gear train calculator

What is a gear train calculator?

A gear train calculator helps you predict how rotational speed and torque change when power passes through gears. Instead of doing repeated hand calculations, you can quickly evaluate different tooth counts and see how they affect reduction, acceleration, and direction of rotation.

This is especially useful in robotics, machine design, bicycles, gearbox prototyping, and educational projects where you need to compare multiple gear combinations quickly.

Core formulas used

Simple gear pair (2 gears)

• Gear ratio = N2 / N1
• Output speed = Input speed × (N1 / N2)
• Ideal output torque = Input torque × (N2 / N1)
• Actual output torque = Ideal output torque × efficiency
• Direction: output reverses relative to input (external spur gears)

Compound train (4 gears, 2 meshes)

• Overall ratio = (B/A) × (D/C)
• Output speed = Input speed × (A/B) × (C/D)
• Ideal output torque = Input torque × overall ratio
• Actual output torque = Ideal output torque × (efficiency per mesh)²
• Direction: two external meshes means final output rotates in the same direction as input

How to use this calculator effectively

1) Pick your train type

Choose Simple Gear Pair for one mesh, or Compound Train when you have two stages. Compound trains allow larger speed reduction in a compact footprint.

2) Enter real tooth counts

Tooth counts must be positive integers. Practical designs usually avoid very low tooth counts to reduce undercut and noise. If you are testing concepts, use whole numbers and iterate quickly.

3) Add efficiency for realistic torque

Real gear trains lose energy due to friction and windage. Set per-mesh efficiency (for example 90–98%) to estimate realistic output torque instead of ideal textbook values.

Worked examples

Example A: speed reduction and torque gain

If N1 = 20, N2 = 60, and input speed is 1200 RPM, the output speed becomes 400 RPM. With 10 N·m input torque, ideal output torque is 30 N·m before losses. This is a classic 3:1 reduction.

Example B: two-stage compound reduction

With A=18, B=54, C=16, D=64, overall ratio is (54/18) × (64/16) = 12. That means a 12:1 reduction: high torque increase and a major drop in output RPM. This approach is common in compact gearboxes and robot drivetrains.

Design tips and common mistakes

• Do not ignore losses: efficiency can significantly reduce usable output torque.
• Check center distance early: if module is known, pitch diameters and center distances can be estimated quickly.
• Mind direction changes: each external mesh flips direction.
• Avoid unrealistic tooth counts: very small gears may suffer from strength and manufacturability issues.
• Validate with load data: ratio alone does not guarantee that the system survives real duty cycles.

When to use simple vs. compound trains

Use a simple pair when you need a straightforward ratio and minimal complexity. Choose a compound train when you need high reduction in limited space or want to distribute ratio across multiple stages for better packaging and performance.