Radian (rad)
SI derived unit of plane angle: the angle subtended by an arc equal in length to the radius.
What is a radian?
- Symbol
- rad
- Quantity
- Angle
- Unit system
- SI
- Definition
- SI derived unit of plane angle: the angle subtended by an arc equal in length to the radius.
- Exact
- Yes, the value is exact by definition
- Source
- SI Brochure, 9th edition (BIPM, 2019)
Common applications
The SI unit of angle. Used in mathematics, physics and programming (most math libraries expect radians).
Radian in other angle units
- 1 rad = 1000 mradMilliradian
- 1 rad ≈ 57.29577951 °Radian to Degree converter
- 1 rad ≈ 3437.746771 ′Arcminute
- 1 rad ≈ 206264.8062 ″Arcsecond
- 1 rad ≈ 63.66197724 gradGradian (gon)
- 1 rad ≈ 0.1591549431 revTurn (revolution)
Radian quick reference
| Radian | Degree | Milliradian | Arcminute |
|---|---|---|---|
| 1 rad | ≈ 57.29577951 ° | = 1000 mrad | ≈ 3437.746771 ′ |
| 10 rad | ≈ 572.9577951 ° | = 10000 mrad | ≈ 34377.46771 ′ |
| 100 rad | ≈ 5729.577951 ° | = 100000 mrad | ≈ 343774.6771 ′ |
| 1000 rad | ≈ 57295.77951 ° | = 1000000 mrad | ≈ 3437746.771 ′ |
Where the radian fits
The next smaller angle unit is the degree (°). 1 rad ≈ 57.29577951 °, and 1 ° ≈ 0.01745329252 rad.
The next larger angle unit is the turn (rev). 1 rad ≈ 0.1591549431 rev, and 1 rev ≈ 6.283185307 rad.
Frequently asked questions
- How many degrees are in one radian?
- One radian ≈ 57.29577951 ° (degrees).
- How many milliradians are in one radian?
- One radian = 1000 mrad (milliradians).
- How many arcminutes are in one radian?
- One radian ≈ 3437.746771 ′ (arcminutes).