Radian to Degree Converter
Convert between radians and degrees instantly using the formula degrees = radians × 180 / π.
Includes a reference table of common angles from 0° to 360°.
Radians and degrees are two different units for measuring angles, just like inches and centimeters are two units for measuring length. Degrees are more common in everyday use, while radians are the standard in mathematics, physics, and engineering.
Converting degrees to radians:
Radians = Degrees × (π / 180)
Converting radians to degrees:
Degrees = Radians × (180 / π)
The conversion factor comes from the fact that a full circle is 360 degrees and also 2π radians. So π radians = 180 degrees, giving us the ratio π/180 (approximately 0.01745).
What is a radian? One radian is the angle created when the arc length along a circle equals the radius of that circle. Since a full circle has a circumference of 2πr, there are 2π radians in a full circle. One radian equals approximately 57.2958 degrees.
Common angles reference table:
| Degrees | Radians | Fraction of π |
|---|---|---|
| 0 | 0 | 0 |
| 30 | 0.5236 | π/6 |
| 45 | 0.7854 | π/4 |
| 60 | 1.0472 | π/3 |
| 90 | 1.5708 | π/2 |
| 180 | 3.1416 | π |
| 270 | 4.7124 | 3π/2 |
| 360 | 6.2832 | 2π |
Practical Example: Convert 75 degrees to radians: 75 x (π / 180) = 75 x 0.01745 = 1.3090 radians Convert 2.5 radians to degrees: 2.5 x (180 / π) = 2.5 x 57.2958 = 143.24 degrees
When to use this converter: Use it when working with trigonometric functions in math or programming (most programming languages expect angles in radians), converting between navigation systems, or solving physics problems involving circular motion and angular velocity.
Tips:
- Most scientific calculators have a DEG/RAD mode switch — make sure you are in the right mode before calculating sine, cosine, or tangent
- In programming languages like JavaScript, Python, and C, the built-in trig functions (sin, cos, tan) always expect radians
- The angles 30, 45, 60, and 90 degrees appear constantly in trigonometry — memorizing their radian equivalents (π/6, π/4, π/3, π/2) saves time