Pulley Types & Calculations: Teeth, Ratios, and a Common-Pulley Table
Jun 28, 2026
Pulleys turn motor rotation into a gear ratio without meshing gears — a small drive pulley and a larger load pulley linked by a belt trade speed for torque exactly like a gear stage. This guide leads with the numbers you need at the drivetrain input — how to size a stage from tooth counts or pulley diameters — then covers the common pulley types, belt length, and how RPM and torque change across a stage.
TL;DR
For a toothed (timing) belt, the ratio is just the tooth counts: ratio = load teeth ÷ drive teeth. A 12-tooth drive into a 48-tooth load is a 4:1 reduction — the output turns 4× slower and (ideally) delivers 4× the torque. For flat or V-belts, use pitch diameters instead of teeth: ratio = load PD ÷ drive PD. Pitch diameter from teeth is PD = (teeth × belt pitch) ÷ π.
Sizing a stage from teeth or diameter
In the Drivetrain Builder each gear stage takes a Drive side and a Load side value — either tooth counts (for timing pulleys/sprockets) or pulley diameters (for flat/V-belts). Both reduce to the same stage ratio.
From tooth counts (timing belts, chain sprockets)
stage ratio = load teeth / drive teeth
The teeth cancel the units, so you can type raw counts straight into the builder. Example: drive 20, load 60 → 3:1 reduction.
From pulley diameters (flat / V-belt)
stage ratio = load pitch diameter / drive pitch diameter
Use the pitch diameter (where the belt's tension line sits), not the outside diameter — for a V-belt the pitch line is below the rim. Mixing OD and PD is the most common sizing error.
Pitch diameter from tooth count
For a timing pulley the pitch diameter follows directly from the tooth count and the belt's tooth pitch p:
PD = (number of teeth × belt pitch p) / π
So a 20-tooth GT2 pulley (p = 2 mm) has PD = (20 × 2) ÷ π ≈ 12.73 mm. This is the number to feed a diameter-based ratio or a belt-length calculation.
Common pulley reference table
Typical pitch and pitch-diameter values for the belt profiles you meet in motion systems. Pitch diameter scales linearly with tooth count, so the table lists the per-tooth pitch and a worked example.
| Profile | Type | Tooth pitch p | PD formula | Example (teeth → PD) |
|---|---|---|---|---|
| GT2 / 2GT | Timing (curvilinear) | 2 mm | teeth × 2 ÷ π | 20T → 12.73 mm |
| GT3 / 3GT | Timing | 3 mm | teeth × 3 ÷ π | 20T → 19.10 mm |
| GT5 / 5GT | Timing | 5 mm | teeth × 5 ÷ π | 20T → 31.83 mm |
| HTD 3M | Timing (HTD) | 3 mm | teeth × 3 ÷ π | 24T → 22.92 mm |
| HTD 5M | Timing (HTD) | 5 mm | teeth × 5 ÷ π | 24T → 38.20 mm |
| HTD 8M | Timing (HTD) | 8 mm | teeth × 8 ÷ π | 30T → 76.39 mm |
| T2.5 | Timing (trapezoidal) | 2.5 mm | teeth × 2.5 ÷ π | 16T → 12.73 mm |
| T5 | Timing (trapezoidal) | 5 mm | teeth × 5 ÷ π | 16T → 25.46 mm |
| T10 | Timing (trapezoidal) | 10 mm | teeth × 10 ÷ π | 18T → 57.30 mm |
| MXL | Timing (imperial) | 2.032 mm (0.080 in) | teeth × 2.032 ÷ π | 20T → 12.93 mm |
| XL | Timing (imperial) | 5.08 mm (0.200 in) | teeth × 5.08 ÷ π | 16T → 25.87 mm |
| L | Timing (imperial) | 9.525 mm (0.375 in) | teeth × 9.525 ÷ π | 18T → 54.59 mm |
For V-belts and flat belts there are no teeth — read the pitch diameter from the sheave spec and use it directly in the ratio.
Pulley types
- Timing / synchronous (GT2, GT3, GT5, HTD, T-series, AT, MXL/XL/L). Toothed pulley + toothed belt. No slip, so motion is positional — the standard choice for steppers, servos, 3D printers, and CNC. Ratio is exact from tooth counts.
- V-belt sheaves. Trapezoidal groove; the belt wedges in and grips by friction. Cheap, tolerant, slips under overload (which can protect the drivetrain). Sized by pitch diameter.
- Flat belt pulleys. Crowned flat face; very high speed, low cost, lowest grip. Common on fans and old line-shaft drives.
- Round-belt (O-ring) pulleys. Light loads, can run skewed/around corners — conveyors and small instrument drives.
- Idler / tensioner pulleys. No ratio contribution; they set belt tension or wrap angle. A toothed idler runs on the toothed side, a flat idler on the back.
Belt length and centre distance
For two pulleys of pitch diameters D (large) and d (small) at centre distance C, the belt pitch length is approximately:
L ≈ 2C + (π/2)(D + d) + (D − d)² / (4C)
Going the other way — solving for C given a stock belt length — is the everyday workshop problem; the Belt Length tool does it directly from pulley sizes.
How RPM and torque change across a stage
A belt stage trades speed for torque by its ratio, just like gears:
output RPM = input RPM / ratio
output torque = input torque × ratio × efficiency
A 4:1 reduction quarters the speed and (at ~95–98% belt efficiency) nearly quadruples the torque. Chain that across stages by multiplying the ratios — which is exactly what the Drivetrain Builder does when you stack gear stages.
FAQ
How do I calculate a pulley ratio from teeth? Divide the load (driven) tooth count by the drive (driver) tooth count: ratio = load teeth ÷ drive teeth. A 48T driven by a 12T is 4:1.
Teeth or diameter — which do I enter? For timing pulleys and sprockets, use tooth counts (exact). For V-belt and flat pulleys, use pitch diameters. The ratio comes out the same either way.
What is pitch diameter and why not use the outside diameter? Pitch diameter is where the belt's tension line runs. For V-belts the pitch line sits below the rim, so the OD overstates the ratio. Always size from pitch diameter.
How do I get pitch diameter from tooth count? PD = (teeth × belt pitch) ÷ π. A 20-tooth GT2 (2 mm pitch) is (20 × 2) ÷ π ≈ 12.73 mm.
Does a belt stage change torque like gears? Yes. Output torque ≈ input torque × ratio × efficiency; output speed = input speed ÷ ratio. Belt efficiency is typically 95–98%.
Try it
Enter the Drive side and Load side teeth (or diameters) for each pulley stage and the builder computes the ratio, output RPM, and reflected torque across the whole drivetrain.