# Gear Ratio Calculator

Calculate gear ratio, speed multiplier, and torque multiplier from gear teeth counts. Understand mechanical advantage in gear systems.

## What this calculates

A gear ratio determines how speed and torque are transmitted between meshing gears. By dividing the number of driven gear teeth by driving gear teeth, you get the gear ratio. A ratio greater than 1 reduces speed but multiplies torque (useful for hill climbing), while a ratio less than 1 increases speed at the cost of torque. This calculator gives you all the key relationships.

## Inputs

- **Driving Gear Teeth** — min 1 — Number of teeth on the input (driving) gear connected to the motor.
- **Driven Gear Teeth** — min 1 — Number of teeth on the output (driven) gear connected to the load.

## Outputs

- **Gear Ratio** — Ratio = driven teeth / driving teeth
- **Speed Multiplier** — Output speed / input speed = 1 / gear ratio
- **Torque Multiplier** — Output torque / input torque = gear ratio
- **Mechanical Advantage** — Force multiplication factor (equals gear ratio)

## Details

The gear ratio = driven teeth / driving teeth. When a 20-tooth gear drives a 40-tooth gear, the ratio is 2:1. The output shaft turns at half the input speed but delivers twice the torque. This is the fundamental trade-off in all gear systems: you cannot increase both speed and torque simultaneously (conservation of energy).

In automotive transmissions, first gear has a high ratio (e.g., 3.5:1) for maximum torque to accelerate from a stop. Higher gears have progressively lower ratios (e.g., 0.7:1 in overdrive) to allow high-speed cruising at lower engine RPM. Bicycles work the same way: a small front chainring with a large rear sprocket gives a low gear for climbing.

Gear systems are everywhere: clocks, industrial machinery, robotics, wind turbines, and power tools. Multi-stage gear trains multiply ratios: two stages of 3:1 give an overall ratio of 9:1. The mechanical advantage equals the gear ratio for an ideal (frictionless) system; real systems lose 1–3% per gear mesh to friction and heat.

## Frequently Asked Questions

**Q: What does a gear ratio of 2:1 mean?**

A: A 2:1 gear ratio means the driven gear has twice as many teeth as the driving gear. The output shaft turns at half the speed of the input but delivers twice the torque. For every 2 revolutions of the input, the output makes 1 revolution.

**Q: How does gear ratio affect speed and torque?**

A: Speed and torque are inversely related through gears. A higher gear ratio (>1) decreases speed but increases torque by the same factor. A lower gear ratio (<1) increases speed but decreases torque. Power (speed × torque) is conserved minus friction losses.

**Q: What is the gear ratio for overdrive?**

A: Overdrive refers to a gear ratio less than 1:1, where the output shaft turns faster than the input. For example, a 0.7:1 overdrive means the output turns 1.43 times for each input revolution, allowing higher road speed at lower engine RPM for fuel efficiency.

**Q: How do I calculate the ratio for a gear train with multiple stages?**

A: Multiply the individual ratios of each stage. If stage 1 has a 3:1 ratio and stage 2 has a 4:1 ratio, the total gear train ratio is 3 × 4 = 12:1. The output turns 12 times slower than the input with 12 times the torque.

**Q: Do gears lose energy?**

A: Yes. Real gears lose approximately 1-3% of power per mesh point due to friction, generating heat. High-quality hardened and lubricated gears have lower losses. A three-stage gear train might lose 3-9% total, which is still much more efficient than belt drives or hydraulics.

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Source: https://vastcalc.com/calculators/physics/gear-ratio
Category: Physics
Last updated: 2026-04-21