Convert Radians to Degrees - Angle Converter
Use this converter to transform an angle measured in radians into degrees. The converter applies the exact mathematical relationship used across science and engineering: 180 degrees per pi radians.
Results are presented with high precision and clear guidance on rounding and measurement limits to help you match instrument tolerances, lab protocols, or reporting standards.
Authority: the radian is the SI-derived unit for plane angle (defined as the ratio of arc length to radius). For formal definitions and SI guidance consult national metrology and international standards organizations.
Interactive Converter
Convert between radian and degree with precision rounding.
Quick reference table
| Radian | Degree |
|---|---|
| 1 rad | 57.2958 ° |
| 5 rad | 286.4788 ° |
| 10 rad | 572.9575 ° |
| 25 rad | 1,432.3939 ° |
| 50 rad | 2,864.7877 ° |
| 100 rad | 5,729.5755 ° |
Methodology
This converter multiplies the input (radians) by 180 and divides by π (pi). The radian is dimensionless in SI terminology because it represents a ratio; degrees are a conventional subdivision of a circle used for communication and many applied workflows.
For computational accuracy we use a high-precision value of π consistent with scientific practice; displayed results may be rounded to the number of significant figures appropriate for your instrument or reporting requirements.
When converting measured angles, match rounding to the measurement uncertainty (for example, if a theodolite reports ±0.01° uncertainty, round converted values to the same precision). For regulatory or lab reporting, follow applicable standards from national metrology institutes and ISO/BIPM guidance.
Worked examples
Input: 1 rad → Output: 57.29577951308232° (exact conversion result).
Input: 3.141592653589793 rad (π) → Output: 180°.
Input: 0.7853981633974483 rad (π/4) → Output: 45°.
Expert Q&A
What is the exact formula to convert radians to degrees?
Multiply radians by 180 and divide by π: degrees = radians × (180 / π).
How many degrees are in one radian?
One radian equals approximately 57.29577951308232 degrees. The exact relationship is 180/π degrees per radian.
Should I worry about rounding or precision when converting measured angles?
Yes. Round converted values to a precision that matches the measurement uncertainty of your instrument or required reporting standard. For example, if your instrument uncertainty is ±0.01°, present converted values to two decimal places and report the uncertainty alongside the value.
Can I convert negative angles or angles greater than 2π radians?
Yes. The conversion formula applies to any real-number angle. Negative radians convert to negative degrees. For angles intended as bearings or normalized rotations, reduce or wrap the result into the desired range (for example, 0°–360°) using modular arithmetic as a separate step.
Is the radian a dimensioned unit? Why does it sometimes say 'dimensionless'?
In SI, the radian is a derived unit representing the ratio of two lengths (arc length divided by radius), so it is treated as dimensionless for dimensional analysis. Practically it encodes an angular measure and is handled explicitly in conversions.
Where can I find authoritative references for unit definitions and best practices?
Refer to national metrology institute guidance and the SI brochure from international bureaus for formal definitions and recommendations. Those sources provide the definitive statements on units, recommended notation, and measurement traceability.
Sources & citations
- NIST Reference on Units and Constants — https://physics.nist.gov/cuu/Units/
- BIPM — The International System of Units (SI Brochure) — https://www.bipm.org/en/publications/si-brochure
- MIT OpenCourseWare — Classical Mechanics and angular measures — https://ocw.mit.edu