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Degrees to Radians Calculator

Degrees to radians in one step.

Result

2.356194
0.7500π

How it is calculated

Enter an angle in degrees. A half turn is 180° and also π radians, so the conversion factor is π ÷ 180: rad = deg × π ÷ 180. The tool prints two results. The first is the value in radians as a decimal, with 6 decimal places. The second is the same angle written as a multiple of π, deg ÷ 180, shown as a decimal with 4 places and the π sign (for instance 0.7500π). It is a decimal multiple, not a reduced fraction such as 3π/4, and rounded values like 0.1667π stand for 1/6. Negative angles, angles above 360° and decimals are all accepted, and the radian value follows the same sign. An empty box gives no result.

Worked example

Convert 135°. Using the formula, 135 × π ÷ 180 = 135 ÷ 180 × π = 0.75 × π. In decimals, 0.75 × 3.141593 ≈ 2.356194, so the radian result is 2.356194. The tool also prints 0.7500π as the multiple of π, which you can read as the fraction 3/4, giving 3π/4. A check by size: 135° is a bit more than a right angle (π/2 ≈ 1.5708) and less than a straight angle (π ≈ 3.1416), and 2.356 fits between those.

Try this example →

Common mistakes

  • Reading the π column as radians. 0.7500π means 0.75 × π, which is 2.3562 radians; the plain number 0.75 would be a much smaller angle.
  • Using 360 instead of 180 in the factor. The ratio is π ÷ 180 (half turn); using π ÷ 360 gives half the correct radians.
  • Expecting fractions like π/3 from the second line. It shows 0.3333π, so you must recognise 1/3 yourself.
  • Typing a value already in radians, such as 1.5708. It will be treated as degrees and will give a tiny result of about 0.0274 radians.
  • Putting the angle in a calculator set to degrees mode after converting. Programming math functions expect radians, so use the first output, not the degree value.

About this calculator

The radian is the natural, dimensionless unit of angle used throughout mathematics: one radian is the angle subtended when the arc length along a circle equals its radius, and a full circle measures exactly 2π radians instead of 360 degrees. Converting is a straightforward ratio: radians = degrees × (π/180), so 90° becomes π/2, 180° becomes π, and 45° becomes π/4.

Nearly every trigonometric function in programming languages and calculus expects radians, not degrees — Math.sin() in JavaScript, sin() in Python’s math module, and the derivative rules for sine and cosine all assume radian input, which is why the conversion trips up so many students moving from geometry to calculus or code. Physicists and engineers also work natively in radians when dealing with angular velocity (rad/s) and angular acceleration, since the radian-based formulas for arc length and rotational motion come out cleanly without extra conversion factors.

Enter an angle in degrees and this calculator converts it to radians both as a decimal number and as a multiple of π rounded to four decimals (45° shows as 0.2500π), so you can compare the two forms. It does not write a fraction such as π/4; read 0.2500π as one quarter of π.

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