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Critical Angle Calculator

Calculate critical angle accurately with clear inputs, formulas, and supporting results.

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Critical Angle

Critical Angle Calculator

Critical angle—
Index ratio n₂/n₁—
Results are estimates for informational purposes. Verify critical calculations and project requirements independently.

Calculator Inputs and Outputs

Inputs

  • Higher refractive index — example: 1.5
  • Lower refractive index — example: 1

Results

  • Critical angle (°)
  • Index ratio n₂/n₁

Formula used

Critical angle = arcsin(n₂ ÷ n₁), for light traveling from the higher index to the lower index.

How to Use the Critical Angle Calculator

Enter the requested values, confirm the units and assumptions, then select Calculate Critical Angle. The default inputs provide a complete working example, and the supporting outputs help you verify the primary result.

Formula

Critical angle = arcsin(n₂ ÷ n₁), for light traveling from the higher index to the lower index.

Understanding the Results

The primary answer appears first, followed by useful supporting values. Calculations retain additional internal precision before displayed values are rounded.

Accuracy Tips

  • Use consistent units and measured values.
  • Review whether the assumptions match your situation.
  • For estimates, include realistic waste, fees, efficiency, or contingency values where provided.

Important Note

This calculator is for informational estimation. Verify critical financial, health, construction, scientific, tax, legal, or safety decisions with an appropriately qualified professional.

Calculation Standards

This tool uses documented formulas and high-precision internal values. Displayed results may be rounded for readability. Review the assumptions and verify important decisions with a qualified professional.

Read our calculation methodology