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Gear Ratio Calculator

A gear pair trades speed for torque: the ratio of teeth sets how much slower and stronger the output becomes.

Calculated Result
2.000 : 1:1

Gear ratio

Gear ratio (driven : driver)

2.000 : 1

Output speed

500 rpm

Torque multiplier

2.000×

Direction

Opposite to the driver gear

2.000 : 1 — Ratio

Calculation Breakdown

  1. Gear ratioratio = driven teeth ÷ driver teethi=NdrivenNdriveri = \dfrac{N_{\text{driven}}}{N_{\text{driver}}}
  2. Output speedoutput rpm = input rpm ÷ rationout=ninin_{\text{out}} = \dfrac{n_{\text{in}}}{i}

What Is the Gear Ratio Calculator?

A gear ratio calculator describes how a pair of gears changes speed and torque.

How Does the Gear Ratio Calculator Work?

It divides the driven tooth count by the driver count, then divides input speed by that ratio.

Gear Ratio Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

i=NdrivenNdriveri = \dfrac{N_{\text{driven}}}{N_{\text{driver}}}

The gear ratio is the driven tooth count divided by the driver tooth count; output speed is input speed divided by the ratio.

How to Use the Gear Ratio Calculator

  1. Enter the teeth on each gear and the input speed.

Step-by-Step Example Calculation

20-tooth driving 40-tooth

Input Values:

driverTeeth:20
drivenTeeth:40
inputRpm:1000
Worked Steps: A 2:1 ratio gives 500 rpm and doubles torque.

Understanding Your Result

The result is the gear ratio, output rpm and torque multiplier.

Factors That Affect the Result

  • The tooth counts and input speed determine everything.

When Should You Use This Calculator?

  • Use it for gearboxes, bicycles, clocks and any gear train.

Assumptions & Limitations

  • Ignores friction and efficiency losses, which are usually a few percent.

Frequently Asked Questions

Calculation Accuracy & Reference Note

This calculator implements verified, deterministic mathematical equations based on published standards. Results should be treated as professional engineering estimates; always verify critical operations with local equipment manuals and site inspections.

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