Angle Converter

Convert between degrees, radians, gradians, and turns for any angle measurement quickly.

Angle Converter tool

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Example

Input: 90 degrees (deg) to radians (rad)

Result: 1.57079633 rad

Radians = degrees x pi / 180, so 90 x 3.14159265 / 180 = pi / 2 = 1.57079633 rad.

Common Angles in Every Unit

DegreesRadiansGradiansTurns
10.017453291.111111110.00277778
300.5235987833.333333330.08333333
450.78539816500.125
601.0471975566.666666670.16666667
901.570796331000.25
1803.141592652000.5
2704.712388983000.75
3606.283185314001

Values from this converter, rounded to 8 decimal places.

  1. Select the angle unit you are converting from (degrees, radians, gradians, or turns).
  2. Enter the angle value in the input field - decimal values and negative angles are supported.
  3. Instantly see the equivalent angle in the other three measurement systems.
  4. Use the radian result for programming trigonometric functions or the degree result for everyday measurements.
  5. Copy any converted angle value to your clipboard by clicking the copy button next to it.

When to Use Degrees, Radians or Gradians

To convert degrees to radians, multiply by pi/180. So 90 degrees is pi/2, or about 1.5708 radians, and one radian is about 57.3 degrees. This converter also handles gradians, which put 400 in a circle, and turns, where one turn is a full circle.

You will need radians most often in math and code. Calculus formulas assume radians. So do the trig functions in JavaScript, Python and most other languages. A classic bug is passing 30 to a sine function and expecting the sine of 30 degrees. You get the sine of 30 radians instead. A calculator left in the wrong DEG or RAD mode causes the same kind of error.

The other units have narrower uses. Gradians split a right angle into 100 parts, so a right angle is 100 grad. Some surveying tools and calculators still offer them. Turns count whole rotations: a quarter turn is 90 degrees. CSS accepts turns, degrees, radians and gradians for rotations.

The converter does not wrap angles into a single circle. An input of 450 degrees stays 450 degrees, which is 7.854 radians or 1.25 turns. Negative angles also convert as they are. To solve a triangle from its angles, use the Triangle Calculator. To evaluate a formula such as sin(30 deg), try the Math Expression Evaluator.

Formula / How It Works

360 degrees = 2*pi radians = 400 gradians = 1 turn | 1 degree = 0.0174533 rad = 1.11111 grad = 0.00277778 turns

Sources

Frequently Asked Questions

Multiply the degrees by pi and divide by 180. So 90 degrees is pi/2, or 1.5708 radians, and 180 degrees is pi, or 3.1416 radians. To go from radians to degrees, multiply by 180 and divide by pi. The converter does both and shows up to 8 decimal places.
One radian is about 57.2958 degrees. A radian is the angle you get when the arc along a circle is as long as its radius. A full circle holds 2 x pi radians, about 6.28, which is why 360 degrees equals 2 x pi.
A gradian, also called a gon or grad, splits a right angle into 100 parts. So a full circle is 400 gradians and 1 gradian is 0.9 degrees. It was made to fit the metric system. Some surveyors still use it, and many scientific calculators have a GRAD mode for it.
Radians make the math of circles and waves simpler, so most programming languages expect them. For example, the sine functions in JavaScript and Python take radians. Passing 90 when you mean 90 degrees gives a wrong answer. Convert first, or use pi/2.

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