Radians to Degrees Converter (rad to °)
Table of Contents
- How to Convert Radians to Degrees (rad to °)?
- Conversion Example: Radians to Degrees
- Radians to Degrees Conversion Table
- Frequently Asked Questions
How to Convert Radians to Degrees (rad to °)?
The conversion from radians to degrees is simple: 1 radian equals 180/π degrees. To convert, multiply the number of radians by 180/π.
Formula
Conversion Example: Radians to Degrees
With these steps, you can easily convert radians to degrees. Below, we provide practical examples to ensure the procedure is clear and easy to follow.
Example 1
Example 1: Convert π radians to degrees.
Result: π radians equals 180 degrees.
Example 2
Example 2: Convert π/4 radians to degrees.
Result: π/4 radians equals 45 degrees.
Decimal radians to degrees: a 2.5 rad example
Not every angle comes written with π. To convert 2.5 radians: 2.5 × 180/π ≈ 143.24°. As a reference, 1 radian is about 57.2958°.
How much is π in degrees?
π radians is exactly 180°, a half turn. The rest follow from it: π/2 = 90°, 2π = 360° and 3π/2 = 270°.
Mental shortcut: replace π with 180
When the angle is given as a fraction of π, just swap π for 180 and do the arithmetic. For example, 3π/4 → 3 × 180 / 4 = 135°, and 5π/6 → 5 × 180 / 6 = 150°.
Common mistakes
- Multiplying by π/180 instead of 180/π. That is the inverse formula, used to go from degrees to radians.
- Rounding π to 3.14 too early. If you need an exact result, keep π symbolic and simplify at the end.
- Mixing up calculator modes: it does not matter for these conversions, but it does when you compute sines and cosines afterwards.
Radians to Degrees Conversion Table
| Radians | Degrees | Decimal Value (rad) |
|---|---|---|
| π/6 rad | 30° | 0.5236 rad |
| π/4 rad | 45° | 0.7854 rad |
| π/3 rad | 60° | 1.0472 rad |
| π/2 rad | 90° | 1.5708 rad |
| 2π/3 rad | 120° | 2.0944 rad |
| 3π/4 rad | 135° | 2.3562 rad |
| 5π/6 rad | 150° | 2.6180 rad |
| π rad | 180° | 3.1416 rad |
| 7π/6 rad | 210° | 3.6652 rad |
| 5π/4 rad | 225° | 3.9269 rad |
| 4π/3 rad | 240° | 4.1888 rad |
| 3π/2 rad | 270° | 4.7124 rad |
| 5π/3 rad | 300° | 5.2360 rad |
| 7π/4 rad | 315° | 5.4978 rad |
| 11π/6 rad | 330° | 5.7596 rad |
| 2π rad | 360° | 6.2832 rad |
Frequently Asked Questions
How do I convert radians to degrees?
To convert radians to degrees, multiply the radians by 180 and divide by π. Formula: degrees = radians * (180 / π).
How many degrees are in π radians?
π radians equal 180 degrees.
How many degrees are in π/2 radians?
π/2 radians equal 90 degrees.
How many degrees are in 2π radians?
2π radians equal 360 degrees.
How do I convert 1 radian to degrees?
1 radian is approximately equal to 57.2958 degrees. Use the formula: 1 * (180 / π).
How many degrees are in 3π/2 radians?
3π/2 radians equal 270 degrees.
Cite this page
You can use the following citation format when referencing this calculator in academic or professional work.
Ramos, J., Radians to degrees converter (rad to °), Available at: https://calcuclub.com/convert/radians-to-degrees/ (Accessed: 11 October 2026).