Radians to Degrees Converter
Unit ConversionConvert radians to degrees using the exact 180/pi factor.
Degrees
Equivalent angle in degrees
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SponsoredTo convert radians to degrees, multiply the angle by 180/π (degrees = radians × 180/π). You can type a plain radian value such as 1.5708, or switch the mode to enter a fraction of π: type 3 and 4 for 3π/4 and the result is exactly 135°. For a negative angle, put the minus sign on the first number.
One radian is the angle whose arc is exactly as long as the circle radius, about 57.2958°. Half a turn is π radians, which equals 180°, and that relationship gives the 180/π factor.
Quick answer: 1 rad ≈ 57.2958°, π/6 rad = 30°, π/4 rad = 45°, π/2 rad = 90°, π rad = 180°, and 2π rad = 360°. Negative values convert the same way and describe a clockwise rotation.
This page covers radians to degrees only. The related converters below handle the reverse direction and the arcminute and arcsecond units.
Radians to Degrees Formula
The formula is: degrees = radians × 180/π. For a value written as a multiple of π, the π cancels and you only multiply by 180: 3π/4 rad = 0.75 × 180 = 135°.
Worked example: 2 rad × 180/π = about 114.5916°.
Inverse trig functions are a common source of radian answers: the Arcsine Calculator and the Arctangent Calculator show the resulting angle in both degrees and radians, so you can check a conversion against them.
How to Convert Radians to Degrees
- Write down the angle in radians, for example 2π/3.
- Multiply by 180/π: (2π/3) × (180/π).
- Cancel π and simplify: 2 × 180/3 = 120°.
- For a plain decimal such as 2 rad, multiply by 57.2958: 2 × 57.2958 is about 114.59°.
How Many Degrees Is 1 Radian?
One radian is 180/π degrees, about 57.2958°. It is a little less than one sixth of a full turn, because a full turn holds 2π, roughly 6.2832, radians.
What Is a Radian?
A radian measures an angle by how far it reaches around a circle. Take the radius of a circle and lay that same length along the curved edge: the angle it spans, measured from the center, is 1 radian. In general, the angle in radians is the arc length divided by the radius, so the answer is the same for a coin or a planet.
The whole circumference is 2π times the radius, so a full circle holds 2π radians, a little over 6 radius lengths. That single fact gives every conversion on this page: 2π rad = 360°, π rad = 180°, and 1 rad = 180/π, about 57.2958°. The radian is the SI unit of angle, which is why calculus and physics formulas are written in it.
Radians to Degrees Table
Common angles, from their exact π form to degrees:
| Radians (exact) | Radians (decimal) | Degrees |
|---|---|---|
| 0 rad | 0 rad | 0° |
| π/12 rad | 0.261799 rad | 15° |
| π/6 rad | 0.523599 rad | 30° |
| π/4 rad | 0.785398 rad | 45° |
| π/3 rad | 1.047198 rad | 60° |
| π/2 rad | 1.570796 rad | 90° |
| 2π/3 rad | 2.094395 rad | 120° |
| 3π/4 rad | 2.356194 rad | 135° |
| 5π/6 rad | 2.617994 rad | 150° |
| π rad | 3.141593 rad | 180° |
| 7π/6 rad | 3.665191 rad | 210° |
| 5π/4 rad | 3.926991 rad | 225° |
| 4π/3 rad | 4.18879 rad | 240° |
| 3π/2 rad | 4.712389 rad | 270° |
| 5π/3 rad | 5.235988 rad | 300° |
| 7π/4 rad | 5.497787 rad | 315° |
| 11π/6 rad | 5.759587 rad | 330° |
| 2π rad | 6.283185 rad | 360° |
Radians to Degrees Without π
Plain radian values, such as answers from a calculator, convert like this:
| Radians | Degrees |
|---|---|
| 0.1 rad | 5.7296° |
| 0.5 rad | 28.6479° |
| 1 rad | 57.2958° |
| 1.5 rad | 85.9437° |
| 2 rad | 114.5916° |
| 2.5 rad | 143.2394° |
| 3 rad | 171.8873° |
| 4 rad | 229.1831° |
| 5 rad | 286.4789° |
| 6 rad | 343.7747° |
Where Radians to Degrees Conversion Is Used
Students convert textbook answers such as 5π/6 into degrees to picture them, and engineers do the same when reading angular data. Spreadsheets and software often work in radians, so a result is converted to degrees before people read it. For the equivalent angle between 0° and 360°, the Coterminal Angle Calculator normalizes any result.
Geometry tools usually work in degrees: the Rectangular to Polar Coordinates Calculator gives the polar angle θ in degrees, and the Perimeter of a Sector Calculator takes the angle in degrees and returns the arc length.
Frequently Asked Questions
How do you convert radians to degrees?
Multiply the angle in radians by 180/π. For example, 1.5 rad × 180/π is about 85.94°.
How do I convert π radians to degrees?
π radians is exactly 180°. For any fraction of π, replace π with 180 and simplify: π/3 rad is 180/3 = 60°, and 3π/2 rad is 3 × 180/2 = 270°. Choose the fraction of π mode above and type the two numbers to do this directly.
How do I convert radians to degrees in Excel?
Use =DEGREES(A1), where A1 holds the angle in radians, or multiply by 180/PI() with =A1*180/PI(). For 1 radian both return about 57.2958.
What unit is an angle written without a unit?
Radians. In math, an angle with no unit is read as radians, so sin(2) means the sine of 2 radians, about 114.59°, not 2°.
Can radians be negative?
Yes. A negative angle means a clockwise rotation, and it converts the same way: -π/2 rad is -90°.
Can I convert degrees back to radians?
Yes. Use the Degrees to Radians Converter, which multiplies by π/180 instead.
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