What is the pulley ratio formula?

For a simple belt drive, pulley ratio can be expressed as driven pulley diameter divided by driver pulley diameter. Under ideal no-slip conditions this also equals driver RPM divided by driven RPM.

How do I calculate driven pulley RPM?

Driven RPM equals driver RPM multiplied by driver pulley diameter and divided by driven pulley diameter.

Does a larger driven pulley reduce speed?

Yes. In a simple belt drive, a larger driven pulley normally reduces output rotational speed when the driver remains unchanged.

How is pulley belt speed calculated?

Belt speed can be calculated as pi multiplied by pulley diameter in meters multiplied by RPM, divided by 60.

Does belt slip affect pulley speed?

Yes. Belt slip can make actual driven speed lower or otherwise different from the theoretical no-slip pulley ratio calculation.

Pulley Ratio Calculator

Q: What does a 2 to 1 pulley ratio mean?

Using a driven-to-driver diameter convention, a 2 to 1 ratio means the driven pulley is twice the diameter of the driver, producing approximately half the driver RPM under ideal conditions.

Calculate pulley ratio, driver or driven RPM, and pulley diameter for belt-drive systems with automatic unit conversion and belt-speed results.

Calculate Pulley Ratio

What would you like to calculate?

Driver Pulley Speed (RPM)

Driven Pulley Speed (RPM)

Driver Pulley Diameter (D₁)

Unit

Driven Pulley Diameter (D₂)

Unit

Result Diameter Unit

Pulley Speed Relationship N₁ × D₁ = N₂ × D₂. Therefore N₂ = N₁ × D₁ / D₂.

Calculation Result

Driven Pulley Speed

0 RPM

Formula Used N₂ = N₁ × D₁ / D₂

Drive Behavior Waiting for calculation

Pulley Ratio 0 : 1

Driver Speed 0 RPM

Driven Speed 0 RPM

Driver Diameter 0 mm

Driven Diameter 0 mm

Belt Speed 0 m/s

Driver Pulley Belt Drive Driven Pulley

Results assume an ideal belt drive with no belt slip and use pulley pitch/effective diameters. Real speeds can differ because of slip, belt stretch, and operating conditions.

What Is a Pulley Ratio Calculator?

A Pulley Ratio Calculator determines the speed relationship between a driver pulley and a driven pulley in a belt-drive system. The ratio depends on the effective diameters of the two pulleys.

When the driven pulley is larger than the driver pulley, the driven shaft normally rotates more slowly. When the driven pulley is smaller, the driven shaft rotates faster.

This calculator can solve for driven RPM, driver RPM, either pulley diameter, or pulley ratio. It also calculates the theoretical belt linear speed when driver RPM and diameter are available.

Pulley Ratio Calculator Formulas

Basic Pulley Relationship N₁D₁ = N₂D₂

The ideal speed-diameter relationship for a two-pulley belt drive.

Driven RPM N₂ = N₁ × D₁ / D₂

Calculates driven shaft speed from driver speed and pulley sizes.

Driver RPM N₁ = N₂ × D₂ / D₁

Calculates required driver speed for a specified driven speed.

Driven Diameter D₂ = N₁ × D₁ / N₂

Calculates the driven pulley diameter required for a target RPM.

Driver Diameter D₁ = N₂ × D₂ / N₁

Calculates the driver pulley size needed for the required speed.

Pulley Ratio Ratio = D₂ / D₁

Driven-to-driver diameter ratio, equivalent to N₁/N₂ for an ideal belt drive.

Pulley Belt Speed Formula

The linear speed of the belt can be estimated from driver pulley diameter and rotational speed.

v = πDN / 60

In this formula, D is pulley diameter in meters, N is rotational speed in revolutions per minute, and v is belt speed in meters per second.

The ideal calculation assumes the belt moves at the same linear speed around both pulleys without slipping.

Pulley Ratio Formula Symbols

N₁ — Driver RPM

Rotational speed of the driving pulley or input shaft.

N₂ — Driven RPM

Rotational speed of the driven pulley or output shaft.

D₁ — Driver Diameter

Effective or pitch diameter of the driver pulley.

D₂ — Driven Diameter

Effective or pitch diameter of the driven pulley.

Ratio

Driven pulley diameter divided by driver pulley diameter.

v — Belt Speed

Theoretical linear speed of the belt.

How to Use the Pulley Ratio Calculator

Select What You Want to Calculate

Choose driven RPM, driver RPM, driven diameter, driver diameter, or pulley ratio.

Enter Pulley Speeds

Enter the known driver and driven RPM values required for your selected calculation.

Enter Pulley Diameters

Enter the effective pulley diameters and select millimeters, centimeters, inches, meters, or feet.

Calculate

Click Calculate Pulley Ratio to display the main answer, ratio, RPM values, and theoretical belt speed.

Pulley Ratio Calculation Example

Suppose a motor turns a 4-inch driver pulley at 1800 RPM, and the driven pulley has a diameter of 8 inches.

Calculate the pulley ratio:

Ratio = D₂ / D₁ Ratio = 8 / 4 = 2

Now calculate the driven RPM:

N₂ = N₁ × D₁ / D₂ N₂ = 1800 × 4 / 8 N₂ = 900 RPM

The system therefore has a 2:1 pulley ratio and reduces the output speed from 1800 RPM to approximately 900 RPM under ideal no-slip conditions.

Pulley Ratio and Speed Reduction

A pulley system can increase or decrease shaft speed by changing the relative diameters of the driver and driven pulleys.

Speed Reduction

If the driven pulley is larger than the driver pulley, the driven shaft rotates more slowly.

D₂ > D₁ → N₂ < N₁

Speed Increase

If the driven pulley is smaller than the driver pulley, the driven shaft rotates faster.

D₂ < D₁ → N₂ > N₁

1:1 Drive

When both pulleys have equal effective diameters, their theoretical rotational speeds are equal.

How Pulley Ratio Affects Torque

Ignoring system losses, reducing rotational speed with a larger driven pulley can increase available output torque. Increasing output speed normally decreases available torque.

The actual torque transmitted by a belt-drive system also depends on belt tension, pulley geometry, friction, belt type, and mechanical efficiency, so pulley ratio alone does not determine the safe torque capacity of the system.

Pulley Ratio Calculator Applications

Industrial Machinery

Estimate shaft speed relationships in belt-driven machines.

Fans & Blowers

Estimate driven fan speed from motor RPM and pulley sizes.

Mechanical Drives

Compare speed reduction and speed-increase pulley arrangements.

Workshop Equipment

Calculate belt-drive ratios for common rotating equipment.

Engineering

Solve RPM, diameter, belt-speed, and ratio problems.

Frequently Asked Questions

For a simple belt drive, the driven-to-driver pulley ratio can be calculated as D₂/D₁. Under ideal no-slip conditions this is also equal to N₁/N₂.

Driven RPM is calculated using N₂ = N₁ × D₁ / D₂, where N₁ is driver RPM, D₁ is driver diameter, and D₂ is driven diameter.

Yes. In a simple belt drive, increasing the driven pulley diameter while keeping the driver unchanged reduces driven RPM.

Using the driven-to-driver diameter convention, a 2:1 ratio means the driven pulley is twice the diameter of the driver pulley and the ideal driven speed is approximately half the driver speed.

Belt speed can be estimated using v = πDN/60 when pulley diameter D is in meters and rotational speed N is in RPM.

Yes. Belt slip can cause actual driven RPM to differ from the theoretical value calculated from pulley diameters.