RPM to Linear Speed Calculator (Surface Speed)
Convert rotational speed to linear or surface speed from wheel, pulley, roller, spindle or tyre diameter — m/s, km/h, mph, ft/min (SFM) and m/min — find the rpm needed for a target speed or the diameter that gives it, read a tyre size such as 205/55R16, allow for a gear or pulley ratio and slip, and see speed across a range of rpm.
How it works
v = π × D × rpm ÷ 60 (m/s with D in metres); rpm = v × 60 ÷ (π × D); D = v × 60 ÷ (π × rpm); SFM = π × D(in) × rpm ÷ 12; cutting speed (m/min) = π × D(mm) × rpm ÷ 1000; wheel rpm = motor rpm ÷ ratio; with slip s: v × (1 − s); tyre D = rim × 25.4 + 2 × width × aspect ratio
Every revolution moves a point on the rim one circumference forward, so linear speed is circumference times revolutions per unit time. The same arithmetic serves very different jobs: a car’s road speed from tyre size and wheel rpm, a conveyor belt’s speed from its drive pulley, the surface speed of a lathe workpiece or grinding wheel (machinists call it surface feet per minute, or cutting speed in m/min, and pick the rpm from the material’s recommended value), and the tip speed of a fan or propeller. You can solve for the speed, for the rpm that gives a target speed, or for the diameter that gives it at a fixed rpm. Under More options you can type a tyre size — car (205/55R16), off-road (31x10.50R15) or bicycle (700x25c, 25-622) — instead of measuring the diameter, add a gearbox or pulley reduction so the rpm you enter is the motor’s, and allow for belt slip or the few per cent a tyre loses when it is loaded.
Worked example
A 660 mm (26″) bicycle wheel at 600 rpm: circumference 2.0735 m → 20.73 m/s, or 74.64 km/h. The same wheel needs 482.3 rpm for 60 km/h. A 205/55R16 car tyre is 16 × 25.4 + 2 × 205 × 0.55 = 632 mm across; at 60 km/h it turns 503.7 rpm, and with a 3.5:1 final drive the shaft before it turns 1,763 rpm.
Sources: Machining speeds and feeds — Wikipedia · Tire code (ISO metric sizing) — Wikipedia
Frequently asked questions
How do I get wheel rpm from engine rpm?
Divide by the gear ratio and the final-drive ratio: 3,000 rpm in a 1.0:1 gear with a 3.5:1 differential is 857 rpm at the wheels. Enter the combined ratio under More options and type the engine rpm.
What rpm for a 100 mm workpiece in aluminium at 90 m/min?
rpm = 90 × 1000 ÷ (π × 100) ≈ 286. Choose “RPM for a target speed”, enter 100 mm and 90 with m/min as the speed unit.
How do I convert SFM to rpm?
rpm = SFM × 12 ÷ (π × diameter in inches). For 300 SFM on a 2 in bar that is 300 × 12 ÷ (π × 2) ≈ 573 rpm. Pick ft/min (SFM) as the speed unit and inches as the diameter unit.
How is a tyre diameter worked out from its size?
For a size like 205/55R16, the sidewall is 55% of the 205 mm width, so the outside diameter is 16 × 25.4 + 2 × 205 × 0.55 = 632 mm. Under load the rolling diameter is about 2–3% smaller; enter that as slip if you need road speed to within a few per cent.
What is the difference between angular and linear speed?
Angular speed (rpm or rad/s) is how fast the part turns and is the same everywhere on it. Linear speed is how fast a point moves and grows with diameter, which is why a large wheel at the same rpm covers more ground.
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This calculator is for educational purposes. Double-check important results before acting on them.