Revolutions (rev) to Radians (rad) Conversion
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
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 (rev) | Radians (rad) |
|---|---|
| 0.1 rev | 0.62831853071796 rad |
| 1 rev | 6.2831853071796 rad |
| 2 rev | 12.566370614359 rad |
| 3 rev | 18.849555921539 rad |
| 5 rev | 31.415926535898 rad |
| 10 rev | 62.831853071796 rad |
| 20 rev | 125.66370614359 rad |
| 30 rev | 188.49555921539 rad |
| 50 rev | 314.15926535898 rad |
| 100 rev | 628.31853071796 rad |
| 1000 rev | 6283.1853071796 rad |