Degrees to Radians Converter
Convert degrees to radians in one step. Enter an angle in degrees, positive or negative, and get radians with the formula, worked examples and a table of common angles below.
Radians = Degrees × π ÷ 180
Degrees to Radians Formula
A half turn is 180 degrees, which equals π radians, so multiplying the degrees by π and dividing by 180 gives radians. To convert radians to degrees, multiply by 180 and divide by π. The result is shown as a decimal; π ≈ 3.14159265358979 is used at full precision.
About Degrees and Radians
A degree (°) splits a full circle into 360 equal parts. It is the unit most people meet first, on protractors, maps, compasses and construction drawings. A radian (rad) is defined by the circle itself: one radian is the angle at the centre that cuts off an arc exactly as long as the radius. A full circle is therefore 2π radians, about 6.283185. Because radians connect angle directly to arc length, they are the standard unit in calculus, physics and most programming languages.
How to Convert Degrees to Radians
- Enter the angle in degrees. Decimals such as 22.5 work, and so do negative angles, which represent rotation in the opposite direction.
- The answer in radians appears instantly, or press Convert Now. Gradians and full turns are shown as side values.
- Use Swap Units to convert radians to degrees, Copy Result to copy the answer, or Clear to start again.
By hand: multiply the degrees by 0.0174533 (which is π ÷ 180). To keep an exact answer, write it as a fraction of π: 60° is 60/180 of π, which simplifies to π/3 (≈ 1.04719755 rad).
Practical Examples
- Right angle: 90° × π ÷ 180 = π/2 ≈ 1.57079633 rad.
- Straight line: 180° = π ≈ 3.14159265 rad.
- Equilateral triangle corner: 60° = 1.04719755 rad (π/3).
- Small tilt: 5° = 0.08726646 rad.
- Negative angle (clockwise): −45° = -0.78539816 rad (−π/4).
Degrees to Radians – Common Values
Quick reference for frequently used conversions
| Degrees | Radians (decimal) | Radians (in π) |
|---|---|---|
| 0° | 0 rad | 0 rad |
| 15° | 0.26179939 rad | π/12 rad |
| 30° | 0.52359878 rad | π/6 rad |
| 45° | 0.78539816 rad | π/4 rad |
| 60° | 1.04719755 rad | π/3 rad |
| 90° | 1.57079633 rad | π/2 rad |
| 120° | 2.0943951 rad | 2π/3 rad |
| 135° | 2.35619449 rad | 3π/4 rad |
| 150° | 2.61799388 rad | 5π/6 rad |
| 180° | 3.14159265 rad | π rad |
| 225° | 3.92699082 rad | 5π/4 rad |
| 270° | 4.71238898 rad | 3π/2 rad |
| 360° | 6.28318531 rad | 2π rad |
| -90° | -1.57079633 rad | −π/2 rad |
Where and Why This Conversion Is Used
People describe angles in degrees, but formulas and software usually expect radians, so this conversion is a frequent first step before any calculation.
- Trigonometry and calculus: sin, cos and tan in most calculators and spreadsheets can work in radians, and derivatives of trigonometric functions only take their simple form in radians.
- Programming and graphics: JavaScript, Python and C math libraries take radians, while design tools and CSS often show degrees.
- Physics and engineering: angular velocity, frequency and wave phase are expressed in radians.
- Surveying and navigation: bearings and slopes read in degrees are converted for computation.
- Robotics and CAD: joint limits and rotations are often entered in degrees but processed in radians.
For the reverse direction see the Radians to Degrees Converter, which also accepts π forms such as π/4.