Degrees to Radians Converter
Need to convert degrees to radians fast? You're in the right place. Use the converter below to instantly get results, see conversion formulas, and check popular values – all in one place.
Want to convert radians to degrees instead? Try our radians to degrees converter.
How to Convert Degrees to Radians
To convert degrees to radians, multiply the number of degrees by π/180 (about 0.0174533). This is because one degree equals exactly π/180 radians.
Formula: radians = degrees × (π / 180)
Example: 180° × (π / 180) = π rad ≈ 3.1416 rad
Degrees to Radians Conversion Table
| Degrees (°) | Radians (rad) |
|---|---|
| 30° | 0.5236 rad |
| 45° | 0.7854 rad |
| 90° | 1.5708 rad |
| 180° | 3.1416 rad |
| 270° | 4.7124 rad |
| 360° | 6.2832 rad |
What is a Degree?
A degree (°) is a unit of angle equal to 1/360 of a full circle. Degrees are widely used in geometry, navigation, and everyday applications.
What is a Radian?
A radian (rad) is the standard unit of angular measure in mathematics. One radian is the angle created when the arc length equals the radius of the circle. There are 2π radians in a full circle.
Looking to convert the other way? Try our radians to degrees converter.
Common Angle Unit Converters
FAQ
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How many radians is 180 degrees?
180 degrees is exactly π radians (about 3.1416 radians).
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How do you convert 90 degrees to radians?
90 degrees × (π / 180) = π/2 radians (about 1.5708 radians).
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What is the formula to convert degrees to radians?
Multiply degrees by π and divide by 180 radians = degrees × (π/180).
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Why do scientists use radians?
Radians are preferred in science and engineering because they simplify many mathematical equations, especially in trigonometry and calculus.
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Is 360 degrees equal to 2π radians?
Yes, a full circle is 360 degrees or 2π radians.