Linear speed from angular speed calculator

Enter the radius from the rotation axis and the angular speed in radians per unit of time. The calculator multiplies those values using v = rω and returns tangential speed in the corresponding length unit per time unit. It is useful for wheels, shafts, pulleys, rotors, turntables, and any rigid rotating system where the point's distance from the axis is known.

Calculate tangential speed from radius and angular speed

A rotating point has a linear, or tangential, speed even though the object is described by angular motion. Enter the point's radius, measured from the axis of rotation, and its angular speed in radians per unit of time. The calculator applies linear speed = radius × angular speed, commonly written as v = rω. If radius is in metres and angular speed is in radians per second, the result is metres per second. If radius is in centimetres and angular speed is in radians per minute, the result is centimetres per minute. Radians are dimensionless in this relationship, so the length and time units pass directly to the output. Use the radius of the particular point you care about, not automatically the object's outer radius. Two points on the same rigid wheel share angular speed, but the point farther from the axis moves faster along its circular path. Both inputs must be non-negative because this calculator reports speed magnitude rather than a signed directional velocity.

Choose compatible angular and linear units

The angular speed input must be expressed in radians per time unit. Degrees per second, revolutions per minute, and hertz cannot be inserted unchanged because their numerical values represent different angular scales. Convert degrees per second to radians per second by multiplying by π/180. Convert revolutions per minute to radians per second by multiplying by 2π/60. Convert revolutions per second, or hertz, by multiplying by 2π. Once angular speed is in radians per chosen time unit, pair it with the radius in the desired length unit. A radius of 0.25 metres and an angular speed of 8 radians per second give 2 metres per second. The same physical calculation could use 25 centimetres and return 200 centimetres per second. Avoid mixing a per-minute angular speed with an expected per-second result unless you first convert the time base. The calculator does not infer units or convert them automatically; it performs the exact product supplied, which keeps the result predictable for engineering worksheets and automated API calls.

Interpret the ideal rotating-point result

The result is the instantaneous tangential speed of a point at the stated radius in ideal rigid rotation. Its direction is tangent to the circular path and continuously changes as the object turns, even when the speed magnitude remains constant. This calculator returns only that magnitude. For a rolling wheel without slipping, the rim's tangential speed relative to the axle also equals the axle's linear speed relative to the ground. That convenient equivalence stops being exact when the wheel slips, the tyre deforms, or the effective rolling radius differs from the measured geometric radius. Belts and pulleys can likewise experience slip, while wound cable changes a drum's effective radius as layers build. Use a calibrated or instantaneous radius when those effects matter. The formula also assumes that radius and angular speed refer to the same rotating component and moment. It does not calculate angular acceleration, centripetal acceleration, torque, or travel distance. For repeatable integrations, the API runs the same deterministic multiplication for $0.002 per request and returns the inputs, computed speed, and formula used.