Pulley System Calculator
This pulley calculator analyzes a system of two pulleys joined by a conveyor belt (belt drive). Use it to calculate pulley RPM (revolutions per minute), belt velocity, belt length, belt tension, and torque for both driver and driven pulleys.
What is a Pulley System?
A pulley system consists of two pulleys (usually of different diameters) connected by a belt loop. The driver pulley receives power and rotates; the driven pulley turns because of the force transmitted through the belt. Pulleys are simple machines that transmit rotational motion and change speed or torque between shafts.
Pulley Formulas
1. RPM and Speed Relationship
For a two-pulley belt drive, the product of diameter and RPM is equal for both pulleys:
d₁ × n₁ = d₂ × n₂
where d₁ and d₂ are pulley diameters, and n₁, n₂ are their angular velocities in RPM. You can use this formula to find any of the four values.
2. Belt Velocity
The speed of the belt is calculated as:
v = π × d₁ × n₁ / 60
where the angular frequency is in RPM and belt velocity in meters per second (m/s).
3. Belt Length
The belt length depends on both pulley diameters and the center-to-center distance D:
L = (d₁ × π / 2) + (d₂ × π / 2) + 2D + (d₁ − d₂)² / (4D)
Leave the center distance blank if you only need RPM and belt velocity calculations.
4. Belt Tension
The tension in the belt depends on belt velocity and transmitted power P:
F = P / v
Enter power in Watts (metric) or horsepower (imperial).
5. Torque
Drive torque (and driven torque) can be calculated as:
T = P / (2 × π × n / 60)
where n is the pulley's RPM. The calculator returns both driver and driven torque values.
Metric vs. Imperial Systems
The calculator supports both measurement systems:
- Metric: diameters and distances in millimeters (mm), power in Watts (W), belt velocity in m/s, torque in N·m
- Imperial (American): diameters and distances in inches (in), power in horsepower (hp), belt velocity in m/s, torque in N·m
How to Use This Calculator
- Select your unit system (metric or imperial)
- Enter the driver pulley diameter and its RPM
- Enter the driven pulley diameter (the driven RPM will be calculated automatically)
- Optionally enter the center-to-center distance to get belt length
- Optionally enter the transmitted power to calculate belt tension and torque
- Click Calculate
Frequently Asked Questions
What is the speed ratio of pulleys?
The speed ratio equals d₁/d₂. A ratio greater than 1 means the driven pulley spins faster (speed increase). A ratio less than 1 means it spins slower (torque increase).
How does pulley size affect RPM?
A smaller driven pulley spins faster than the driver (higher RPM). A larger driven pulley spins slower. This is the principle behind gear reduction and speed multiplication in belt drives.
What units does this calculator use?
In metric mode: mm for dimensions, W for power, m/s for belt speed, N for tension, N·m for torque. In imperial mode: inches for dimensions, hp for power; output remains in SI units (m/s, N, N·m).
Can I use this for timing belts or V-belts?
Yes. The geometric formulas apply to any flat, V-belt, or timing belt system. The tension formula assumes an ideal (no-slip, no-loss) belt drive.