What is gear reduction ratio?

The gear reduction ratio is the number of times the input gear turns for every one turn of the output gear. A ratio of 4:1 means the output shaft spins at one-quarter the input speed and produces four times the input torque (before efficiency losses).

How is output torque calculated?

Output torque = input torque × gear ratio × efficiency. Efficiency accounts for friction in the mesh; a typical spur gear mesh is 95–98%, while worm gears can be 50–90% depending on lead angle.

What efficiency value should I use?

For spur or helical gears use 95–98%. For bevel gears use 93–97%. For worm gears use 50–90% depending on the lead angle and number of starts. When in doubt, 90% is a conservative starting estimate.

Can I calculate a two-stage gearbox?

Yes — run the first stage, then use the output RPM and output torque as the input values for a second calculation with the second stage's tooth counts. Multiply the individual efficiencies together for the overall drivetrain efficiency.

Does this tool account for motor back-EMF or load curves?

No. This tool uses the simplified linear torque model: torque scales linearly from stall torque at 0 RPM to 0 Nm at free-run RPM. For precision sizing, cross-reference with the motor's full torque-speed curve.

Gear Reduction Calculator (Robotics)

Name: Gear Reduction Calculator (Robotics)
Availability: InStock
Author: Nham Vu

Enter driver/driven tooth counts and motor specs to instantly compute gear reduction ratio, output RPM, and output torque.

Gear Parameters

Driver teeth (input gear)

Driven teeth (output gear)

Motor Specs

Free-run RPM

Stall torque (Nm)

Drivetrain efficiency (%)

Spur gears: 95–98%. Worm gears: 50–90%. Use 90% as a safe default.

Results

Gear Reduction Ratio

driven ÷ driver teeth

4.00 : 1

Output Shaft Speed

free-run RPM ÷ ratio

1500 RPM

Output Torque

stall torque × ratio × efficiency

1.800 Nm

Mechanical Advantage

output torque ÷ input stall torque

3.60 ×

Operating point at half speed

At 50% of free-run speed the motor produces roughly half its stall torque. The values below show the estimated output at that load point.

RPM at half load

750 RPM

Torque at half load

0.900 Nm

Summary

Enter driver/driven tooth counts and motor specs to instantly compute gear reduction ratio, output RPM, and output torque.

How it works

Enter the number of teeth on the driver (input) gear.
Enter the number of teeth on the driven (output) gear.
Input your motor's free-run RPM and stall torque.
Optionally enter a drivetrain efficiency percentage (default 90%).
The calculator instantly shows the reduction ratio, output RPM, and output torque.

Use cases

Select the right gear pair for a robot arm joint to meet torque requirements.
Verify that a servo-driven wheel achieves the target ground speed.
Design multi-stage gearboxes by chaining the output of one stage as input to the next.
Compare different tooth-count combinations to find the best speed-torque trade-off.
Size a gearmotor for a conveyor or actuator in industrial automation.
Quickly sanity-check a purchased gearbox specification against your application needs.

Frequently Asked Questions

Last updated: 2026-07-23 · Reviewed by Nham Vu