# What is the RPM?

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.

- Page: https://www.acalculator.org/physics/rpm-calculator
- JSON spec: https://www.acalculator.org/physics/rpm-calculator.json
- Version: bbf3f026f4da

## Default answer

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

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| v | Edge speed | The speed of a point on the rim; for a rolling wheel, the vehicle’s speed. |
| d | Diameter | The distance across the wheel, tire or pulley through its centre. |
| rpm | Revolutions per minute | How many full turns the wheel makes each minute. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| speed | Edge speed | The speed of a point on the rim; for a rolling wheel, the vehicle’s speed. |
| diameter | Diameter | The distance across the wheel, tire or pulley through its centre. |
| rpm | RPM | Full turns per minute. |
| omega | Angular velocity (rad/s) | ω = 2π × rpm ÷ 60, in radians per second. |
| hz | Turns per second (Hz) | rpm ÷ 60: the frequency of rotation. |
| period | Time for one turn (s) | 60 ÷ rpm seconds. |

## Method

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.

## Assumptions

- 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.

## Worked examples

1. rpm = 250, d = 0.7 gives omega = 26.179939, hz = 4.166667, v = 9.162979. 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. v = 4.4704, d = 0.6604 gives rpm = 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. v = 3, rpm = 60 gives d = 0.95493, period = 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).

## FAQ

### 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.

## Sources

- OpenStax, University Physics Volume 1, §10.1 Rotational Variables (tangential speed v_t = rω; angular velocity 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)