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Physics

Snell’s Law Calculator

n₁ sinθ₁ = n₂ sinθ₂. Free online Snell’s Law Calculator. Calculate snell’s law online — fast, accurate, mobile-friendly, no signup needed.

n₁·sin θ₁ = n₂·sin θ₂.
θ₂ (°)
19.471221

Derivation

  1. ├── 01Givenn1 = 1, theta1 = 30, n2 = 1.5
  2. ├── 02Formula180 × asin(t / n × sin(a × π / 180)) / π
  3. └── 03Compute θ₂ (°)19.471221
Did you know?

Willebrord Snellius derived n₁ sin θ₁ = n₂ sin θ₂ in 1621 — though ibn Sahl of Baghdad wrote down an equivalent relation around 984 CE.

§01What is

Understanding the Snell’s Law Calculator

The Snell’s Law Calculator computes θ₂ (°) from 3 inputs: n₁, θ₁ (°), n₂. n₁ sinθ₁ = n₂ sinθ₂.

Physics is the toolkit for turning a real-world observation into a prediction. Whether it’s a falling object, a moving car, or a stressed beam, the equations here are the same ones every engineer relies on. The Snell’s Law Calculator sits in that toolkit — it n₁ sinθ₁ = n₂ sinθ₂. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

180 × asin(t / n × sin(a × π / 180)) / π

Where

n1
n₁
theta1
θ₁ (°)
n2
n₂
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: n₁ = 1, θ₁ (°) = 30, n₂ = 1.5.

  1. 01Start by noting the input — n₁: 1.
  2. 02Start by noting the input — θ₁ (°): 30.
  3. 03Start by noting the input — n₂: 1.5.
  4. 04Substitute these values into the formula: 180 × asin(t / n × sin(a × π / 180)) / π
  5. 05Compute θ₂ (°): the calculator returns 19.4712.
  6. 06Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Snell’s Law Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

n₁ halved

n1 = 0.5 (from 1)

Keep every other input at its default and halve the n₁. See how θ₂ (°) responds.

  1. 01New n₁: 0.5
  2. 02Baseline θ₂ (°): 19.4712
  3. 03New θ₂ (°): 9.59407
  4. 04θ₂ (°) decreases by 50.7% → use this sensitivity to plan for real-world variation.
02 · PATTERN

n₁ doubled

n1 = 2 (from 1)

Keep every other input at its default and double the n₁. See how θ₂ (°) responds.

  1. 01New n₁: 2
  2. 02Baseline θ₂ (°): 19.4712
  3. 03New θ₂ (°): 41.8103
  4. 04θ₂ (°) increases by 114.7% → use this sensitivity to plan for real-world variation.
03 · PATTERN

θ₁ (°) halved

theta1 = 15 (from 30)

Keep every other input at its default and halve the θ₁ (°). See how θ₂ (°) responds.

  1. 01New θ₁ (°): 15
  2. 02Baseline θ₂ (°): 19.4712
  3. 03New θ₂ (°): 9.93588
  4. 04θ₂ (°) decreases by 49% → use this sensitivity to plan for real-world variation.
04 · PATTERN

θ₁ (°) doubled

theta1 = 60 (from 30)

Keep every other input at its default and double the θ₁ (°). See how θ₂ (°) responds.

  1. 01New θ₁ (°): 60
  2. 02Baseline θ₂ (°): 19.4712
  3. 03New θ₂ (°): 35.2644
  4. 04θ₂ (°) increases by 81.1% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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