Turn linear speed at a rotating surface into revolutions per minute by finding the distance traveled in each revolution. Follow diameter units and compare two wheel sizes.
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The calculation
RPM = surface speed (m/min) ÷ [π × diameter (m)]
Worked example
For 60 m/min and diameter 100 mm = 0.1 m, circumference is π × 0.1 ≈ 0.314159 m. RPM = 60 ÷ 0.314159 ≈ 190.986, or 191 RPM. Doubling diameter to 0.2 m halves the required RPM to about 95.493.
The formula uses surface speed at the stated diameter. Illustrative rotation is slowed for visibility. The arithmetic alone does not select a safe machine operating speed.
Video chapters
- 0:00 — Distance per minute is not turns per minute
- 0:15 — One revolution covers one circumference
- 0:32 — Divide distance per minute by distance per turn
- 0:49 — Check backward with the circumference
- 1:04 — Double the diameter, halve the RPM
- 1:18 — The factor of 1,000 is a unit conversion
- 1:35 — Use the correct physical speed
- 1:54 — Circumference connects the two speeds
Read the full transcript
A rotating rim moves at sixty meters per minute. How many revolutions per minute is that? We need its diameter. A larger wheel travels farther around its edge in one turn, so the same surface speed can correspond to fewer revolutions. Watch the rim marker complete a single loop.
The distance around a circle is pi times its diameter. For a one-hundred-millimeter diameter, first convert to meters: one hundred divided by one thousand equals zero point one meter. The circumference is pi times zero point one, or approximately zero point three one four one five nine meters per revolution.
Divide sixty meters per minute by zero point three one four one five nine meters per revolution, keeping pi's full precision in the calculation. Meters cancel and revolutions per minute remain. The result is approximately one hundred ninety point nine eight six R P M, or one hundred ninety-one when rounded to a whole revolution per minute.
Multiply the unrounded R P M by pi times zero point one meter per revolution. The result returns sixty meters per minute. Using the rounded one hundred ninety-one gives a tiny difference. That is expected from rounding; it does not change the underlying circumference relationship.
Keep sixty meters per minute, but double the diameter to two hundred millimeters. The circumference doubles, so only half as many turns are needed. The result is about ninety-five point four nine three R P M. The larger rim covers twice the distance per revolution at the same linear speed.
If diameter is entered in millimeters, an equivalent formula is one thousand times surface speed, divided by pi times diameter in millimeters. Do not use that extra one thousand when diameter is already in meters. Also use diameter, not radius; substituting radius would make the calculated R P M twice as large.
In machining, cutting or surface speed is different from feed speed along the workpiece. The circumference formula needs speed at the relevant rotating diameter. For a belt-driven wheel, the simple relationship also assumes no slip. A calculated rotation rate is a geometric result, not confirmation that a particular machine can operate safely at it.
Match the length units, calculate circumference as pi times diameter, and divide surface speed by that circumference. Multiply back to check. For sixty meters per minute at a one-hundred-millimeter diameter, the answer is about one hundred ninety-one revolutions per minute, with rotation shown slowed in this illustration.