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Linear to Angular Speed Calculator

Angular speed in rad/s and RPM for a point moving at a given linear speed.

Result

45.4545 rad/s
434.06 rpm

How it is calculated

The tool applies ω = v / r, where v is the linear (tangential) speed of a point on the rim and r its distance from the axis of rotation. If you enter speed in metres per second and radius in metres, ω is in radians per second. It then converts to revolutions per minute with rpm = ω × 60 / (2π). The tool does not convert units itself, so the speed and the radius must use the same length unit and the speed must be per second for the rad/s answer to hold. The radius must be above zero. A negative speed simply gives a negative result, which means the opposite direction of rotation. Slip between a tyre and the road is not considered.

Worked example

A car drives at 15 m/s (54 km/h) on wheels with a radius of 0.33 m. Angular velocity: 15 / 0.33 = 45.4545 rad/s. Revolutions per minute: 45.4545 × 60 / (2π) = 2,727.27 / 6.2832 = 434.06 rpm. So each wheel turns about 7.2 times every second. A bigger wheel would turn more slowly at the same road speed: with a 0.66 m radius the result would drop to half, about 217 rpm.

Try this example →

Common mistakes

  • Entering speed in km/h and radius in metres. The units must match, so convert 54 km/h to 15 m/s first, otherwise the rad/s result is 3.6 times too large.
  • Entering the diameter instead of the radius. A 66 cm wheel has a 33 cm radius; using the diameter halves the angular speed.
  • Entering the radius in centimetres while the speed is in metres per second. Convert to 0.33 m, or the answer is 100 times too large.
  • Confusing rad/s with rpm. One rad/s is about 9.55 rpm; the tool shows both, so read the right line.
  • Using the speed of the vehicle for a point not on the rim, such as the hub. Every point has its own tangential speed, which scales with its radius.

Sources

About this calculator

Linear speed converts to angular velocity using ω = v / r, where v is the linear (tangential) speed at a point, r is the radius from the axis of rotation, and ω comes out in radians per second — multiply by 60/(2π) to get RPM. The relationship reflects that points farther from the center must move faster in a straight line to complete the same rotation.

Mechanical engineers, machinists, and physics students use it to relate a wheel, pulley, gear, or turntable's rim speed to its rotational speed — for example, finding the RPM of a wheel of known radius from a vehicle's road speed, or the required spindle speed for a given cutting speed on a lathe.

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Comments (1)

  • Editorial team

    Machinists often quote cutting speed in metres per minute, but this tool expects speed per second to give rad/s and rpm correctly. Divide by 60 first: 120 m/min is 2 m/s, and on a 0.025 m radius that gives 80 rad/s and 763.94 rpm. If you enter 120 straight in, the rpm line comes out 60 times too high. For a vehicle, use the loaded rolling radius of the tyre. What are you converting, a wheel or a spindle?

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