How do I convert RPM to radians per second?

To convert RPM to rad/s, multiply by π/30 (approximately 0.10472). For example, 1000 RPM = 1000 × 0.10472 = 104.72 rad/s. This works because one revolution = 2π radians, and there are 60 seconds in a minute.

What's the difference between angular velocity and linear velocity?

Angular velocity measures rotation rate (radians or degrees per time), while linear velocity measures straight-line speed (distance per time). They're related: linear velocity = angular velocity × radius. A point farther from the axis moves faster linearly at the same angular velocity.

Why do engineers use rad/s instead of RPM?

Radians per second is the SI unit and works directly in physics equations without conversion factors. Formulas for centripetal force, angular momentum, and rotational kinetic energy use rad/s. RPM is more intuitive for practical applications but requires conversion for calculations.

How fast does a car wheel spin at highway speed?

At 100 km/h (62 mph) with a typical tire diameter of 0.65m, the wheel spins at about 820 RPM or 86 rad/s. You can calculate this using: RPM = (speed in m/s × 60) / (π × diameter).

What is the angular velocity of Earth's rotation?

Earth rotates once every 24 hours (approximately), giving an angular velocity of about 7.27 × 10⁻⁵ rad/s or 0.0042°/s. This equals about 0.00069 RPM—one revolution per 1,440 minutes (24 hours).

Angular Velocity Converter

About Angular Velocity Conversion

Angular velocity measures how fast an object rotates or revolves around an axis—a fundamental concept in mechanics that describes rotational motion. Unlike linear speed which measures distance traveled over time, angular velocity describes the rate of rotation, measured in angles (radians, degrees, or revolutions) per unit time. This property is essential for understanding and designing motors, wheels, turbines, centrifuges, propellers, and any rotating machinery from tiny computer fans to massive wind turbines.

The SI unit is radians per second (rad/s), which integrates seamlessly into physics equations for rotational dynamics, but practical applications often use revolutions per minute (RPM) for intuitive understanding of motor speeds and machine performance. Degrees per second (°/s) appears frequently in navigation systems, gyroscopes, and robotics where angular displacement is more naturally thought of in degrees. Understanding these conversions is crucial in mechanical engineering, robotics, aerospace, automotive design, and physics.

Our converter handles all standard angular velocity units for engineering and scientific applications, from specifying motor speeds to analyzing satellite orbits.

Common Angular Velocity Conversions

From	To	Multiply By
RPM	rad/s	0.10472 (π/30)
rad/s	RPM	9.5493 (30/π)
RPM	°/s	6
°/s	RPM	0.16667 (1/6)
rad/s	°/s	57.2958 (180/π)
°/s	rad/s	0.01745 (π/180)
Hz (rev/s)	RPM	60
RPM	Hz (rev/s)	0.01667 (1/60)
Hz (rev/s)	rad/s	6.2832 (2π)
rad/s	Hz (rev/s)	0.1592 (1/2π)

Angular Velocity Unit Reference

Radian per second (rad/s) – The SI unit of angular velocity, defined as the angular displacement in radians divided by time in seconds. One rad/s means the angle changes by one radian (≈57.3°) every second. Preferred in physics and engineering calculations because it simplifies rotational dynamics equations—centripetal acceleration, angular momentum, and rotational kinetic energy all use rad/s directly without conversion factors.

Revolution per minute (RPM) – The most common practical unit for rotational speed, measuring complete rotations per minute. Universally used for motors, engines, fans, hard drives, and industrial machinery because it's intuitive—people can easily visualize complete turns. Car engines idle at 600-1000 RPM; hard drives spin at 5400-15000 RPM; jet engines reach 10000+ RPM.

Degree per second (°/s) – Angular change measured in degrees per second. Common in navigation systems, inertial measurement units (IMUs), robotics, and gyroscope specifications. Easy to visualize since most people think in degrees. Drone stabilization systems and smartphone rotation sensors often report in °/s.

Hertz (Hz, rev/s) – Revolutions per second, where 1 Hz = 1 complete rotation per second = 60 RPM = 2π rad/s. Used for high-speed rotation analysis and when relating rotational motion to frequency. Audio turntables run at 0.55-0.78 Hz (33⅓ or 45 RPM).

Revolution per second (rps) – Functionally identical to Hertz for rotational contexts, measuring complete turns per second. Sometimes preferred in mechanical engineering to distinguish from electrical frequency (which also uses Hz).