Gear Ratio (Teeth) Calculator

Formula first

Overview

The gear ratio is a mechanical measurement that defines the relationship between two or more interlocking gears. It is specifically calculated as the ratio of the number of teeth on the driven gear (output) to the number of teeth on the driver gear (input).

Symbols

Variables

T_{driven} = Teeth (Driven), T_{driver} = Teeth (Driver), GR = Gear Ratio

Apply it well

When To Use

When to use: This equation is used when designing mechanical systems like gearboxes, winches, or bicycle drivetrains to determine mechanical advantage. It assumes that the gears are in direct contact and share the same diametral pitch or module.

Why it matters: Gear ratios allow engineers to manipulate the trade-off between speed and torque. A high gear ratio provides more torque for lifting or climbing, while a low gear ratio allows for higher rotational speeds at the output.

Avoid these traps

Common Mistakes

• Driver / Driven (getting Speed Ratio).
• Confusing Input/Output.

One free problem

Practice Problem

An electric motor is attached to a driver gear with 15 teeth. This gear drives a larger gear with 60 teeth. What is the resulting gear ratio?

Solve for: $GR$

Hint: The gear ratio is found by dividing the number of teeth on the driven gear by the number of teeth on the driver gear.

The full worked solution stays in the interactive walkthrough.

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Related Formulas

References

Sources

1. Britannica: Gear
2. Wikipedia: Gear
3. Wikipedia: Gear ratio
4. Shigley's Mechanical Engineering Design, 10th Edition (Budynas and Nisbett)
5. Machine Design: An Integrated Approach, 5th Edition (Norton)
6. AQA GCSE Engineering — Mechanical Systems