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

Frequently Asked Questions

How much belt slip should I expect?

Well-tensioned V-belts typically have 1-3% slip. Timing (synchronous) belts have zero slip. Flat belts may slip 2-5%. Account for slip by reducing the calculated driven speed accordingly.

How do I select a standard belt size?

Calculate the required belt length, then choose the next available standard size from the manufacturer. Standard V-belt lengths come in set increments (typically 25 mm steps for industrial belts).

What determines the centre distance?

Minimum centre distance should be at least the larger pulley diameter. Maximum is limited by belt sag and tension requirements. Ideal range: C = 0.7 to 2.0 times the sum of pulley diameters.

Learn More

Guide

How to Calculate Gear Ratios: Complete Engineering Guide

Learn how to calculate gear ratios for spur gears, compound gear trains, and planetary systems. Covers speed, torque, and efficiency relationships with practical examples.

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