What is angular velocity?

Angular velocity measures how fast an object rotates or revolves, expressed as angle per unit time. Common units: radians per second (rad/s, SI standard), degrees per second (deg/s), revolutions per minute (RPM), revolutions per second (RPS), and rotations per hour.

How do I convert RPM to radians per second?

Multiply RPM by 2*pi/60 = 0.10472. Formula: rad/s = RPM x (2*pi/60). Example: 1,000 RPM = 1,000 x 0.10472 = 104.72 rad/s. Reverse: RPM = rad/s x 60 / (2*pi) = rad/s x 9.5493.

What is a typical RPM for car engines?

Car engine idle RPM: 600-900 RPM. City driving: 1,500-2,500 RPM. Highway: 2,000-3,000 RPM. Maximum (redline): 5,000-8,000 RPM for standard cars, up to 20,000 RPM for F1 engines. Electric motors can spin much faster, up to 20,000+ RPM in some EV applications.

What is the difference between angular velocity and angular frequency?

Angular velocity (omega) is the rate of rotation in rad/s, a vector quantity with direction. Angular frequency (also omega) is the same magnitude but is a scalar used for oscillating systems (like AC current at 60 Hz = 377 rad/s). In many contexts they are used interchangeably when direction is implied.

Angular Velocity Converter

Convert between rad/s, rpm, deg/s, rev/s, rev/h and more.

About Angular Velocity

Angular velocity measures how fast an object rotates. The SI unit is radian per second (rad/s). In everyday use, RPM (revolutions per minute) is the most common unit, widely used in engines, turbines, and motors.

Quick Reference Table

Unit	In rad/s
1 RPM	0.10472 rad/s
1 rev/s	6.28318 rad/s
1 deg/s	0.017453 rad/s

Related Converters

Acceleration Converter • Angular Acceleration Converter • Speed Converter

Angular Velocity Explained

Angular velocity measures how fast something rotates. The SI unit is radians per second (rad/s), but engineers often use RPM for motors. A car engine idling at 800 RPM rotates at 800/60 = 13.3 rev/s = 83.8 rad/s. Angular velocity (ω) relates to linear speed (v) by v = ω × r, where r is the radius. A point on the Earth's equator moves at about 465 m/s because the Earth's angular velocity is tiny (7.27 × 10⁻⁵ rad/s) but the equatorial radius is large (6,378 km).

Angular Velocity Conversion Reference

Unit	rad/s	Example
1 RPM	0.10472	Slow motor
1 rev/s	6.2832	AC motor at 1 Hz
1,000 RPM	104.72	Car engine idle
7,200 RPM	753.98	HDD spin speed

Angular Velocity: RPM, rad/s, and Beyond

Angular velocity describes how fast an object rotates, measured in angle per unit time. Common units are radians per second (rad/s, the SI unit), degrees per second (°/s), revolutions per minute (rpm), and revolutions per second (rps). Key conversions: 1 rpm = 2π/60 rad/s ≈ 0.10472 rad/s; 1 rps = 2π rad/s ≈ 6.2832 rad/s; 1 rad/s ≈ 9.5493 rpm. The linear speed at a point on a rotating object is v = ω × r, where ω is angular velocity and r is the radius.

RPM is the practical unit for motors, engines, and drills. A car engine at highway speed runs at 2,000–3,000 rpm. An electric motor might run at 3,000–6,000 rpm. Hard disk drives (HDDs) rotate at 5,400 or 7,200 rpm. Professional audio turntables run at exactly 33⅓ or 45 rpm. Centrifuges use very high rpm (10,000–100,000+) to separate materials by density.

Angular Velocity Conversions

rpm	rad/s	deg/s	rps
1	0.10472	6.0	0.01667
10	1.0472	60.0	0.1667
33.3	3.491	2000	0.5556
60	6.283	360	1.000
1000	104.72	6000	16.67

Angular Velocity Units in Rotation and Mechanics

Angular velocity measures how fast an object rotates or revolves, expressed as the angle swept per unit of time. The SI unit is radians per second (rad/s), where one radian is the angle subtended by an arc equal in length to the circle's radius. Revolutions per minute (RPM) is the most common practical unit in mechanical engineering: engine speeds, motor speeds, drill bits, and hard disk drives are all rated in RPM. Degrees per second (°/s) appears in motion sensors, gyroscopes, and animation software. Hertz (Hz) or cycles per second is used for rotating machinery frequency analysis. Converting between units: 1 RPM = 2π/60 rad/s ≈ 0.10472 rad/s; 1 rad/s ≈ 9.5493 RPM. A car engine idling at 800 RPM has an angular velocity of about 83.8 rad/s. Understanding angular velocity is essential for calculating centripetal acceleration, power output of rotating machinery, and peripheral speed at the rim of a gear or wheel.

Angular Velocity Reference Table

Unit	rad/s equivalent	RPM equivalent
1 RPM	0.10472	1
1 rad/s	1	9.5493
1 °/s	0.017453	0.16667
1 Hz (rev/s)	6.2832	60
Engine idle (800 RPM)	83.78	800