Gear Ratio Calculator

Calculate gear ratio, output speed, output torque, and mechanical advantage for a simple gear pair.

About this calculator

This calculator works through the basic kinematics and torque transfer of a single external gear pair. The gear ratio is simply the driven gear's tooth count divided by the driver's — a 60-tooth driven gear turned by a 20-tooth driver gives a 3:1 ratio, meaning the driver must turn three times for every one turn of the driven gear. Output speed then falls straight out of that ratio (input RPM divided by the ratio), while output torque runs the other way, multiplying the input torque by the gear ratio — a speed reduction always comes with a proportional torque increase, since power (speed × torque) is conserved apart from losses. Those losses are represented by a fixed 98% mesh efficiency, a reasonable assumption for a well-lubricated spur gear pair but optimistic for worm gears, gears with poor tooth finish, or high-slip contact — swap in your own efficiency figure by hand if your application isn't a typical spur mesh.

Mechanical advantage here is reported as the gear ratio times that efficiency, essentially telling you the realistic torque multiplication after mesh losses rather than the theoretical maximum. Speed reduction percentage frames the same ratio as "how much slower" the output turns relative to the input. One common mixup: this calculator models a single gear pair, not a full gearbox or compound gear train — for multi-stage reductions, you'd need to multiply the ratios of each stage together and apply this calculator's math to the combined ratio, or run each mesh through it separately.

Inputs

Driver Gear Teeth

Driven Gear Teeth

Input Speed

RPM

Input Torque

ft·lb

Tab to move between fields

Results

Gear Ratio

3:1

Output Speed

600 RPM

Output Torque

147 ft·lb

Speed Reduction66.7%

Mechanical Advantage2.94

How to Use This Calculator

Enter the number of teeth on the Driver Gear (pinion) — the input gear connected to the motor.
Enter the number of teeth on the Driven Gear — a larger tooth count reduces output speed and multiplies torque.
Enter the Input Speed in RPM — common motor speeds are 1200, 1800, and 3600 RPM.
Enter the Input Torque in ft·lb, or calculate it as T = 5252 × HP / RPM.
Read the Gear Ratio, Output Speed in RPM, and Output Torque in ft·lb — these are the key design values.
Check the Mechanical Advantage and Speed Reduction % to confirm they meet your application requirements.

How the result changes with Driver Gear Teeth

Driver Gear Teeth	Gear Ratio	Output Speed	Output Torque
10	6:1	300 RPM	294 ft·lb
15	4:1	450 RPM	196 ft·lb
30	2:1	900 RPM	98 ft·lb
50	1.2:1	1,500 RPM	58.8 ft·lb

What each input means

Driver Gear Teeth: Number of teeth on the driving (input) gear or pinion. Minimum practical tooth count is ~12 for spur gears.
Driven Gear Teeth: Number of teeth on the driven (output) gear. Larger tooth count means more speed reduction and torque multiplication.
Input Speed: Rotational speed of the driver gear, typically from a motor. Common motor speeds: 1200, 1800, 3600 RPM.
Input Torque: Torque available from the driving source. T = 5252 × HP / RPM.

How this is calculated

Worked example, using the default values

Identify Input Parameters
4 parameters
Driver Gear Teeth = 20, Driven Gear Teeth = 60, Input Speed = 1800, Input Torque = 50 = 4 input(s) provided
Calculate Gear Ratio
Gear Ratio
3 = 3
Calculate Output Speed
Output Speed
600 = 600
Calculate Output Torque
Output Torque
147 = 147
Calculate Speed Reduction
Speed Reduction
66.7 = 66.7
Calculate Mechanical Advantage
Mechanical Advantage
2.94 = 2.94

Engine last updated September 1, 2026. Checked against 1 independently-derived test — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.

Frequently Asked Questions

Why does output torque go up when output speed goes down?

Power equals speed times torque, and this calculator assumes power is conserved through the mesh apart from a small efficiency loss. So when a large driven gear reduces output speed relative to input speed, torque increases proportionally (scaled by the gear ratio) to keep power roughly balanced — that's the fundamental trade every reduction gearset makes.

Why is mechanical advantage different from the gear ratio itself?

The gear ratio (driven teeth ÷ driver teeth) is a pure kinematic number describing the theoretical speed/torque trade-off with no losses. Mechanical advantage here is that same ratio multiplied by the assumed 98% mesh efficiency, so it reflects the realistic torque multiplication you'd actually get after friction losses in the mesh.

Can I use this calculator for a gearbox with multiple gear stages?

Not directly — it models a single external gear pair, one driver and one driven gear. For a multi-stage gearbox, multiply the individual ratios of each stage together first to get the overall ratio, then run that combined ratio through this calculator once, or run each mesh through separately and compound the results.

Is the 98% mesh efficiency accurate for all gear types?

No — 98% is reasonable for a well-lubricated, well-finished spur or helical gear pair, but it's optimistic for worm gears (which can run 50-90% efficient due to high sliding friction), gears with rough tooth finish, or high-slip contact. If your application isn't a typical spur/helical mesh, substitute your own efficiency estimate into the output torque and mechanical advantage figures by hand.

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