Angle Converter
Angle Converter: convert between 6 angle units, for example 1 rad = 57.29577951 °.
| Unit | Value |
|---|---|
| radian (rad) | 1 rad |
| radian to degree | 57.29577951 ° |
| radian to gradian | 63.66197724 gon |
| radian to revolution | 0.1591549431 rev |
| radian to minute of arc | 3437.746771 ′ |
| radian to second of arc | 206264.8062 ″ |
Convert angles between degrees, radians, gradians, revolutions, arcminutes and arcseconds. Every factor is exact through π: 180° = π rad, so 1 rad = 57.29577951…°.
When to use radians
Geometry and navigation use degrees, but calculus and physics formulas such as arc length s = rθ and angular speed v = ωr assume radians. Set your calculator to the mode that matches the formula; a wrong mode is the most common trigonometry mistake.
Angle unit definitions
- radian (rad)
- A radian is the angle at the centre of a circle that cuts off an arc as long as the radius. A full turn is 2π radians, so π radians is 180° and 1 radian is about 57.2958°.
- degree (°)
- The degree divides a full turn into 360 equal parts. It is the everyday unit for angles in geometry, navigation and engineering drawings; 180° equals π radians.
- gradian (gon)
- The gradian (gon) divides a right angle into 100 parts, so a full turn is 400 gon. Surveyors in continental Europe use it because decimal angles simplify calculations.
- revolution (rev)
- A revolution (turn) is one complete rotation: 360° or 2π radians. Rotational speeds in rpm count revolutions per minute.
- minute of arc (′)
- A minute of arc is one sixtieth of a degree. It is used for latitude and longitude, telescope resolution and rifle scopes (MOA).
- second of arc (″)
- A second of arc is one sixtieth of an arcminute, or 1/3600 of a degree. Astronomers measure star positions and parallax in arcseconds.
Popular angle conversions
Show all 30 angle conversions
From radians
From degrees
From gradians
From revolutions
From minutes of arc
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Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures.
- Guide for the Use of the International System of Units (SI), NIST Special Publication 811, 2008 Edition, National Institute of Standards and Technology.
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