Primary formula
n1 sin(theta1) = n2 sin(theta2); theta2 = arcsin((n1/n2) sin(theta1)).
Physics calculator
Snell's Law Calculator
Calculate refraction angle from two refractive indices and incident angle, including total internal reflection checks.
Last reviewed: July 21, 2026Physics formula engine v3.0.0
Physics calculator
Snell's Law Calculator
Enter values, select units and calculate locally. Results use SI internally and show rounded display values.
Decimal.js physics math
Mode
Find refracted angle from n1, n2 and incident angle.
Result and visual stay hidden until you choose Calculate.
Formula and assumptions
Input assumptions
Refractive indices are at least 1. Angles are converted to degrees internally for display. The boundary is smooth and the media are uniform.
Precision note
Physics calculators convert compatible inputs into SI units before calculating. Decimal.js is used for arithmetic where practical; trigonometric angle factors are rounded for display.
Physics calculation flow
Parse
Read labelled inputs, selected units and calculation mode from the calculator card.
Convert
Convert compatible values to SI base or derived units without calling external services.
Calculate
Apply the selected deterministic mechanics formula and validate against NaN, Infinity and invalid divisors.
Label
Display the result, supporting unit rows, formula steps, warnings and dynamic visual below the input card.
What Snell's Law Calculator does
Use this calculator for single-boundary refraction problems where light passes between two smooth media.
The calculator is deterministic and runs from manual inputs only. It is a physics formula tool, so it should not be confused with a unit converter that only changes labels after a value is already known.
Formula and variables
n1 sin(theta1) = n2 sin(theta2); theta2 = arcsin((n1/n2) sin(theta1)).
The calculator converts supported units into SI base or derived units for the actual calculation, then formats the result in the selected display unit.
- n1 is incident-medium refractive index
- n2 is refracted-medium refractive index
- theta1 is incident angle
- theta2 is refracted angle
Worked examples
Use the examples below to check expected order of operations and unit handling before applying the tool to your own values.
- n1 = 1.0, n2 = 1.5, theta1 = 30 deg gives theta2 about 19.4712 deg
- n1 = 1.5, n2 = 1.0, theta1 = 50 deg gives total internal reflection
- n1 = 1.5 and n2 = 1.0 gives critical angle about 41.8103 deg
Unit conversions
Length, time, mass, area, volume, speed, force, pressure, density, frequency, energy and power units reuse the central NexaCalc conversion registry. Acceleration, angle and spring-constant units use the same SI-first convention where applicable.
The displayed conversion rows are supporting context. They do not change the physical assumptions of the selected formula.
Common mistakes
Most errors come from mixing physical quantities that sound similar in everyday language or choosing a unit that belongs to a different dimension.
- Measuring angle from the surface instead of the normal.
- Ignoring total internal reflection.
- Using incompatible sign or angle units.
Assumptions and limitations
This page is intended for educational and planning calculations, not professional engineering certification.
This calculator uses idealized physics formulas and the input values you provide. Real systems may require additional effects such as friction, drag, rotation, deformation, losses or measurement uncertainty.
- Refractive indices are at least 1.
- Angles are converted to degrees internally for display.
- The boundary is smooth and the media are uniform.
- The calculator does not model polarization, dispersion, rough surfaces or multi-layer optics.
- Real refraction can depend on wavelength and material data.
Frequently asked questions
What is Snell's Law?
Use this calculator for single-boundary refraction problems where light passes between two smooth media. Refractive indices are at least 1.
How do I calculate the refracted angle?
Snell's Law Calculator uses n1 sin(theta1) = n2 sin(theta2); theta2 = arcsin((n1/n2) sin(theta1)). The result is calculated from the values and units entered in the form.
What do n1 and n2 mean?
Use this calculator for single-boundary refraction problems where light passes between two smooth media. Refractive indices are at least 1.
Why does light bend when entering another medium?
Use this calculator for single-boundary refraction problems where light passes between two smooth media. Refractive indices are at least 1.
What is total internal reflection?
Use this calculator for single-boundary refraction problems where light passes between two smooth media. Refractive indices are at least 1.
How is critical angle calculated?
Snell's Law Calculator uses n1 sin(theta1) = n2 sin(theta2); theta2 = arcsin((n1/n2) sin(theta1)). The result is calculated from the values and units entered in the form.
Why does arcsin fail in total internal reflection?
Use this calculator for single-boundary refraction problems where light passes between two smooth media. Refractive indices are at least 1.
What angle is measured from the normal?
Use this calculator for single-boundary refraction problems where light passes between two smooth media. Refractive indices are at least 1.
Can Snell's Law use degrees and radians?
Use this calculator for single-boundary refraction problems where light passes between two smooth media. Refractive indices are at least 1.
When should I use Refractive Index Calculator?
Use this calculator for single-boundary refraction problems where light passes between two smooth media. Refractive indices are at least 1.
References
- NIST Special Publication 811, Guide for the Use of the International System of Units. Relevance: SI unit symbols and derived-unit naming. Last verified: July 21, 2026. Source.
- BIPM, The International System of Units SI Brochure. Relevance: SI base and derived units used in mechanics, fluids, waves and optics. Last verified: July 21, 2026. Source.
- OpenStax University Physics Volume 1. Relevance: introductory formulas for motion, force, work, energy, momentum, fluids, waves and optics. Last verified: July 21, 2026. Source.
- NIST CODATA internationally recommended values. Relevance: physical constants for electricity, modern physics, gravitation and radiation formulas. Last verified: July 21, 2026. Source.
- OpenStax University Physics Volume 2. Relevance: electric circuits, capacitance, magnetic force and electromagnetic waves. Last verified: July 21, 2026. Source.
- OpenStax University Physics Volume 3. Relevance: photons, nuclear decay and blackbody radiation concepts. Last verified: July 21, 2026. Source.
Physics references verified for SI units, mechanics, fluids, waves, sound and optics formulas on July 21, 2026.
Educational disclaimer
This calculator provides mathematical results from the values, conventions and methods you enter. Verify important academic, engineering or professional work independently.