Belt Pulley Ratio Calculator
The belt pulley ratio (gear ratio) determines the relationship between input and output shaft speed and torque in a belt-driven system. It is the ratio of the number of teeth on the driven (output) pulley to the number of teeth on the driver (input) pulley. Knowing the gear ratio allows you to calculate output speed from input RPM, determine torque multiplication, and configure stepper motor parameters in 3D printer firmware and CNC controller software.
Belt pulley ratio formula
Gear ratio = Driven teeth / Driver teeth
Output RPM = Input RPM / Gear ratio
Torque ratio = Gear ratio (at 100% efficiency)
A gear ratio of 2:1 means the output shaft turns at half the input speed and delivers twice the input torque (ignoring belt losses, typically 95 to 99% efficient).
Common belt drive applications
- 3D printer X/Y axes: 1:1 ratio (both pulleys same tooth count), direct drive for accuracy.
- Extruder gear drives: 3:1 to 5:1 reduction for torque multiplication.
- CNC router spindle belt drives: often 1:1 or 2:1 to match motor and spindle speed ranges.
- Laser cutter gantry: typically 1:1 with 20-tooth pulleys.
- Timing belt efficiency is typically 97 to 99%, much higher than chain drives.
Belt pulley ratio calculator: frequently asked questions
What is a belt pulley ratio?
The belt pulley ratio (gear ratio) is the ratio of driven pulley teeth to driver pulley teeth. A ratio greater than 1 means the output shaft turns slower than the input (torque multiplication). A ratio less than 1 means the output turns faster (speed multiplication).
How does gear ratio affect torque?
Torque is inversely proportional to speed. If the gear ratio is 2:1 (output turns at half input speed), output torque is doubled (minus efficiency losses). This is why lead screw Z-axes use large gear reductions: to convert motor torque into the force needed to lift the print bed.
What is the difference between gear ratio and speed ratio?
They are reciprocals. If the gear ratio (driven/driver) is 2, the speed ratio (output/input RPM) is 0.5. The output shaft turns at half the input speed. In 3D printing and CNC, 'ratio' usually means driven/driver teeth.
How is this used in 3D printer extruder design?
BMG, Orbiter, and similar high-ratio extruders use a 3:1 to 5:1 gear reduction between the stepper motor and the drive gear. This allows using smaller, lighter motors while maintaining adequate grip force on the filament.
What tooth counts are standard for GT2 pulleys?
Common GT2 pulleys for 3D printers have 16, 20, or 40 teeth. The 20-tooth pulley is most common for X/Y axes. Using a 40-tooth pulley with a 20-tooth driver gives a 2:1 reduction and doubles torque at half speed.
Official sources
- Industrial Press: Machinery's Handbook (gear and belt drive formulas).
- NIST: Measurement Needs for Additive Manufacturing.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.