Conversion method
A complete turn is 360 degrees or 2π radians. An arcminute is 1/60 degree and an arcsecond 1/3600 degree. Negative angles remain signed; the converter does not wrap them into a single turn.
rad = x × 0.0174532925199433
10 ° = 0.174533 rad.
| ° | rad |
|---|---|
| 1 | 0.017453 |
| 5 | 0.087266 |
| 10 | 0.174533 |
| 25 | 0.436332 |
| 50 | 0.872665 |
| 100 | 1.745329 |
Unit definitions and sources
Degree and turn relationships are exact in terms of π; numerical calculations approximate π.
4 of the 10 definitions below were checked against the cited sources on 2026-09-20 (AI-assisted check).
| Unit and system | Use | Definition | Relationship |
|---|---|---|---|
| Radian (rad); si | Common units | Radian measures angle. rad = (value in rad) × 1. Common use: Rotation and geometry. | Exact definition; numerical display may be rounded |
| Degree (°); other | Common units | Degree measures angle. rad = (value in °) × 0.017453292519943295. Common use: Rotation and geometry. | Exact definition; numerical display may be rounded |
| Turn (tr); other | Common units | Turn measures angle. rad = (value in tr) × 6.283185307179586. Common use: Rotation and geometry. | Exact definition; numerical display may be rounded |
| Gradian (gon); other | Specialist units | Gradian measures angle. rad = (value in gon) × 0.015707963267948967. Common use: Rotation and geometry. | Exact definition; numerical display may be rounded |
| Arcminute (′); other | Specialist units | Arcminute measures angle. rad = (value in ′) × 0.0002908882086657216. Common use: Rotation and geometry. | Exact definition; numerical display may be rounded |
| Arcsecond (″); other | Specialist units | Arcsecond measures angle. rad = (value in ″) × 0.00000484813681109536. Common use: Rotation and geometry. | Exact definition; numerical display may be rounded |
| Milliradian (mrad); si | Specialist units | A milliradian is exactly one thousandth of a radian. Common use: Small angular measurements. Not interchangeable with the angular mil defined as 1/6400 of a turn. | Exact definition; numerical display may be rounded |
| Quadrant (quadrant); other | Specialist units | Quadrant: multiply by 1.5707963267948966 to obtain the category base unit. Common use: Rotation and geometry. | Exact definition; numerical display may be rounded |
| Sextant (sextant); other | Specialist units | Sextant: multiply by 1.0471975511965976 to obtain the category base unit. Common use: Rotation and geometry. | Exact definition; numerical display may be rounded |
| Microradian (µrad); other | Specialist units | Microradian: multiply by 1e-06 to obtain the category base unit. Common use: Rotation and geometry. | Exact definition; numerical display may be rounded |
Sources: BIPM: International System of Units; NIST: SP 811 Appendix B.8: conversion factors; BIPM: SI prefixes
Precision of angle conversions
All 10 angle units convert through Radian (rad). 10 have an exact defined relationship to the base unit and 0 are conventional or measured values. Results and the tables on this page come from the same engine, so a table value can be checked against the converter directly.
Standard display shows up to six decimal places, switching to scientific notation for very large or small values. Calculation uses JavaScript binary floating point independently of display rounding, so extra digits are not a claim about measurement accuracy. Each unit lists its own source; a citation records where the definition comes from, not an independent review. See Conversion methodology for the review and correction process.