The Snell's Law Calculator solves n₁·sin(θ₁) = n₂·sin(θ₂) for the refraction angle when light crosses the boundary between two media, with angles measured from the normal. When light passes into a less dense medium it also reports the critical angle θc = arcsin(n₂/n₁), and correctly detects total internal reflection when the incidence angle exceeds it. Indices must be positive and the incidence angle between 0° and 90°.
How to use the Snell's Law calculator
- Enter the quantities you know, using the units shown on each field.
- Read the computed results — they update instantly as you type.
- Use the visual explanation to see how the quantities relate.
- Copy the page URL to share the exact calculation.
Common examples
- Air to glass (n₁ = 1, n₂ = 1.5) at 30° → refraction angle ≈ 19.47°, bent toward the normal
- Water to air (n₁ = 1.33, n₂ = 1) at 45° → refracts at ≈ 70.13°; critical angle ≈ 48.75°
- Glass to air (n₁ = 1.5) at 60° → total internal reflection (critical angle ≈ 41.81°)
- Air to water (n₂ = 1.33) at 60° → refraction angle ≈ 40.63°
Frequently asked questions
How does the Snell's Law calculator work?
Enter the known quantities and the calculator applies the governing physical law or scientific formula to find the unknowns, stating the equation it used and the units of every result. Computations run at high precision.
When would I use the Snell's Law calculator?
It suits physics and chemistry homework, lab work, engineering estimates, and any time you want to explore how changing one quantity affects the others in a well-defined scientific relationship.
How accurate are the results?
The formula itself is evaluated at 30 significant digits of precision. Keep in mind that idealized models — such as neglecting friction, air resistance or measurement error — bound the real-world accuracy more than the arithmetic does.
Can I share a specific calculation with someone else?
Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same calculation for whoever clicks it.