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Math

Degrees to Radians Calculator.

Convert an angle from degrees to radians instantly.

Results update live as you type.
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Your inputs

How it works

  1. 1

    Enter the angle in degrees.

  2. 2

    Multiply the degree value by π (pi).

  3. 3

    Divide the result by 180.

  4. 4

    The result is the angle in radians.

degrees * pi / 180

Frequently asked questions

Why multiply by π and divide by 180?

Because 180° equals π radians, so the conversion factor is π/180.

Can I convert radians to degrees with this calculator?

No, this calculator only converts degrees to radians. Use the inverse formula (radians × 180/π) for the reverse.

What is the radian value of 360°?

360° equals 2π radians, approximately 6.2832.

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How it works

Convert an angle from degrees to radians instantly.

  1. Enter the angle in degrees.
  2. Multiply the degree value by π (pi).
  3. Divide the result by 180.
  4. The result is the angle in radians.

Formulas

The math behind this calculator, written out so you can verify the result.

Degrees to Radians

radians = degrees × (π / 180)

Multiply the angle in degrees by π divided by 180 to get the angle in radians.

Example:

Input: degrees = 45

Calculation: 45 × (π / 180)

Result: ≈ 0.7854 rad

Real-world use cases

Where this calculation shows up in everyday life.

Trigonometry

Convert angles to radians for sine, cosine, and tangent calculations in math and physics.

Example: sin(30°) = sin(π/6)

Programming

Many programming languages use radians for trigonometric functions, so convert degrees to radians.

Example: Math.sin(degrees * Math.PI / 180)

Engineering

Angular measurements in engineering often require radian units for rotational calculations.

Example: Angular velocity in rad/s

Tips and common mistakes

Tips

  • Remember: 180° = π radians, 90° = π/2, 360° = 2π.
  • Use the constant π ≈ 3.14159 for manual calculations.
  • For quick mental conversion, multiply degrees by 0.0174533 (π/180).
  • Check your result: 1 radian ≈ 57.2958°.

Common Mistakes to Avoid

  • Forgetting to divide by 180, which gives degrees × π instead of radians.
  • Using 3.14 instead of π, leading to slight inaccuracies.
  • Confusing radians with degrees in trigonometric functions.

Assumptions and limitations

  • Use the stated inputs and units.
  • Results are estimates for planning and education.
  • Check measurements and source data before making an important decision.