Angle Converter
Angles are measured in multiple units depending on discipline and application. The radian is the SI unit, defined geometrically as the angle subtended by an arc equal to the radius. Since a full circle is 2 pi radians (approximately 6.28318), one radian equals approximately 57.3 degrees. Degrees are the most familiar unit, dividing a circle into 360 equal parts. One degree is further subdivided into 60 arcminutes, each of which is divided into 60 arcseconds. Gradians (also called grads or gons) divide a circle into 400 parts, designed to work with decimal systems. Gradians are used primarily in surveying in some countries. A turn (or revolution) is one complete rotation, equal to 360 degrees. Military and surveying applications use NATO mils, where a circle contains approximately 6,400 mils. Converting between angle units is essential in mathematics, physics, engineering, navigation, surveying, and astronomy. A 45-degree angle equals pi/4 radians (about 0.785 radians) or 50 gradians. This calculator displays seven angle units for instant conversion.
NIST conversion factors
All conversions below use standard factors, with all units expressed relative to the degree.
| Unit | Symbol | Degrees |
|---|---|---|
| Degree | ° | 1 |
| Radian | rad | 57.29577951 |
| Gradian | grad | 0.9 |
| Arcminute | ' | 0.016667 |
| Arcsecond | " | 0.000277778 |
| Turn | turn | 360 |
| Mil (NATO) | mil | 0.05625 |
Angle converter: frequently asked questions
What is a radian?
A radian is the SI unit of angle, equal to the angle subtended by an arc length equal to the radius. There are exactly 2 pi radians (about 6.28318) in a full circle, so 1 radian equals about 57.3 degrees.
What is a degree?
A degree is a unit where a full circle equals 360 degrees. One degree equals about 0.01745 radians. Degrees are divided into 60 arcminutes, each of which is divided into 60 arcseconds.
What is a gradian?
A gradian (also called a gon or grad) divides a full circle into 400 gradians, making conversions with the decimal system easier. It is used in surveying in some countries. One gradian equals 0.9 degrees.
What is a turn or revolution?
A turn (also called a revolution) is one complete rotation, equal to 360 degrees or 2 pi radians. Multiple turns are used in physics and engineering for rotating systems.
Why are there so many angle units?
Radians are preferred in mathematics and physics because they simplify formulas. Degrees are used in navigation, geography, and everyday applications. Gradians are used in surveying. NATO mils are used in military contexts. Converting ensures clarity across disciplines.
Official sources
- NIST Handbook 44: Specifications, Tolerances, and Other Technical Requirements for Weighing and Measuring Devices.
- NIST Special Publication 330: The International System of Units.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.