RPM Calculator

How to use the rpm calculator

1. Fill in the fields — they start with a worked example.
2. Read the answer, and the arithmetic shown beneath it.
3. Copy the results, or adjust the inputs to compare scenarios.

About this tool

Rotational speed only means something once a diameter is attached to it. A point on the rim of a large wheel travels much further per revolution than a point on a small one, so the same RPM is a gentle rotation on one and a dangerous surface speed on the other. Every calculation here is that relationship in one direction or another.

In machining it is the governing number. Tooling is specified by cutting speed — how fast the material should pass the cutting edge — and the spindle speed that produces it depends entirely on the diameter of the tool or workpiece. Turning that speed into RPM is the calculation done before every job: multiply the cutting speed by a thousand and divide by pi times the diameter in millimetres, or by twelve over pi times the diameter for the imperial form.

That also explains why a lathe turning a tapered part needs constant surface speed control. As the diameter falls, the RPM must rise to keep the same speed at the cutting edge, and a fixed spindle speed produces a finish that changes along the workpiece.

The pulley calculation is the same idea applied to a drive: the small pulley turns faster in exact proportion to the diameter ratio. The belt itself travels at one speed, so the ratio of the speeds is the inverse ratio of the diameters — which is why a pulley change is the simplest way to alter the speed of a machine.

Common uses

• Setting a spindle speed from a tooling supplier's cutting speed.
• Finding the surface speed a given RPM produces on a diameter.
• Working out the driven speed through a pulley or belt ratio.

Frequently asked questions

How do I convert cutting speed to RPM?

RPM = (1000 × cutting speed in metres per minute) ÷ (π × diameter in millimetres). In imperial, RPM = (12 × surface feet per minute) ÷ (π × diameter in inches).

Why does a smaller diameter need more RPM?

Because a point on a smaller circumference travels less distance per revolution. To keep the same speed at the cutting edge, the spindle has to turn faster.

How do pulley sizes change speed?

In inverse proportion to their diameters. A 100 mm pulley driving a 50 mm one doubles the speed, since the belt travels at one speed and the smaller wheel must turn twice as often.