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Pulley Speed and Belt Length Calculation

Guide · Updated October 28, 2026

Belt-driven drill presses, lathes, grinders and many shop fixtures set speed by pulley size. The rule is simple: the surface speed of the belt is the same on both pulleys, so driver diameter × driver rpm = driven diameter × driven rpm. The same idea gives belt speed, and a standard formula gives the belt length you need for a given center distance.

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Step by step

Measure pulley diameters: Use the pitch diameter of a V-belt pulley, where the belt rides, not the outside diameter.
Know the motor speed: Common induction motor speeds are about 1725 or 3450 rpm at 60 Hz.
Find driven rpm: Driven rpm = driver rpm × driver diameter ÷ driven diameter.
Check belt speed: Belt speed (ft/min) = π × D × rpm ÷ 12.
Find belt length: L ≈ 2C + π(D + d)/2 + (D − d)²/(4C).
Pick a stock belt: Choose the nearest standard length and set the motor mount to take up the difference.

The formulas

Speed ratio: N2 = N1 × D1 ÷ D2
Pulley size for a target speed: D2 = D1 × N1 ÷ N2
Belt speed: V (ft/min) = π × D × rpm ÷ 12, with D in inches
Open belt length: L ≈ 2C + 1.5708 × (D + d) + (D − d)² ÷ (4C)
Compound drive: multiply the ratios of each stage

C is the center distance between shafts, D the large pulley and d the small pulley, all in the same units.

Worked example: drill press speed

A 1725 rpm motor has a 2 in pulley driving a 6 in spindle pulley. Spindle speed = 1725 × 2 ÷ 6 = 575 rpm. To drill a 1/2 in hole in mild steel at about 80 SFM you want 3.82 × 80 ÷ 0.5 ≈ 611 rpm, so this step is close. For a 1/4 in drill at 1222 rpm you would move to steps closer to 1:1.5.

Worked example: belt length

Motor pulley d = 3 in, driven pulley D = 6 in, center distance C = 12 in. L = 2 × 12 + 1.5708 × 9 + (3)² ÷ 48 = 24 + 14.14 + 0.19 = 38.3 in. You would pick a stock belt near 38 in pitch length and adjust the motor mount. Belt speed on the motor pulley = π × 3 × 1725 ÷ 12 ≈ 1355 ft/min.

Worked example: compound drive

A countershaft has 2:1 from motor to countershaft and 3:1 from countershaft to spindle. With a 1725 rpm motor, spindle speed = 1725 ÷ 2 ÷ 3 = 288 rpm. Torque at the spindle goes up by about the same ratio, less belt losses.

Belt speed and safety

Most V-belts are rated for speeds up to several thousand ft/min; check the belt maker limit. Keep all belts guarded. On grinders, never change pulleys to run a wheel faster than the maximum rpm marked on the wheel blotter.

Common problems

Using pulley outside diameter instead of pitch diameter, forgetting motor slip (actual 1725 rpm motors run near nameplate, not 1800), and choosing a belt that bottoms in the groove. Check actual spindle rpm with a tachometer.

FAQ

How do I calculate driven pulley rpm?

Driver rpm × driver diameter ÷ driven diameter.

How do I find belt length?

L ≈ 2C + 1.5708(D + d) + (D − d)²/(4C).

What is pitch diameter?

The diameter where the belt rides in a V-groove, smaller than the outside diameter.

How do I check a shaft diameter for a pulley bore?

Check the gage itself before trusting a measurement: gage blocks set mics, calipers and indicators; build any stack free at gageblockcalc.com.

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