Angular Velocity Calculator

Angular velocity describes how fast something spins, and this calculator finds it for you and links it to the everyday quantities people actually measure, like revolutions per minute and the speed at the rim. Choose to work from RPM, the way motors, wheels and discs are usually rated, or from an angle turned over a time, and the calculator returns the angular velocity in radians per second along with degrees per second and revolutions per minute, and, if you enter a radius, the linear speed of a point at that distance from the axis. Everything updates as you type. The core idea is that angular velocity measures the angle swept out per unit of time, so it is the rotational twin of ordinary velocity, with the radian, the natural mathematical measure of angle, taking the place of distance. Converting from RPM is a common need and a common stumbling block: one revolution is two pi radians and one minute is sixty seconds, so multiplying RPM by two pi over sixty turns it into radians per second. The link to linear speed is just as useful, because a point at radius r races along at a speed equal to the angular velocity times r, which is why the outer edge of a grinding wheel or a merry-go-round moves so much faster than a point near the centre, even though both share the same spin rate. That makes the tool genuinely useful for physics and engineering students learning circular motion and checking homework, and for practical work with motors, fans, wheels, turntables and machinery where RPM, radians per second and rim speed all need to line up. Using metres for the radius gives the linear speed in metres per second. The formulas and a worked example are explained clearly below.

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