acalculator

What is the RPM?

Type the speed at the edge of a wheel, tire or pulley and its diameter to get its rpm. Or type the rpm and one of the others to find the speed or the diameter. The RPM calculator also gives the angular velocity in rad/s, turns per second and the time for one turn.

Your numbers

Units
RPM
129.28

It turns at 129.28 rpm, or 13.5385 rad/s.

Angular velocity (rad/s)
13.5385
Turns per second (Hz)
2.1547
Time for one turn (s)
0.4641

RPM: 129.28. It turns at 129.28 rpm, or 13.5385 rad/s.

How to calculate

Finds revolutions per minute (rpm) from the speed at the edge of a wheel, tire or pulley and its diameter, or the speed or diameter from the rpm, with the angular velocity and frequency.

Example with the default inputs (Edge speed 10 mph, Diameter 26 in): It turns at 129.28 rpm, or 13.5385 rad/s.

Formula: rpm = 60 × v ÷ (π × d): one turn moves the rim π × d, and there are 60 seconds in a minute. ω = 2π × rpm ÷ 60 = v ÷ r.

  • The speed is the speed of the rim (tangential speed); for a wheel rolling without slipping it equals the vehicle speed.
  • The diameter is the outside diameter where the speed is measured; tire wear and squash are not modelled.
  • Values run in metres and seconds, in double precision.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Revolutions per minute 250, Diameter 27.56 in gives Angular velocity (rad/s) 26.179939, Turns per second (Hz) 4.166667, Edge speed 20.5 mph.Source: OpenStax, University Physics Volume 1, §10.1 Rotational Variables (v_t = rω; ω in rad/s; 250 rev/min × 2π rad/rev × 1 min/60 s = 26.2 rad/s), https://openstax.org/books/university-physics-volume-1/pages/10-1-rotational-variables (retrieved 2026-10-02)
  2. Edge speed 10 mph, Diameter 26 in gives Revolutions per minute 129.282785.Source: OpenStax, University Physics Volume 1, §10.1 Rotational Variables (v_t = rω; ω in rad/s; 250 rev/min × 2π rad/rev × 1 min/60 s = 26.2 rad/s), https://openstax.org/books/university-physics-volume-1/pages/10-1-rotational-variables (retrieved 2026-10-02)
  3. Edge speed 6.711 mph, Revolutions per minute 60 gives Diameter 37.6 in, Time for one turn (s) 1.Source: OpenStax, University Physics Volume 1, §10.1 Rotational Variables (v_t = rω; ω in rad/s; 250 rev/min × 2π rad/rev × 1 min/60 s = 26.2 rad/s), https://openstax.org/books/university-physics-volume-1/pages/10-1-rotational-variables (retrieved 2026-10-02)

How it works

A point on the rim of a wheel of diameter d travels the circumference, π × d, in one turn. At an edge speed v:

  • rpm = 60 × v ÷ (π × d), with v in meters per second and d in meters
  • speed v = rpm × π × d ÷ 60; diameter d = 60 × v ÷ (π × rpm)
  • angular velocity ω = 2π × rpm ÷ 60 rad/s, which equals v ÷ r with r = d ÷ 2 (OpenStax: v = rω)
  • turns per second = rpm ÷ 60 (Hz); time for one turn = 60 ÷ rpm seconds

Type any two of speed, diameter and rpm. Units are converted to meters and meters per second first (1 in = 0.0254 m exactly, 1 mph = 1,609.344 m ÷ 3,600 s exactly), and the maths runs in double precision.

Rules

  • Speed, diameter and rpm are each more than 0. A derived value beyond the largest double-precision number is left out.
  • The speed is the rim (tangential) speed. For a wheel rolling without slipping, it equals the vehicle’s speed over the ground.

Output format. rpm with up to 2 decimals; rad/s and Hz with up to 4 decimals; the time for one turn to at most 4 significant figures.

Worked examples by hand

250 rpm, diameter 0.7 m. ω = 2π × 250 ÷ 60 = 26.1799 rad/s; turns per second = 250 ÷ 60 = 4.1667 Hz; v = 250 × π × 0.7 ÷ 60 = 9.163 m/s.

26 in wheel at 10 mph. v = 10 × 1,609.344 ÷ 3,600 = 4.4704 m/s; d = 26 × 0.0254 = 0.6604 m. rpm = 60 × 4.4704 ÷ (π × 0.6604) = 129.28 rpm.

3 m/s at 60 rpm. d = 60 × 3 ÷ (π × 60) = 3 ÷ π = 0.9549 m; one turn takes 60 ÷ 60 = 1 s.

Other questions people ask

How do I calculate rpm from speed and diameter?

One turn moves the rim a distance of π × d (the circumference). Divide the speed by that and multiply by 60 to go from seconds to minutes: rpm = 60 × v ÷ (π × d), with v in meters per second and d in meters.

What rpm is a 26 in bike wheel at 10 mph?

10 mph is 4.4704 m/s and 26 in is 0.6604 m, so rpm = 60 × 4.4704 ÷ (π × 0.6604) ≈ 129.28 rpm.

How do I convert rpm to rad/s?

Multiply by 2π (radians in a turn) and divide by 60 (seconds in a minute): ω = 2π × rpm ÷ 60. A wheel at 250 rpm turns at 26.18 rad/s, as in OpenStax University Physics.

How do I get speed from rpm?

Reverse the formula: v = rpm × π × d ÷ 60. A 0.7 m wheel at 250 rpm has a rim speed of 250 × π × 0.7 ÷ 60 ≈ 9.16 m/s. Type the rpm and the diameter and leave the speed empty.

Is this the engine rpm of my car?

Not directly. This page gives how fast the wheel turns. The engine turns faster by the gear ratio times the final drive ratio; the gear ratio calculator covers that step.

Does a radius work instead of a diameter?

Type twice the radius as the diameter. In terms of the radius r, the formula is rpm = 60 × v ÷ (2π × r), which is the same thing.

What does rpm mean on YouTube?

There it means revenue per mille, money per 1,000 views, which is a different thing. This page is about revolutions per minute.