Gear Train Calculator
Gear Ratio • RPM • Torque — Simple • Compound • Worm — Simulate • Explore • Practice • Quiz
Σ Live equations — values substituted from current state
⚡ Power flow — speed × torque conservation across the train
📈 Time history — rolling output speed & torque
💡 What-if coach — insights from the current configuration
1 Overview
The Gear Train Calculator is an interactive simulator for understanding how gears transmit motion and power. It covers simple, idler, compound, and worm gear trains with animated meshing gears and real-time calculations of gear ratio, output RPM, torque (including realistic efficiency losses), module, and pitch circle diameter.
Directions of rotation are shown by yellow arrows on every gear, centre-distance dimension lines are drawn between mating pairs, and an undercut warning badge flags any gear with fewer than 17 teeth. A full suite of display toggles, a Play/Pause control, an Animation Speed slider, and an SI / Imperial unit toggle are provided for study and comparison.
2 Controls and Getting Started
The simulator opens in Simulate mode with a 2:1 simple gear train at 600 rpm input. Every slider has a paired numeric input so you can dial in exact values.
- Train Type: Simple, Idler, Compound, or Worm.
- Teeth A / B: 10–60 (for Worm, "Teeth A" becomes Worm Starts 1–4).
- Teeth C / D (Compound only): second stage.
- Idler Teeth (Idler only): the middle gear — changes direction, not ratio.
- Module: 1–10 mm — changes physical tooth size and PCD live.
- Input RPM: 1–1200 rpm.
- Power: 0.1–20 kW — feeds the input-torque calculation.
- Worm Efficiency (Worm only): 40–90 % — applied to output torque.
- Presets: Speed Reducer 3:1, Speed Multiplier 1:3, Clock Mechanism, Worm Drive 40:1.
3 Playback, Toggles, and Units
Below the main sliders is a playback row. Play/Pause freezes the animation so you can study rotation direction without motion, and Animation Speed (0.1×–2×) scales the visible rotation without altering the RPM calculation.
Five display toggles control canvas clutter:
- Pitch — dashed pitch circles.
- Dims — centre-distance dimension lines.
- Arrows — rotation-direction arrows on every gear.
- Labels — letter labels (A, B, C, D, I) at gear centres.
- Grid — workshop grid background.
The SI / Imperial pill tabs in the header convert displayed lengths (mm ⇔ inch) and torques (Nm ⇔ lbf·ft) without changing any internal calculation. RPM is unitless.
4 Reading the Canvas
Each gear is rendered with radial-gradient shading and a rounded tooth profile. The blue/green/gold colours match the readout badges and the canvas labels. A subtle yellow glow marks the mesh-contact point on the line joining each pair of pitch circles.
Rotation arrows follow the physical direction: in a simple train A and B are opposite; in an idler train the middle gear flips direction so A and B spin the same way (ratio unchanged); in a compound train A=CW, B=CCW, C=CCW (shared shaft with B), D=CW; in a worm drive the wheel spins once per Nwheel / starts turns of the worm.
5 Show Calculations, Export, and Right-click Menu
Click the blue Show Calculations button on the canvas to open a modal that derives gear ratio, output RPM, input torque, and output torque step by step, with all intermediate values in SI units.
The PNG and CSV buttons export the current canvas image and a readout table respectively. Right-click (or long-press on touch) inside the canvas to open a context menu with the same Export PNG, Export CSV, Copy readouts, Show calculations, Toggle grid, and Reset to default commands.
The Reset to default action restores Simple train, 20T × 40T, 3 mm module, 600 rpm, 2 kW — useful after experimenting.
6 Explore, Practice, Quiz
Explore covers 12 concepts across Basics (gear ratio, module, circular/diametral pitch), Types (spur, helical, bevel, worm), and Applications (speed reducers, compound trains, planetary, rack & pinion). Practice generates random numerical problems with step-by-step solutions. Quiz delivers 5 randomised questions per session.
7 Tips & Best Practices
- Gear ratio > 1 means speed reduction (torque multiplication); < 1 means speed increase.
- For compound trains, overall ratio = (NB/NA) × (ND/NC) — compact way to achieve large ratios.
- An idler reverses direction but not the magnitude of the ratio.
- Worm drives with 1–2 starts are usually self-locking; with 3–4 starts they often are not — check the “Self-locking” badge on the canvas.
- If a gear has fewer than 17 teeth at 20° pressure angle, the undercut warning appears — consider increasing the tooth count or using a profile-shift design in practice.
- Use Pause + Animation Speed together to step through meshing cycles slowly.
Gear Train Calculator — Understanding Gear Ratios, RPM and Torque
A gear train transmits rotation and torque between shafts through meshing gears. The gear ratio (GR = NB/NA) decides the trade-off: a ratio above one cuts speed and multiplies torque (reducer), a ratio below one does the reverse (multiplier). This calculator animates simple, idler, compound, and worm trains, and solves ratio, RPM, and torque for each.
Gear Train Parameters at a Glance
| Parameter | Formula | Typical Range | Unit |
|---|---|---|---|
| Gear ratio (simple) | NB / NA | 0.5 – 10 | :1 |
| Compound ratio | (NB/NA) × (ND/NC) | 2 – 100 | :1 |
| Worm ratio | Nwheel / Nstarts | 10 – 80 | :1 |
| Output RPM | RPMin / GR | 1 – 1200 | rpm |
| Output torque | Tin × GR × η | 0.1 – 1000 | Nm |
| Module | d / N | 1 – 10 | mm |
| Pitch circle dia. | m × N | 10 – 600 | mm |
| Centre distance | (dA + dB) / 2 | — | mm |
Types of Gear Trains
Simple gear trains consist of two meshing gears on separate shafts and provide a single-stage speed change. A simple train with an idler inserts a third gear that reverses direction twice so output spins the same way as input — the ratio magnitude is unchanged. Compound gear trains use four gears sharing an intermediate shaft, giving GR = (NB/NA) × (ND/NC). Worm drives mesh a screw-like worm (with 1–4 starts) against a worm wheel, achieving very high ratios in one stage and usually self-locking when starts ≤ 2.
Key Formulas and Realistic Efficiency
The module (m) relates tooth size to gear diameter: m = d / N. The circular pitch is p = π × m, and both meshing gears must share the same module. The centre distance between spur gears equals (dA + dB) / 2. Output RPM is RPMin / GR. Output torque is Tin × GR × η, where η is the transmission efficiency — roughly 97 % for spur and compound trains and 40–90 % for worm drives depending on lead angle and lubrication (this simulator defaults worm efficiency to 70 %, adjustable on the slider).
How to Use This Simulator
Pick a Train Type (Simple, Idler, Compound, or Worm) and adjust Teeth, Module, Input RPM (1–1200), and Power (kW) sliders — each has a paired numeric input for exact values. For worm drives, set the number of starts (1–4) and tune the efficiency. The canvas animates the mesh with correct rotation directions indicated by yellow arrows on every gear, and an undercut warning appears when any gear has fewer than 17 teeth (risk of tooth interference at 20° pressure angle). Use Play/Pause and Animation Speed to slow down or freeze the motion, and the display toggles (Pitch, Dims, Arrows, Labels, Grid) to declutter. Click Show Calculations to see step-by-step derivations, or right-click the canvas for Export PNG/CSV and reset shortcuts. Toggle SI/Imperial in the header to switch length and torque units (mm ⇔ inch, Nm ⇔ lbf·ft).
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.