# How do I convert radians to degrees?

Converts radians (rad) to degrees (°) and back, with the exact unit definitions.

- Page: https://www.acalculator.org/convert/radians-to-degrees
- JSON spec: https://www.acalculator.org/convert/radians-to-degrees.json
- Version: 308b5a7e756f

## Default answer

Example with the default inputs (Radians (rad) 1): 1 rad = 57.29578 °.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| value | Radians (rad) | The amount in radians to convert. |
| result | Degrees (°) | The same amount in degrees. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| value | Radians (rad) | The amount in radians to convert. |
| result | Degrees (°) | The amount in degrees. |

## Method

° = rad × 57.2957795131

## Assumptions

- 1 radian = 57.2957795131 degrees, from the exact definitions in NIST SP 811.
- The answer shows at most 6 decimal places; the calculation keeps full precision.

## Worked examples

1. value = 1 gives result = 57.29578. Source: Exact unit definitions in NIST SP 811 (2008), Appendix B.8.
2. value = 3.141593 gives result = 180. Source: Exact unit definitions in NIST SP 811 (2008), Appendix B.8.
3. result = 180 gives value = 3.141593. Source: Exact unit definitions in NIST SP 811 (2008), Appendix B.8.

## FAQ

### How many degrees are in a radian?

1 radian is 57.29578 degrees, from the exact unit definitions (NIST SP 811).

### How do I convert radians to degrees?

Multiply by 57.29578: ° = rad × 57.2957795131. For example, 1 rad × 57.29578 = 57.29578 °.

### How do I convert degrees back to radians?

Multiply by 0.017453, or type the degrees into the second box and the converter works it out. 1 degree is 0.017453 radians.

### How many degrees is π radians?

180°. A full turn is 2π radians or 360°, so π radians is half a turn.

### Can an angle be negative?

Yes. A negative angle turns the other way (clockwise in math). −1 radian is −57.29578°. The converter takes negative values.

## Sources

- NIST SP 811 (2008), Guide for the Use of the International System of Units, Appendix B.8. https://www.nist.gov/pml/special-publication-811