Pulley Speed Ratio Calculator

Calculate RPM, speed ratio, and belt speed for two-pulley systems. Includes advanced concepts: pitch diameter, slip/efficiency, and belt speed limits.

Speed Ratio Formula: i = Ddriver / Ddriven    RPMdriven = RPMdriver × i × η

Belt Speed (ft/min): V = (π × Ddriver × RPMdriver) / 12 (D in inches)

Torque Ratio (ideal): Tdriven = Tdriver / i (power constant)

in
in
RPM
in
Subtracted from outer diameter to estimate pitch diameter.
Accounts for slip/belt losses.
1:1 (4",4",1750)
2:1 overdrive (6",3")
1:2 reduction (3",6")
HVAC fan (8",12",1160)
Motor to pump (2.5",5",3450)
Calculating...

Understanding Pulley Speed Ratio

In a belt-driven system, the speed ratio between two pulleys determines how rotational speed and torque are transferred. The fundamental relationship is inverse: a larger driven pulley reduces speed but increases torque.

Core Formulas:

  • Speed Ratio (i) = Ddriver / Ddriven (using pitch diameters)
  • RPMdriven = RPMdriver × i × η (η = efficiency, accounts for slip)
  • Belt Speed (ft/min) = (π × Ddriver × RPMdriver) / 12 (D in inches)
  • Torquedriven = Torquedriver / i (ideal, neglecting losses)
  • Power (hp) = (Torque × RPM) / 5252 (constant across ideal drive)

1. Torque and Power Relationship

In an ideal system (no friction, no slip), the power transmitted is constant: P = Tdriver × ωdriver = Tdriven × ωdriven. Since ω = 2π×RPM/60, we get Tdriven = Tdriver × (RPMdriver/RPMdriven) = Tdriver / i. Thus, a speed reduction (i < 1) increases torque, while an overdrive (i > 1) decreases torque.

2. Pitch Diameter vs. Outside Diameter

For V-belts, the effective diameter is the pitch diameter—the diameter at the neutral axis of the belt. If you only know the outside diameter, subtract a correction factor (typically 0.2 to 0.5 inches depending on belt cross-section). For accurate results, use the manufacturer’s pitch diameter. This calculator allows you to select diameter type and apply an offset.

3. Belt Slip and Efficiency

In real drives, belt slip (both elastic creep and full slip) reduces the driven RPM below the theoretical value. Typical efficiencies range from 95% to 98% for V-belts. The formula RPMactual = RPMtheoretical × η, where η is the efficiency factor. High belt speeds or low tension increase slip.

4. Multi-Stage Drives

When multiple pulley pairs are used in series (e.g., motor → intermediate shaft → load), the overall speed ratio is the product of the individual ratios: itotal = i1 × i2 × … . This calculator handles a single stage; for multi-stage, compute each stage separately and multiply the ratios.

5. Center Distance and Belt Length

While center distance (C) does not affect the speed ratio, it influences belt length and wrap angle. For an open belt drive, the approximate belt length is:

L ≈ 2C + 1.57(Ddriver + Ddriven) + (Ddriver - Ddriven)² / (4C)

Wrap angle on the smaller pulley should ideally exceed 120° to prevent slip.

6. Belt Types and Speed Limits

Common V-belt cross-sections (A, B, C, D) have recommended maximum speeds:

Belt Section Max Speed (ft/min) Typical Applications
A (1/2" top width) 5000 Light machinery, small fans
B (21/32") 6500 General industrial
C (7/8") 7500 Heavy loads, compressors
D (1-1/4") 10000 Large industrial drives

Exceeding these speeds may cause excessive heat and premature failure. The belt speed calculated by this tool should be checked against the belt manufacturer’s rating.

7. Step-by-Step Example

1

Given: Motor RPM = 1750, driver pulley outer diameter = 4", offset = 0.3", efficiency = 0.97, driven pulley outer diameter = 10".

2

Pitch diameters: D1 = 4 - 0.3 = 3.7", D2 = 10 - 0.3 = 9.7".

3

Speed ratio: i = 3.7 / 9.7 = 0.381 (reduction).

4

Driven RPM: 1750 × 0.381 × 0.97 ≈ 647 RPM.

5

Belt speed: (π × 3.7 × 1750) / 12 ≈ 1695 ft/min.

8. Practical Considerations & Safety

  • Tension: Proper belt tension is essential to prevent slip and maximize life. Use a tension gauge.
  • Alignment: Misalignment causes uneven wear and reduces efficiency.
  • Environment: Temperature, oil, and dust affect belt performance.
  • Safety: Always install guards around belt drives to prevent entanglement.

9. References & Standards

For detailed design, refer to ANSI/RMA IP-20, ISO 4184, or manufacturer catalogs (Gates, ContiTech, etc.).

Calculator assumptions: When "Pitch Diameter" is selected, values are used as entered. When "Outer Diameter" is selected, the offset is subtracted to estimate pitch diameter. Efficiency multiplies the theoretical driven RPM. Results are theoretical; always verify with real-world measurements.

Frequently Asked Questions

The driver pulley is connected to the power source (motor). The driven pulley is connected to the load (fan, pump, etc.). Power flows from driver to driven via the belt.

No, the speed ratio is determined solely by the diameters of the pulleys. Belt length affects center distance and wrap angle, but not the ratio.

This calculator uses inches for diameter and RPM for rotational speed. Belt speed is given in feet per minute (common in US engineering). You can convert mm to inches by dividing by 25.4.

Simply rearrange the formula: RPMdriver = RPMdriven / (i × η). You can swap the roles mentally or use our calculator by treating the known as driver.

It assumes no slip and uses pitch diameter. Actual belt speed may vary slightly due to belt thickness and slip, but it's accurate for most design purposes.