Skip to main content
physics

Snell's Law Calculator

Calculate the angle of refraction when light passes between media with different indices of refraction. Foundation of geometric optics.

Reviewed by Christopher FloiedPublished Updated

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.

Results

Angle of Refraction

22.08°

How to Use This Calculator

1

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.

2

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.

3

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.

4

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.

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.

Related Calculators

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

When light travels between media with different refractive indices, its speed changes, causing it to bend. **Refractive indices**: - Air: 1.0003 - Water: 1.333 - Glass: 1.52 - Diamond: 2.42 **Key phenomena**: 1. **Bending**: Light slows entering denser medium and bends toward normal. 2. **Total internal reflection**: Above critical angle θ_c = arcsin(n₂/n₁), light reflects entirely. Fiber optics exploit this. 3. **Dispersion**: Refractive index varies with wavelength, causing prisms to split white light. 4. **Apparent depth**: Objects in water appear shallower than they are.

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

Step 1:sin(θ₂) = (1.00 × sin(30°)) / 1.33
Step 2:= 0.5/1.33 = 0.376
Step 3:θ₂ = arcsin(0.376) = 22.08°

Bends to 22.08°.

Example 2: Water to Air

Light at 40° exiting water

Step 1:sin(θ₂) = (1.33 × sin(40°)) / 1.00
Step 2:= 0.855
Step 3:θ₂ = 58.75°

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

Calculators that build on or apply the concepts from this page:

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.

Embed this calculator on your site

Paste this snippet into your blog, course page, or documentation to drop a live, interactive Snell's Law Calculator into your page.

Free to embed — includes a link back to MegaCalc.