- Enter Angle — Type any numeric value.
- Select Units — Choose from 7 angle units: degrees, radians, gradians, arcminutes, arcseconds, turns, milliradians.
- See Results — Real-time conversion with DMS (degrees-minutes-seconds) display and all equivalents.
- Copy — Click 'Copy' to copy result.
Angle Converter — Convert Between Angular Units
The Angle Converter is a free, instant-use tool for converting between 7 angular measurement units with automatic DMS (degrees-minutes-seconds) display. Whether you're working in mathematics, surveying, navigation, astronomy, engineering, or military applications, this tool provides accurate real-time conversions.
All calculations run entirely in your browser. No data is sent to any server.
Supported Units
- Degree (°) — The most common angle unit. A full circle = 360°. Used in everyday life, navigation, geography, and most practical applications.
- Radian (rad) — The SI unit of angle. A full circle = 2π radians ≈ 6.2832. Used in mathematics, physics, and engineering. Defined as the angle subtended by an arc equal in length to the radius.
- Gradian (gon) — A full circle = 400 gradians. A right angle = 100 gon. Used in surveying and some engineering contexts, particularly in France, Germany, and Scandinavian countries.
- Arcminute (′) — 1/60 of a degree. Used in astronomy, navigation, and cartography. One nautical mile equals one arcminute of latitude along a meridian.
- Arcsecond (″) — 1/3600 of a degree or 1/60 of an arcminute. Used in astronomy for star positions, in geodesy for precise coordinates, and in optics.
- Turn/Revolution (rev) — A complete rotation (360° or 2π radians). Used in mechanical engineering for shaft rotations and in everyday descriptions of rotation.
- Milliradian (mrad) — 1/1000 of a radian. Used in military ballistics, rifle scopes, and artillery. At 1 km distance, 1 mrad ≈ 1 meter. Important: mathematical mrad differs from NATO mil.
Key Conversion Factors
- 1° = π/180 rad ≈ 0.01745 rad = 10/9 gon ≈ 1.1111 gon
- 1 rad = 180/π° ≈ 57.296° = 200/π gon ≈ 63.662 gon
- 1 turn = 360° = 2π rad = 400 gon
- 1° = 60′ = 3600″ ≈ 17.453 mrad
Features
- DMS Display — Automatic degrees-minutes-seconds notation for any angle.
- 7 Units — Covers mathematical, practical, surveying, and military units.
- Real-Time — Instant conversion as you type.
- All-Unit View — See all equivalents simultaneously.
Common Use Cases
- Mathematics — Convert between degrees and radians for trigonometric calculations.
- Surveying — Convert between degrees and gradians for land measurement.
- Astronomy — Convert celestial coordinates between degrees, arcminutes, and arcseconds.
- Navigation — Work with compass bearings and geographic coordinates.
- Military — Convert between degrees, milliradians, and NATO mils.
Privacy
All conversions run in your browser. No data is transmitted. Works offline.