EngineeringFormulaMechanical Engineering
Pulley Ratio Calculator
Calculate ideal belt-drive pulley ratio, driven shaft speed, or the required driver or driven pulley diameter using pitch-diameter relationships.
A two-pulley belt drive trades shaft speed against pulley size. In the ideal no-slip model, the belt has the same pitch-line speed at both pulleys, so driver speed times driver pitch diameter equals driven speed times driven pitch diameter. This calculator uses that relationship to solve for pulley ratio, driven speed, or the pulley diameter needed to hit a target ratio.
D1 · Pitch diameter of the driving pulley connected to the power source.
D2 · Pitch diameter of the driven pulley connected to the output shaft.
Convention used here: i = n1 / n2 = D2 / D1. Ratios above 1 mean speed reduction at the driven shaft; ratios below 1 mean speed increase.
Solution
Enter the required values to calculate pulley ratio.
i = D2 / D1
Formula Sheet
- iPulley Ratio
- n1Driver Speed
- n2Driven Speed
- D1Driver Pulley Diameter
- D2Driven Pulley Diameter
Variables & Units
| Symbol | Variable | Description | Common Units |
|---|---|---|---|
| i | Pulley Ratio | Drive ratio defined on this page as driver speed divided by driven speed, equal to driven pitch diameter divided by driver pitch diameter. | |
| n1 | Driver Speed | Rotational speed of the input or driving pulley. | rpm, rev/s, Hz, rad/s |
| n2 | Driven Speed | Rotational speed of the output or driven pulley. | rpm, rev/s, Hz, rad/s |
| D1 | Driver Pulley Diameter | Pitch diameter of the driving pulley connected to the power source. | mm, cm, m, km, in, ft |
| D2 | Driven Pulley Diameter | Pitch diameter of the driven pulley connected to the output shaft. | mm, cm, m, km, in, ft |
How to Use This Calculator
- 01Choose what to solve for first: pulley ratio, driven speed, driver pulley diameter, or driven pulley diameter.
- 02Enter the known values and select matching units. Diameter values should be pitch diameters when available, not outside diameters.
- 03Use the ratio convention shown on this page: i = n1 / n2 = D2 / D1, where 1 is the driver and 2 is the driven pulley.
- 04Select Calculate to see the result, the active formula, and a substitution line with coherent units.
- 05Use the output as an ideal speed target first, then verify belt length, wrap angle, belt horsepower rating, and slip margin before purchasing pulleys or belts.
How the Formula Works
In an ideal belt drive with no slip, both pulleys share the same belt pitch-line velocity. Because that linear speed equals rotational speed multiplied by pulley radius or diameter, the kinematic relationship becomes n1 D1 = n2 D2. Rearranging gives the common drive-ratio form i = n1 / n2 = D2 / D1.
That inverse size-speed relationship means a larger driven pulley turns more slowly than the driver, while a smaller driven pulley turns faster. On this page, a ratio greater than 1 means speed reduction at the driven shaft; a ratio below 1 means speed increase. Real belt drives can deviate slightly because of slip, creep, and the difference between pitch diameter and outside diameter.
Worked Example 01
Pulley ratio from diameters
Known
- Driver Pulley Diameter (D1): 100 mm
- Driven Pulley Diameter (D2): 250 mm
Formula
i = D2 / D1
Substitution
i = 250 / 100
Result
i = 2.5
A 250 mm driven pulley on a 100 mm driver gives a 2.5:1 reduction ratio, so the driven shaft turns at 1 / 2.5 = 40% of the driver speed.
Worked Example 02
Driven speed from driver speed and pulley sizes
Known
- Driver Speed (n1): 1,800 rpm
- Driver Pulley Diameter (D1): 100 mm
- Driven Pulley Diameter (D2): 250 mm
Formula
n2 = n1 D1 / D2
Substitution
n2 = 1,800 × 100 / 250
Result
n2 = 720 rpm
Because the driven pulley is 2.5 times larger than the driver, the output shaft rotates 2.5 times more slowly in the ideal model.
Worked Example 03
Required driver pulley diameter
Known
- Pulley Ratio (i): 3
- Driven Pulley Diameter (D2): 300 mm
Formula
D1 = D2 / i
Substitution
D1 = 300 / 3
Result
D1 = 100 mm
To achieve a 3:1 reduction with a 300 mm driven pulley, the driver pitch diameter should be 100 mm.
Worked Example 04
Required driven pulley diameter
Known
- Pulley Ratio (i): 0.5
- Driver Pulley Diameter (D1): 8 in
Formula
D2 = i D1
Substitution
D2 = 0.5 × 8
Result
D2 = 4 in
A ratio below 1 means speed increase. Using a 4 in driven pulley with an 8 in driver doubles the driven shaft speed in the ideal model.
Applications
- 01Sizing motor and machine pulleys to hit a target driven RPM
- 02Checking whether a pulley swap will reduce or increase output speed
- 03Early-stage layout work for fans, pumps, compressors, conveyors, and workshop machinery
Assumptions
- 01Uses the ideal no-slip belt-drive relation n1 D1 = n2 D2.
- 02Pulley diameters are treated as pitch diameters; outside diameters can introduce small errors.
- 03The result is purely kinematic and does not include efficiency, torque limits, wrap angle, or belt selection.
Where This Model Stops
- 01Does not model belt slip, creep, stretch, or startup/transient behavior.
- 02Not intended to replace detailed belt-drive design checks such as horsepower rating, center distance, belt length, or wrap-angle verification.
- 03Multi-stage drives, idlers, stepped pulleys, and toothed pulleys with tooth-count-based ratios may need a different analysis approach.
- 04Does not calculate torque capacity, belt tension, bearing load, or whether a selected belt profile is suitable for the motor horsepower.
- 05Outside diameter, pitch diameter, and effective diameter can differ. For close RPM targets, use manufacturer pitch-diameter data instead of measuring the pulley rim.
References
- [1]Belt Drives
ScienceDirect Topics
Summarizes the equal pitch-line velocity relationship and the inverse speed-diameter behavior of belt drives.
- [2]Drive Ratio
PTI Glossary
States the belt-drive ratio convention i = n1 / n2 = D2 / D1 and clarifies that pitch diameters should be used.
- [3]What Is the Belt Drive Ratio and How Is It Calculated?
Engineer Fix
Provides a clear engineering explanation of why pulley speed varies inversely with pulley diameter.
Frequently Asked Questions
What pulley-ratio convention does this calculator use?
It uses i = n1 / n2 = D2 / D1, where 1 is the driver and 2 is the driven pulley. Under that convention, ratios above 1 mean speed reduction and ratios below 1 mean speed increase.
Should I use outside diameter or pitch diameter?
Pitch diameter is the correct quantity for belt-drive ratio calculations because it reflects the belt's effective running line. Outside diameter can be a rough approximation, but it may shift the result slightly, especially with V-belts.
Why might the actual driven speed differ from the calculator result?
Real systems can lose a small amount of speed because of belt slip, creep, flexing, and manufacturing tolerances. The calculator gives the ideal theoretical ratio, which is most useful for early sizing and quick checks.
Does a larger driven pulley increase torque?
Ideally yes: a larger driven pulley reduces output speed and increases output torque by approximately the same ratio. Real torque gain is lower after belt efficiency, slip, and tension limits are considered.
How is this different from the Belt Length or Belt Speed Calculator?
Pulley Ratio solves the speed relationship between two pulleys. Belt Length estimates the belt needed for a center distance and pulley diameters, while Belt Speed calculates the belt's linear speed from pulley diameter and RPM.