What this calculator does
A pulley speed calculator finds how fast a driven pulley turns when it is connected by a belt to a driver pulley of a different size. Whenever two pulleys of different diameters are joined by a belt, the smaller one spins faster and the larger one spins slower, in direct proportion to the ratio of their diameters. This is the same principle behind gearing on a bicycle, a workshop drill press with a step-pulley head, or a motor driving a compressor through a belt.
The calculation only needs three numbers: the diameter of the driver pulley, the driver pulley speed in RPM, and the diameter of the driven pulley. From those it works out the driven pulley speed and the linear speed of the belt itself, which is useful when checking a belt is rated for the speed it will actually run at.
The formula
The belt moves at the same linear speed wherever it touches either pulley, so a smaller-diameter pulley must spin faster to keep up, and a larger one spins slower. Driven RPM equals driver RPM multiplied by the ratio of driver diameter to driven diameter. Belt speed is the driver pulley circumference (π times its diameter) multiplied by its RPM, converted to metres per second.
| Term | Meaning |
|---|---|
| Driver pulley | The pulley connected to the motor or power source, turning at a known, fixed speed. |
| Driven pulley | The pulley on the other end of the belt, whose speed is being worked out. |
| Speed ratio | Driven diameter divided by driver diameter; a ratio above 1 means the driven pulley turns slower than the driver. |
The inputs explained
| Field | What to enter |
|---|---|
| Driver pulley diameter (mm) | The diameter of the pulley attached to the motor or drive shaft. |
| Driver pulley speed (RPM) | The rotational speed of the driver pulley, in revolutions per minute. |
| Driven pulley diameter (mm) | The diameter of the pulley being driven by the belt. |
When to use it
Sizing a step-pulley drive
Workshop machines such as drill presses and lathes often use stepped pulleys so a single motor speed can be converted into several spindle speeds. Checking each diameter pairing against the target spindle RPM confirms the step chosen gives a usable speed.
Matching a compressor or pump to a motor
A motor running at a fixed RPM often needs to drive a compressor or pump at a slower, specific speed. Picking pulley diameters that give the right ratio avoids running the equipment too fast or too slow.
Checking belt speed against its rating
Belts are rated for a maximum safe surface speed. Working out the belt speed from the driver pulley diameter and RPM confirms the setup stays within that limit before it is built.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does driven pulley speed change with driven pulley diameter?
Holding the driver pulley diameter and speed fixed, and varying the driven pulley diameter.
| Driven pulley diameter | Driven pulley speed | Speed ratio (driven:driver) |
|---|---|---|
| 50 mm | 2,900.0 RPM | 0.50:1 |
| 100 mm | 1,450.0 RPM | 1.00:1 |
| 150 mm | 966.7 RPM | 1.50:1 |
| 200 mm | 725.0 RPM | 2.00:1 |
| 250 mm | 580.0 RPM | 2.50:1 |
| 300 mm | 483.3 RPM | 3.00:1 |
Questions
Does the belt speed depend on the driven pulley at all?
No. Belt speed is set entirely by the driver pulley diameter and its RPM, since that is where the belt picks up its speed. The driven pulley diameter only determines how fast that pulley turns to keep pace with the belt, not the belt speed itself.
What happens if the two pulleys are the same diameter?
The driven pulley turns at exactly the same speed as the driver, a 1:1 ratio. This is the simplest case, used when a belt is only there to transmit power over a distance rather than to change speed.
Does belt thickness affect the result?
This calculation uses the pulley diameters as entered, which should be the effective diameter where the belt centreline sits, not the outer edge of the pulley groove. For a close result on a V-belt drive, measure to the belt centreline rather than the pulley rim.
Can this be used for gears instead of a belt?
The same diameter-ratio relationship applies to two meshed gears, though gears reverse the direction of rotation while a simple belt drive does not. The speed maths is identical either way.
For the belt length itself, given the same two pulley diameters and the distance between their centres, see the Belt Length Calculator. To convert a rotational speed into other units, see the RPM Converter.