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Use this Snell's Law calculator to find refraction angles, incidence angles, and refractive indexes with degrees or radians.
The Snell's Law calculator finds how light bends between two media. It can find the angle of refraction, angle of incidence, or either refractive index. You can enter angles in degrees or radians. The tool also checks for total internal reflection. It suits students, teachers, optics work, and anyone studying light refraction. Use the calculator above to get a quick result without doing the trigonometry by hand.
A Snell's Law calculator uses Snell's law to study light at a boundary. The law links two refractive indexes with two light angles.
The calculator can find four values:
The result shows the value you asked the tool to find. Angle results are also converted to degrees for display. The tool formats numeric results to four decimal places.
The calculator starts with two key inputs: refractive indexes and light angles.
The refractive index tells how light behaves in a medium. The code includes common choices such as air, water, ice, glass, quartz, and diamond. You can also enter a custom value.
For angle calculations, the input angle must be from 0° up to, but not including, 90°. For refractive-index calculations, both angles must be above 0° and below 90°.
The tool supports degrees and radians. It converts degree values to radians before using the sine function. It then converts angle results back to degrees.
If the required sine value is above 1, no real refraction angle exists. The calculator flags this case as total internal reflection.
The main Snell's Law formula is:
n₁ × sin(θ₁) = n₂ × sin(θ₂)
Here:
To find the angle of refraction:
θ₂ = sin⁻¹[(n₁ × sin(θ₁)) ÷ n₂]
To find the angle of incidence:
θ₁ = sin⁻¹[(n₂ × sin(θ₂)) ÷ n₁]
To find the second refractive index:
n₂ = [n₁ × sin(θ₁)] ÷ sin(θ₂)
To find the first refractive index:
n₁ = [n₂ × sin(θ₂)] ÷ sin(θ₁)
The angles are measured from the normal, not from the surface.
Suppose light moves from vacuum into water.
Input values
n₁ = 1.000
n₂ = 1.333
θ₁ = 30°
Find θ₂.
Step 1: Use Snell's law
n₁ × sin(θ₁) = n₂ × sin(θ₂)
Step 2: Rearrange the formula
θ₂ = sin⁻¹[(n₁ × sin(θ₁)) ÷ n₂]
Step 3: Insert the values
θ₂ = sin⁻¹[(1.000 × sin(30°)) ÷ 1.333]
Step 4: Calculate
sin(30°) = 0.5
θ₂ = sin⁻¹(0.5 ÷ 1.333)
θ₂ = sin⁻¹(0.3750938)
Final result
θ₂ = 22.0301°
So, the refracted light travels at about 22.03° from the normal.
The calculator saves time when you need repeated refraction calculations. It also reduces manual sine and inverse-sine work.
It can help you compare how light bends in water, glass, acrylic, quartz, or other media. It can also help you check a hand calculation.
The built-in unit choice is useful when your source gives angles in radians.
The Snell's Law calculator makes refraction calculations simple. It can find angles and refractive indexes from the standard Snell's law equation. It also supports degrees and radians and checks for total internal reflection. For best results, enter the correct refractive indexes and measure every angle from the normal.
It is a tool that applies Snell's law to calculate a light angle or refractive index. It can solve for θ₁, θ₂, n₁, or n₂.
The main equation is n₁ × sin(θ₁) = n₂ × sin(θ₂). The calculator rearranges this equation based on the value you want to find.
The required inputs depend on the selected mode. You may need one or two refractive indexes and one or two angles. You also choose degrees or radians for angle input.
The calculator converts degree inputs to radians before its trigonometric calculation. It then converts calculated angles to degrees for the displayed result.
No. Snell's law uses angles measured from the normal line. The normal is perpendicular to the surface.
Yes. For angle calculations, the calculator checks the calculated sine value. If it is greater than 1, it flags total internal reflection.
The result depends on the values you enter and the refractive indexes you use. The calculator displays numeric results to four decimal places, so the shown value is rounded.