Gear Ratio Calculator — Formula, Example & Step-by-Step Guide
Gear ratio calculation determines the speed reduction and torque multiplication between meshing gears. The gear ratio i = N₂/N₁ (driven teeth / driver teeth) tells you how many times the input shaft rotates for each output revolution. A ratio greater than 1 means speed reduction with torque increase; less than 1 means speed increase with torque decrease. This is fundamental to every power transmission system — from bicycle derailleurs to industrial gearboxes, automotive transmissions, and robotic actuators. Multi-stage gear trains multiply individual ratios: a 3:1 followed by 4:1 gives 12:1 total. Understanding gear ratios is essential for matching motor speed to load requirements.
Formula
Quick Calculation Result
Interactive Calculator:
How to Calculate Gear Ratio Calculator (Step-by-Step)
- 1
Count the teeth on the driver (input) gear N₁ and driven (output) gear N₂.
- 2
Calculate the gear ratio: i = N₂ / N₁.
- 3
Calculate output speed: n_out = n_in / i.
- 4
Calculate output torque: T_out = T_in × i × η (where η is efficiency, typically 0.95–0.98 per stage).
- 5
For multi-stage trains: i_total = i₁ × i₂ × i₃ and η_total = η₁ × η₂ × η₃.
- 6
Verify the gear module and face width can handle the transmitted torque using Lewis bending stress formula.
Why This Matters
Gear ratio selection is the bridge between motor characteristics and load requirements. Electric motors run most efficiently at high speed (1000–3000 rpm) but many loads require low speed with high torque. A conveyor drive needing 50 rpm from a 1500 rpm motor requires a 30:1 ratio, achievable with a two-stage helical gearbox. In automotive transmissions, first gear provides high ratio (3.5–4:1) for starting torque, while top gear provides low ratio (0.7–1:1) for highway cruising. Planetary gear sets achieve high ratios in compact packages, making them ideal for robotics and wind turbines. The efficiency loss per gear stage (2–5%) becomes significant in multi-stage reducers, affecting thermal management and lubrication requirements.
Worked Example
Problem: A motor at 1500 rpm drives a conveyor through a two-stage gearbox. Stage 1: 18T driver, 72T driven. Stage 2: 20T driver, 80T driven. Efficiency per stage: 97%. Solution: i₁ = 72/18 = 4:1. i₂ = 80/20 = 4:1. i_total = 4 × 4 = 16:1. Output speed = 1500/16 = 93.75 rpm. η_total = 0.97 × 0.97 = 0.9409 = 94.1%.
Typical Gear Efficiency
| Type | η |
|---|---|
| Spur gear | 97–99% |
| Helical gear | 96–98% |
| Worm gear | 40–90% |
| Planetary | 95–97% |
✓ Design Checklist
- • Verify center distance compatibility
- • Check gear module for bending strength
- • Account for efficiency losses in heat calculations
⚠ Common Pitfalls
- • Confusing speed ratio with torque ratio direction
- • Ignoring worm gear irreversibility
Frequently Asked Questions
What is a gear ratio?+
A gear ratio is the ratio of teeth between two meshing gears, determining how speed and torque are converted between the input and output shafts.
How do you calculate gear ratio?+
Divide the number of teeth on the driven gear by the number of teeth on the driver gear: i = N₂/N₁. For multi-stage, multiply individual ratios.
Does a higher gear ratio mean more torque?+
Yes. A higher gear ratio (>1) reduces output speed but proportionally increases output torque (minus efficiency losses). A 10:1 ratio gives approximately 10× the input torque.