Radians (rad)
The radian is the SI unit of angle: the angle at the center of a circle where the arc length equals the radius.
Convert radians to any angle unit
1 radian = 57.29577951 degrees
Quick facts
- Unit
- Radian (plural: radians)
- Symbol
- rad
- Measures
- Angles
- System
- Common
- Definition
- The angle subtended by an arc equal to the radius (360°/2π ≈ 57.3°).
1 radian in other units
| Degrees | 57.29577951 ° |
| Arcminutes | 3,437.746771 ′ |
| Arcseconds | 206,264.8062 ″ |
| Gradians | 63.66197724 grad |
| Milliradians | 1,000 mrad |
| Turns | 0.1591549431 tr |
| NATO mils | 1,018.591636 mil |
What is a radian?
The radian is the SI unit of angle: the angle at the center of a circle where the arc length equals the radius. A full circle is 2π radians. Radians make calculus and physics formulas simple, so they are the default in mathematics, programming languages and engineering.
Where the radian sits among angle units
The radian is number 21 of 24 on our scale of angle units, ordered from smallest to largest.
What radians are used for
- Mathematics and calculus
- Physics: angular velocity, oscillations
- Programming (sin, cos and other math functions take radians)
Radians in real life
- A full circle is 2π ≈ 6.283 rad
- A right angle is π/2 ≈ 1.571 rad
- 1 rad ≈ 57.3°
Top radian conversions
Common amounts of radians
- 0.1 rad
- 0.2 rad
- 0.3 rad
- 0.4 rad
- 0.5 rad
- 0.6 rad
- 0.7 rad
- 0.8 rad
- 0.9 rad
- 1 rad
- 1.5 rad
- 2 rad
- 2.5 rad
- 3 rad
- 3.5 rad
- 4 rad
- 4.5 rad
- 5 rad
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- 7 rad
- 7.5 rad
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- 1,000 rad
- 1,200 rad
- 1,500 rad
- 2,000 rad
- 2,500 rad
- 3,000 rad
- 4,000 rad
- 5,000 rad
- 10,000 rad
Convert radians to all 23 other units
Common
Astronomy & precision
Traditional & military
Convert to radians
Frequently asked questions
What is a radian?
The radian is the SI unit of angle: the angle at the center of a circle where the arc length equals the radius.
How is the radian defined?
The angle subtended by an arc equal to the radius (360°/2π ≈ 57.3°).
How many degrees are in a radian?
One radian equals 57.29577951 degrees.
How many arcminutes are in a radian?
One radian equals 3,437.746771 arcminutes.
How many arcseconds are in a radian?
One radian equals 206,264.8062 arcseconds.