Snell's Law Calculator
Calculate the angle of refraction when light passes between media with different indices of refraction. Foundation of geometric optics.
This free online snell's law calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.
How to Use This Calculator
Enter your input values
Fill in all required input fields for the Snell's Law Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.
Review your inputs
Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.
Read the results
The Snell's Law Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.
Explore parameter sensitivity
Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.
Formula Reference
Snell's Law Calculator Formula
See calculator inputs for the governing equation
Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.
When to Use This Calculator
- •Use the Snell's Law Calculator when you need accurate results quickly without the risk of manual computation errors or unit conversion mistakes.
- •Use it to verify calculations made by hand or in spreadsheets — an independent check can catch errors before they lead to costly decisions.
- •Use it to explore how changing input parameters affects the output — a quick way to develop intuition and identify the most influential variables.
- •Use it when collaborating with others to ensure everyone is working from the same numbers and applying the same assumptions.
About This Calculator
The Snell's Law Calculator is a free, browser-based calculation tool for engineers, students, and technical professionals. Calculate the angle of refraction when light passes between media with different indices of refraction. Foundation of geometric optics. It implements standard formulas and supports both metric (SI) and imperial unit systems with automatic unit conversion. All calculations are performed instantly in your browser with no data sent to a server. Use this calculator as a quick reference and sanity-check tool during design, analysis, and learning. Always verify results against primary engineering references and applicable standards for any safety-critical application.
About Snell's Law Calculator
The Snell's Law Calculator determines the angle at which light bends when passing from one medium to another. First described by Ibn Sahl in 984 and rediscovered by Willebrord Snellius in 1621, Snell's law is the foundation of geometric optics. It explains why a straw appears bent in water, how lenses focus light, and how rainbows form.
The Math Behind It
Formula Reference
Snell's Law
n₁ sin(θ₁) = n₂ sin(θ₂)
Variables: angles from normal
Worked Examples
Example 1: Air to Water
Light at 30° entering water
Bends to 22.08°.
Example 2: Water to Air
Light at 40° exiting water
Bends away from normal to 58.75°.
Common Mistakes & Tips
- !Measuring angles from surface instead of from normal.
- !Forgetting total internal reflection occurs above critical angle.
- !Inconsistent degree/radian usage.
Related Concepts
Used in These Calculators
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Frequently Asked Questions
What is total internal reflection?
When light travels from dense to less dense medium at angle beyond critical, it reflects entirely. This is how fiber optics and diamonds sparkle.
Why does light bend?
Light travels at different speeds in different media. When hitting an interface at an angle, one side enters first and slows, causing the wavefront to tilt.