gt2 pulley calculator

What this GT2 pulley calculator does

A GT2 pulley system appears simple, but small design decisions can dramatically change speed, force, and precision. This calculator helps you quickly evaluate:

• Pitch diameter of each pulley from tooth count and belt pitch
• Drive ratio and resulting driven RPM
• Belt linear speed from pulley circumference and motor speed
• Linear axis resolution in mm per step and steps per mm
• Approximate center distance when belt length is known

Core formulas (GT2, 2 mm pitch)

1) Pitch diameter

Pitch diameter is derived from teeth count and pitch:

Pitch Diameter = (Teeth × Pitch) / π

2) Ratio and output speed

For two pulleys connected by a belt:

Reduction Ratio = Driven Teeth / Driver Teeth

Driven RPM = Driver RPM × (Driver Teeth / Driven Teeth)

3) Belt linear speed

Driver pulley circumference at the pitch line is Teeth × Pitch, so:

Belt Speed (mm/s) = (Driver Teeth × Pitch × RPM) / 60

4) Motion resolution

For belt-driven linear motion:

• Travel per rev (mm) = Driver Teeth × Pitch
• mm/full-step = Travel per rev / Steps per rev
• mm/microstep = mm/full-step / Microsteps

How to choose pulley tooth count

Higher tooth count

• Higher linear speed at the same motor RPM
• Lower effective mechanical advantage
• Often better for fast, light loads

Lower tooth count

• Lower linear speed
• Higher effective force per motor torque
• Common for heavier gantries and conservative acceleration profiles

Practical design tips

• For many CNC/3D printer axes, 16T to 20T pulleys are common starting points.
• Check motor torque margin at peak acceleration, not only at cruise speed.
• Use proper belt tension; too loose increases backlash-like behavior, too tight increases wear.
• If precision matters, validate real travel with a dial indicator and calibrate steps/mm in firmware.
• Keep idlers aligned to minimize belt edge wear and periodic positional errors.

Center distance estimate notes

This calculator uses the standard open-belt approximation:

L = 2C + (π/2)(D1 + D2) + (D2 − D1)² / (4C)

Where:

• L = belt pitch length
• C = center distance
• D1, D2 = pulley pitch diameters

The result is an engineering estimate. Real assemblies can vary based on belt construction, tolerances, and tensioner preload.

Frequently asked questions

Is this only for GT2?

It defaults to GT2 (2 mm pitch), but you can enter other pitch values if you are analyzing different timing belt profiles.

Does ratio change belt speed?

Belt speed is set by the driver pulley pitch circumference and driver RPM. Ratio changes driven RPM and torque multiplication, not the belt’s own linear speed at the driver.

Why is my real travel slightly different?

Microstepping nonlinearity, belt stretch, pulley manufacturing tolerance, and frame flex can all contribute. Always verify motion with physical measurement.