Gear Ratio Calculator (Mechanical)

The Gear Ratio Calculator (Mechanical) works out the gear ratio, output speed (RPM), and output torque of a two-gear mechanical system from the number of teeth on the driving (input) and driven (output) gears. It also shows an animated pair of meshing gears spinning at the real calculated speed ratio, the simplified whole-number ratio, the mechanical advantage, and a full step-by-step breakdown so you can see exactly how the numbers come together.

What Is a Gear Ratio?

A gear ratio is the ratio of the number of teeth on the driven gear to the number of teeth on the driving gear. It describes how a gear pair trades rotational speed for torque. When two gears mesh, the teeth force them to move together: the larger gear turns more slowly than the smaller one, but it can deliver more turning force. The gear ratio captures that trade-off in a single number.

Gear Ratio Formula

The core formula uses only the tooth counts. From the ratio you can then derive output speed and output torque.

Notice the symmetry: speed is divided by the ratio while torque is multiplied by it. This is conservation of power in action — ignoring friction, the power going in equals the power coming out, so any speed you give up is returned as torque, and vice versa.

Driving Gear vs Driven Gear

The driving gear (also called the input or drive gear) is the one connected to the power source, such as a motor or engine. The driven gear (the output gear) is the one it turns. Power always flows from driving to driven through the meshing teeth. Two externally meshing gears always rotate in opposite directions, which is why the animated gears above spin the opposite way from each other.

Types of Gear Systems

Worked Example

Suppose a motor drives a 12-tooth gear that meshes with a 36-tooth gear, with an input of 1500 RPM and 50 N·m of torque:

• Gear ratio = 36 ÷ 12 = 3, written as 3:1.
• Output speed = 1500 ÷ 3 = 500 RPM (three times slower).
• Output torque = 50 × 3 = 150 N·m (three times stronger).

This is a classic reduction drive: it trades two-thirds of the speed for triple the torque, which is exactly what you want when a small fast motor has to move a heavy or stubborn load.

Where Gear Ratios Are Used

How to Use This Calculator

1. Enter the gear tooth counts: Type the number of teeth on the driving (input) gear and the driven (output) gear.
2. Add optional input speed and torque: Enter the input RPM and input torque (in N·m or lb·ft) to also calculate the output speed and output torque.
3. Click Calculate: The tool computes the gear ratio and all outputs instantly.
4. Review the results: See the gear ratio, the animated meshing gears spinning at the real speed ratio, the mechanical advantage, the output speed and torque, and the step-by-step breakdown.

Frequently Asked Questions

What is a gear ratio?

A gear ratio is the ratio of the number of teeth on the driven (output) gear to the number of teeth on the driving (input) gear. It tells you how the speed and torque change between the two gears. A ratio of 3:1 means the input gear turns three times for every single turn of the output gear.

How do you calculate gear ratio from teeth?

Divide the number of teeth on the driven gear by the number of teeth on the driving gear. For example, a 36-tooth driven gear and a 12-tooth driving gear give a gear ratio of 36 divided by 12, which equals 3, written as 3:1.

How does gear ratio affect speed and torque?

Gears trade speed for torque. A reduction ratio greater than 1 makes the output slower than the input but multiplies torque by the same factor. An overdrive ratio less than 1 makes the output faster but reduces torque. Output speed equals input speed divided by the ratio, and output torque equals input torque multiplied by the ratio.

What is the difference between a driving gear and a driven gear?

The driving gear is the input gear that receives power, for example from a motor or engine. The driven gear is the output gear that the driving gear turns. Power flows from the driving gear to the driven gear through their meshing teeth.

What does a 2:1 gear ratio mean?

A 2:1 gear ratio means the driven gear has twice as many teeth as the driving gear. The input gear must turn twice for the output gear to turn once, so the output runs at half the speed and produces twice the torque of the input.

What is mechanical advantage in a gear system?

Mechanical advantage is the factor by which a gear system multiplies torque. For an ideal gear pair it equals the gear ratio. A 4:1 reduction has a mechanical advantage of 4, meaning the output torque is four times the input torque, ignoring friction losses.

Additional Resources

• Gear Train - Wikipedia
• Gear Ratio - Wikipedia