EngineeringMechanismsGCSE
NESAEdexcelAQAOCRCCEAWJECIBBrevet (DNB)

Belt/Pulley Drive Ratio Calculator

Calculate speed ratio for belt and pulley systems.

Use the free calculatorCheck the variablesOpen the advanced solver
Open Advanced Calculator
This is the free calculator preview. Advanced walkthroughs stay in the app.
Result
Ready
Driven Speed

Formula first

Overview

The Belt/Pulley Drive Ratio equation defines the relationship between the rotational speeds and diameters of two pulleys linked by a continuous belt. It assumes that the tangential velocity at the surface of both pulleys is equal, which implies the absence of belt slippage during operation.

Symbols

Variables

n_1 = Driver Speed, n_2 = Driven Speed, D_1 = Driver Diameter, D_2 = Driven Diameter

Driver Speed
Driven Speed
Driver Diameter
Driven Diameter

Apply it well

When To Use

When to use: Apply this formula when designing or troubleshooting mechanical transmissions where power is transferred via belts between two parallel shafts. It is the standard calculation for V-belts, synchronous belts, and flat belts in systems where precise speed control or torque multiplication is required. It assumes the belt is inextensible and maintains constant contact without significant slipping.

Why it matters: This equation allows engineers to accurately step down high motor speeds to usable machine speeds, or vice-versa, without the complexity of gears. Mastering this ratio is crucial for optimizing the mechanical advantage of a system, as changing pulley diameters directly influences the torque and velocity delivered to the driven component.

Avoid these traps

Common Mistakes

  • Inverting the ratio.
  • Confusing driver and driven.
  • Forgetting units match.

One free problem

Practice Problem

A motor rotating at 1750 RPM is equipped with a driver pulley that has a diameter of 4 inches. This motor is connected to a pump with a driven pulley diameter of 10 inches. Calculate the resulting rotational speed of the pump.

Driver Speed1750 rpm
Driver Diameter4 mm
Driven Diameter10 mm

Solve for:

Hint: The driven speed is the product of the driver speed and the ratio of the driver diameter to the driven diameter.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Machine Elements in Mechanical Design by Robert L. Mott
  2. Fundamentals of Machine Component Design by Juvinall, Marshek, Brown, and Stone
  3. Wikipedia: Belt (mechanical)
  4. Science for Engineering by John Bird
  5. Britannica
  6. Shigley's Mechanical Engineering Design
  7. Shigley's Mechanical Engineering Design, 11th Edition by Richard G. Budynas and J. Keith Nisbett
  8. OCR GCSE Engineering — Mechanical Engineering