Radians (rad) to Revolutions (rev) Conversion
Radians
The radian (rad) is the SI derived unit of plane angle, defined as the angle subtended at the centre of a circle by an arc whose length equals the radius. One full rotation equals exactly 2π radians (≈ 6.2832 rad), and one radian equals approximately 57.2958°. The radian is preferred in mathematics and physics because it makes the derivatives of trigonometric functions algebraically clean — d/dx(sin x) = cos x only when x is in radians. Rotational speed (rad/s) and angular frequency in oscillatory systems are always expressed in radians.
Revolutions
A revolution (rev) is a unit of angle equal to exactly one complete rotation — 360 degrees, 2π radians, or 400 gradians. It is used in engineering and mechanics to describe rotational motion, most commonly as revolutions per minute (RPM) — the standard measure of rotational speed for engines, motors, turbines, and drill bits. A car engine at idle typically runs at 700–900 RPM; at highway cruising speed, 2,000–3,000 RPM. In astronomy, the orbital period of Earth is exactly one revolution around the Sun per year.
| Radians (rad) | Revolutions (rev) |
|---|---|
| 0.1 rad | 0.0159 rev |
| 1 rad | 0.1592 rev |
| 2 rad | 0.3183 rev |
| 3 rad | 0.4775 rev |
| 5 rad | 0.7958 rev |
| 10 rad | 1.5915 rev |
| 20 rad | 3.1831 rev |
| 30 rad | 4.7746 rev |
| 50 rad | 7.9577 rev |
| 100 rad | 15.9155 rev |
| 1000 rad | 159.1549 rev |
Frequently Asked Questions (FAQ)
How many revolutions are in 1 radians?
1 radians (rad) is exactly 0.159155 revolutions (rev).
How do I convert radians to revolutions?
Multiply the value in radians by 0.159155 to get the result in revolutions. Or use the converter above — type any number and see the result instantly.