Degrees to Radians Calculator
Enter an angle in degrees to convert it to radians.
Radians to Degrees Calculator
Enter an angle in radians to convert it to degrees. You can enter a decimal (e.g. 3.14159) or a multiple of pi (e.g. 0.5 for pi/2).
Angle Unit Converter
Convert between degrees, radians, gradians, and turns.
Degrees to Radians Conversion Table
| Degrees | Radians (decimal) | Radians (pi form) |
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What is a Radian?
A radian is the standard unit of angular measure in mathematics and physics. One radian is the angle subtended at the center of a circle by an arc whose length equals the radius of the circle. A full circle is 2pi radians, which equals 360 degrees.
How to Convert Degrees to Radians
To convert from degrees to radians, multiply the angle in degrees by pi divided by 180.
For example, to convert 90 degrees to radians: 90 x (pi / 180) = pi/2, which is approximately 1.5708 radians.
How to Convert Radians to Degrees
To convert from radians to degrees, multiply the angle in radians by 180 divided by pi.
For example, to convert pi radians to degrees: pi x (180 / pi) = 180 degrees.
Why Two Units?
Degrees are convenient for everyday use and navigation, dividing a circle into 360 equal parts. Radians are the natural unit in mathematics and physics because they simplify formulas in calculus, trigonometry, and wave equations. When working with sine, cosine, and tangent in higher mathematics, radians are always preferred.
Other Angle Units
1 degree = pi/180 radians = 1.11111 gradians = 1/360 turn
1 radian = 180/pi degrees = 57.2958 degrees (approx.)
1 gradian = 0.9 degrees = pi/200 radians