Radian to Degree Converter
Convert between radians and degrees using this angle conversion method. If you are working on geometry, this calculator makes it easy for you to convert radians to degrees.
Rad to Deg Calculation Steps
The calculation step is very simple, you just need to multiply radians by (180/π), so
1 rad × (180/π) = 57.296°
What are Radians and Degrees?
Radians and degrees are two units for measuring angles:
- Degrees are the more familiar unit, where a full circle is 360°
- Radians are based on the radius of a circle, where a full circle is 2π radians (about 6.283)
- Radians are often used in higher mathematics and physics because they simplify many formulas
How to Convert Radians to Degrees
The conversion between radians and degrees is based on the mathematical calculation between the circumference of a circle and its angles. A full circle has 360 degrees, which is equal to 2π radians. Therefore, a half of a circle is 180 degrees, which is equal to π radians. This ratio 180° = π radians and it allows to convert between these two units of angle measurement.
180° = π radians
This means a full half circle is equal to 180 degrees or π radians.
To convert radians to degrees:
Use the formula:
Degrees = Radians × (180 / π)
Example: Convert 2 radians to degrees:
Degrees = 2 × (180 / π) = 114.59°
To convert degrees to radians:
Use the formula:
Radians = Degrees × (π / 180)
Example: Convert 90° to radians:
Radians = 90 × (π / 180) = π/2 = 1.57 radians
Note: Use a calculator with a π (pi) value, that is 3.1416.
This conversion is important in mathematics, physics, or engineering, where angles are measured in radians.
Radian to Degree Conversions
| Radians | Degrees |
|---|---|
| 0 rad | 0° |
| π/6 rad (0.5236) | 30° |
| π/4 rad (0.7854) | 45° |
| π/3 rad (1.0472) | 60° |
| π/2 rad (1.5708) | 90° |
| π rad (3.1416) | 180° |
| 2π rad (6.2832) | 360° |
| 1 rad | 57.2958° |
