Velocity - Angular Converter

Angular velocity describes how fast an object rotates around an axis — the rate at which an angle sweeps past over time. It's the rotational counterpart to ordinary (linear) speed, and it shows up wherever something spins: motor shafts, wheels, turbines, planets, and clock hands all have an angular velocity, even though they may look very different from one another.

Our Velocity - Angular converter supports 12 units organized into three natural families. The radian-based units — radian/second (the SI unit, rad/s), radian/minute, radian/hour, and radian/day — are the ones used directly in physics and engineering formulas, since the radian is the natural unit of angle in calculus-based rotational equations (torque, angular momentum, and centripetal acceleration all use radians per second). The degree-based units — degree/second, degree/minute, degree/hour, and degree/day — use the everyday 360°-per-circle angle measure, and the degree/day and degree/hour units in particular are useful for describing very slow rotations, like the apparent motion of celestial bodies. The revolution-based units — revolution/second, revolution/minute, revolution/hour, and revolution/day — measure rotation in full turns, with revolution/minute (RPM) being the unit most commonly printed on motor nameplates, fan specifications, and vehicle tachometers.

Converting between these families always comes back to two fixed relationships: one revolution equals 360 degrees equals 2π radians (about 6.2831853 radians). So, for example, a motor rated at 3,000 RPM is spinning at 3,000 × 0.1047197551 ≈ 314.16 radians per second, or equivalently 3,000 × 6 = 18,000 degrees per second. Because these ratios are exact, the converter's results are precise to up to 12 significant digits, not rounded approximations.

To use the tool, pick your starting unit and target unit from the two dropdown selectors, then type a value into the input box — the converted result appears immediately as you type. This makes it quick to translate a manufacturer's RPM rating into rad/s for a physics calculation, or to convert a slow astronomical rotation rate given in degrees/day into a more familiar unit.

Angular velocity is also the starting point for several related quantities used elsewhere in this Engineering Converters section: multiply it by a radius to get linear (tangential) speed, differentiate it with respect to time to get angular acceleration, and multiply it by moment of inertia to get angular momentum — so getting a clean, precise angular-velocity value first makes every downstream calculation more reliable.

Angular velocity conversions are essential across many fields: mechanical and electrical engineers convert between RPM and rad/s constantly when working with motor torque-speed curves and control system equations; robotics engineers use rad/s when programming joint velocities; automotive engineers convert wheel and engine RPM into angular velocity for drivetrain calculations; and astronomers and physics students use the degree- and radian-based units when describing planetary rotation, orbital motion, and gyroscopic precession.

All conversion factors used here are exact mathematical relationships between radians, degrees, and revolutions, so you can rely on the results for coursework, technical documentation, or product specifications. The converter is completely free, requires no account, and works equally well on desktop and mobile.