What is a gear train?

A gear train is a system of two or more gears that transmits motion and power from one shaft to another. Types include simple gear trains (each shaft has one gear), compound gear trains (shafts carry multiple gears), epicyclic/planetary gear trains (gears revolve around a central axis), and reverted gear trains (input and output shafts are coaxial).

How do you calculate the gear ratio?

The gear ratio (velocity ratio) is calculated as: Gear Ratio = Number of teeth on driven gear ÷ Number of teeth on driver gear = N₂/N₁. For compound gear trains, multiply individual ratios. A gear ratio greater than 1 means speed reduction (torque multiplication); less than 1 means speed increase.

What is the difference between spur gears and helical gears?

Spur gears have straight teeth parallel to the shaft axis — they are simple, cheap, but noisy at high speeds. Helical gears have angled teeth that engage gradually, producing smoother and quieter operation with higher load capacity, but they generate axial thrust. Double helical (herringbone) gears eliminate this thrust.

Gear Train Calculator

Gear Ratio • RPM • Torque — Simple • Compound • Worm — Simulate • Explore • Practice • Quiz

Mode

📖 User Guide

Gear A1000 rpm

Gear B500 rpm

Ratio2.00

Torque Out19.1 Nm

Train Type

Teeth A 20

Teeth B 40

Input RPM 1000 rpm

Presets

Gear Ratio

2.00 :1

Output RPM

500 rpm

Input Torque

9.55 Nm

Output Torque

19.10 Nm

Teeth A

20 T

Teeth B

40 T

Module

3 mm

Pitch Circle D

60 mm

User Guide — Gear Train Calculator

1 Overview

The Gear Train Calculator is an interactive simulator for understanding how gears transmit motion and power. It covers simple, compound, and worm gear trains with animated meshing gears and real-time calculations of gear ratio, output RPM, torque, module, and pitch circle diameter.

Whether you are learning basic RPM speed calculation or studying how sun, planet, and ring gear arrangements work in epicyclic systems, this tool provides visual, hands-on understanding of gear mechanics. The simulator uses standard spur gear geometry and demonstrates how tooth counts determine speed and torque relationships.

2 Getting Started

The simulator opens in Simulate mode with a simple 2:1 gear train. Animated gears rotate on the canvas with readout badges showing RPM, ratio, and torque.

Select a Train Type (Simple, Compound, or Worm) to change the configuration.
Adjust Teeth A and Teeth B sliders to set the number of teeth on each gear.
Set the Input RPM to change the driver speed.
For compound trains, a second row of sliders (Teeth C and D) appears for the additional gear stage.
Use presets like Speed Reducer 3:1, Clock Mechanism, or Worm Drive 40:1 to explore common configurations.

3 Simulate Mode

The canvas renders animated spur gears with correct tooth meshing. Gear A (driver) and Gear B (driven) rotate at speeds determined by the gear ratio. For compound trains, intermediate gears share a common shaft, multiplying the overall ratio. For worm drives, the worm (single-start or multi-start) meshes with the worm wheel at 90°.

Readout cards display gear ratio, output RPM, input and output torque, teeth counts, module, and pitch circle diameter. The fundamental relationships are: Gear Ratio = N_B / N_A, Output RPM = Input RPM / Ratio, and Output Torque = Input Torque × Ratio (assuming 100% efficiency). For compound trains, the overall ratio is the product of individual stage ratios.

4 Explore Mode

Explore mode covers 12 gear concepts across three categories:

Gear Basics — Gear terminology (module, pitch circle, addendum, dedendum), the fundamental law of gearing, and involute tooth profile.
Gear Types — Spur, helical, bevel, worm, rack-and-pinion, and internal gears with their advantages and applications.
Applications — Speed reducers, clock mechanisms, automotive transmissions, differential drives, and epicyclic (planetary) gear systems.

5 Practice & Quiz

Practice mode generates random gear calculation problems covering gear ratio, output RPM, torque, module, pitch circle diameter, and compound train analysis. Solutions are provided with clear step-by-step workings.

Quiz mode presents 5 randomised questions testing both conceptual understanding and numerical problem-solving across all gear train types.

6 Tips & Best Practices

Remember: gear ratio > 1 means speed reduction (torque multiplication); ratio < 1 means speed increase (torque reduction).
For compound gear trains, overall ratio = (N_B/N_A) × (N_D/N_C) — this allows very large ratios in a compact arrangement.
Worm drives achieve ratios of 40:1 or more in a single stage and are often self-locking (cannot be back-driven).
Two gears must have the same module to mesh properly — module = d/N where d is pitch circle diameter and N is number of teeth.
Use the presets to compare different configurations and observe how the animation speed changes with gear ratio.
In Explore mode, study the involute tooth profile to understand why it is the universal standard for power gearing.

Gear Train Calculator — Understanding Gear Ratios, RPM and Torque

A gear train is a mechanical system of two or more meshing gears used to transmit rotational motion and torque between shafts. The gear ratio is the fundamental parameter that determines how speed and torque are exchanged: it equals the number of teeth on the driven gear divided by the number of teeth on the driver gear (GR = N_B / N_A). When the driven gear has more teeth, the output speed decreases but torque increases proportionally — this is a speed reducer. Conversely, fewer teeth on the driven gear produce a speed multiplier with higher RPM but lower torque.

Types of Gear Trains

Simple gear trains consist of two meshing gears on separate shafts and provide a single-stage speed change. Compound gear trains use four or more gears arranged so that two gears share an intermediate shaft, allowing the overall gear ratio to be the product of individual ratios (GR = (N_B/N_A) × (N_D/N_C)). This enables very large or very small ratios in a compact arrangement. Worm gear drives use a screw-like worm meshing with a worm wheel and can achieve very high ratios (often 40:1 or more) in a single stage while also providing a self-locking feature that prevents back-driving.

Key Formulas for Gear Calculations

The module (m) relates tooth size to gear diameter: m = d / N, where d is the pitch circle diameter and N is the number of teeth. The circular pitch is the arc distance between adjacent teeth along the pitch circle: p = pi × m. For two gears to mesh properly they must have the same module. The centre distance between two meshing spur gears equals (d_A + d_B) / 2. Output RPM is calculated as RPM_in / GR, and output torque (assuming 100% efficiency) equals input torque multiplied by the gear ratio.

How to Use This Simulator

In Simulate mode, select a train type (Simple, Compound, or Worm), adjust teeth counts and input RPM, and watch animated gears rotate with correct meshing behaviour. Readout cards display gear ratio, output RPM, torque values, module, and pitch circle diameter in real time. Use presets like Speed Reducer 3:1, Clock Mechanism, or Worm Drive 40:1 to explore common configurations. Switch to Explore mode to study 12 gear concepts across Basics, Types, and Applications. Practice mode generates random calculation problems, and Quiz tests your knowledge with 5 questions per session.

Who Uses This Simulator?

This gear train calculator is designed for mechanical engineering students, machine design trainees, workshop instructors, automotive technicians, and anyone studying power transmission systems. It provides visual, interactive understanding of gear mechanics without requiring physical gear sets or laboratory equipment.

Explore Related Simulators

If you found this Gear Trains simulator helpful, explore our Belt & Chain Drive simulator, Four-Bar Linkage simulator, Cam & Follower simulator, Power Screw Calculator, and Governor simulator for more hands-on practice.