Belt Drive Calculator Formula

Understand the math behind the belt drive calculator. Each variable explained with a worked example.

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Formulas Used

Speed Ratio

speed_ratio = ratio

Driven Pulley Speed

driven_rpm = driver_rpm / ratio

Approx. Belt Length

belt_length = 2 * centre_dist + pi * (dia_driver + dia_driven) / 2 + pow(dia_driven - dia_driver, 2) / (4 * centre_dist)

Variables

VariableDescriptionDefault
dia_driverDriver Pulley Diameter (D1)(mm)150
dia_drivenDriven Pulley Diameter (D2)(mm)300
centre_distCentre Distance (C)(mm)500
driver_rpmDriver Speed(RPM)1750
ratioDerived value= dia_driven / dia_drivercalculated

How It Works

Belt Drive Speed and Belt Length

Belt drives transmit power between shafts using friction between a belt and pulleys.

Speed Ratio

N2 = N1 x D1 / D2 (assuming no belt slip)

Belt Length (open drive)

L = 2C + pi(D1 + D2)/2 + (D2 - D1)^2 / (4C)

where C is the shaft centre distance. This approximate formula works well for standard configurations.

Worked Example

150 mm driver at 1750 RPM driving a 300 mm pulley, centres 500 mm apart.

dia_driver = 150dia_driven = 300centre_dist = 500driver_rpm = 1750
  1. 01Speed ratio = 300/150 = 2.0
  2. 02Driven speed = 1750 / 2.0 = 875 RPM
  3. 03Belt length = 2x500 + pi(150+300)/2 + (300-150)^2/(4x500)
  4. 04L = 1000 + 706.9 + 11.25 = 1718 mm

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