RPM Calculator

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Driven pulley rpm from the diameters, spindle rpm from cutting speed for lathe, milling and drilling (and back), and a motor's synchronous speed from frequency and poles

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Enter the values

What to work out

Driver pulley speed (N₁)

Driver pulley diameter (D₁)

Driven pulley diameter (D₂)

Belt slip (optional)

Result

Driven pulley speed (N₂)

480rpm

Velocity ratio (N₁ ÷ N₂): 3
Belt speed: 7.54 m/s

The same rule works for gears with tooth counts in place of diameters: N₂ = N₁ × T₁ ÷ T₂ (see the gear ratio calculator).

Working

N₂ = N₁ × D₁ ÷ D₂ = 1440 × 100 ÷ 300 = 480 rpm
v = π × D₁ × N₁ ÷ 60 = π × 0.1 × 1440 ÷ 60 = 7.54 m/s

Formulas

N₂ = N₁ × D₁ ÷ D₂ (with slip: × (1 − s))
N = 1000 × V ÷ (π × D) (V in m/min, D in mm)
V = π × D × N ÷ 1000
Ns = 120 × f ÷ P, N = Ns × (1 − s)

N₁, N₂: driver and driven speeds (rpm)
D₁, D₂: driver and driven diameters
V: cutting speed (m/min)
D: work diameter (lathe) or cutter/drill diameter (milling, drilling) (mm)
f: frequency (Hz)
P: number of poles
s: slip (as a fraction)

Assumptions

Belt thickness is ignored for the pulleys; allowing for a thickness t, use (D + t) in place of D.
Cutting speed is the surface speed at the work (or cutter) diameter.

Sources: R. S. Khurmi & J. K. Gupta, Theory of Machines · Hajra Choudhury, Elements of Workshop Technology (Vol. II: Machine Tools) · B. L. Theraja, Electrical Technology (Vol. II: AC Machines)

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