Core formula to convert radians to degrees
To convert radians to degrees, multiply the radian measure by 180 and divide by π. The formula is degrees = radians × (180 / π). This relationship comes from the fact that π radians equals 180 degrees, so one radian equals 180/π degrees (approximately 57.2958°). Using this formula lets you convert any angle accurately.
Practical examples
Use degrees = radians × (180 / π) for each conversion. For common angles, multiply the radian value by 180/π and simplify when possible.
- π/6 radians: (π/6) × (180/π) = 30°
- π/4 radians: (π/4) × (180/π) = 45°
- π/3 radians: (π/3) × (180/π) = 60°
- π/2 radians: (π/2) × (180/π) = 90°
- π radians: π × (180/π) = 180°
- 2π radians: 2π × (180/π) = 360°
Step-by-step conversion process
Follow these steps to convert radians to degrees reliably.
- Identify the angle in radians.
- Multiply by 180/π (or multiply by 180 and divide by π).
- Calculate the numeric result, keeping π symbolic if you prefer an exact expression.
- Round to the desired number of decimal places only for the final answer.
Radian and degree relationship
The formulas link radians and degrees through π. One full rotation is 2π radians and 360 degrees. This yields the key equivalences: π radians = 180°, 1 radian ≈ 57.2958°, and 1° ≈ 0.0174533 radians. These conversions are foundational when moving between angular units.
| Radians | Degrees | Notes |
|---|---|---|
| 0 | 0° | Zero angle |
| π/6 | 30° | Common exact value |
| π/4 | 45° | Common exact value |
| π/3 | 60° | Common exact value |
| π/2 | 90° | Right angle |
| π | 180° | Half rotation |
| 2π | 360° | Full rotation |
Calculator use and decimal form
On a calculator, compute radians × (180 ÷ π) to obtain degrees. Using π ≈ 3.141592653589793, 180/π ≈ 57.295779513. For example, 1 radian ≈ 57.2958°. Keep precision high during intermediate steps for better accuracy in results.
Converting degrees back to radians
To convert degrees to radians, multiply degrees by π/180. This is the inverse operation and is useful when moving the other way. Example: 90° × (π/180) = π/2 radians.
Use the exact formulas—degrees = radians × (180/π) to convert radians to degrees, and radians = degrees × (π/180) to convert degrees to radians—for consistent, accurate results in mathematics, programming, and engineering contexts.