Engineering

How to Calculate Gear Ratio

Calculate simple or compound gear ratio from driver and driven teeth, then estimate output speed and torque.

gear-ratio
Calculate simple or compound gear ratio from driver and driven teeth, then estimate output speed and torque after efficiency.
Total gear ratio
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Output speed—
Output torque—
Active stages—
Direction note—
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How do you calculate gear ratio?

Gear ratio compares the number of teeth on the driven gear with the number of teeth on the driver gear. For a simple external gear pair, divide driven teeth by driver teeth. If a 12-tooth driver turns a 36-tooth driven gear, the ratio is 36 / 12 = 3. That means the driven gear turns at one third of the input speed, while torque is increased in the ideal case. This calculator handles one, two, or three active gear stages and multiplies the stage ratios together for a compound train.

Gear ratio is one of the easiest mechanical calculations to start, but it is also easy to misuse. A ratio above 1 usually reduces speed and increases torque. A ratio below 1 usually increases speed and reduces torque. In real machines, torque is not gained for free. Friction, bearing drag, sliding contact, lubrication, misalignment, and gear quality all reduce output power. That is why the calculator includes an efficiency input. KHK explains tooth-count relationships and gear dimensions in its gear reference material.

This calculator is useful for small machines, conveyors, robotics, vehicle projects, winches, hand-cranked mechanisms, prototype gearboxes, and educational examples. It can help you compare speed and torque before drawing a gearbox. It also helps you understand why a small pinion driving a large gear creates a reduction, and why a large driver gear turning a smaller driven gear creates an overdrive. For compound trains, the result can grow quickly because every stage multiplies the total ratio.

Formula and worked example

Single stage ratio = driven teeth / driver teeth Compound ratio = ratio 1 × ratio 2 × ratio 3 Output speed = input RPM / total ratio Output torque ≈ input torque × total ratio × efficiency Example: Driver = 12 teeth Driven = 36 teeth Input speed = 1800 RPM Ratio = 36 / 12 = 3:1 Output speed = 1800 / 3 = 600 RPM If input torque is 10 N·m and efficiency is 95%, output torque ≈ 28.5 N·m

For multiple stages, enter the extra driver and driven tooth counts. Leave unused stages as zero. The calculator treats every active stage as a gear reduction or increase based only on tooth count. If the driven gear has more teeth than the driver, that stage ratio is above 1. If the driven gear has fewer teeth than the driver, that stage ratio is below 1. The total ratio is the product of all active stages.

Common mistakes with gear ratio

The most common mistake is reversing the formula. For a reduction pair, use driven teeth divided by driver teeth. If you accidentally divide the driver by the driven gear, the speed and torque predictions will be inverted. Another mistake is ignoring compound stages. In a compound gear train, the first driven gear may share a shaft with the second driver gear. The ratio of each mesh must be calculated and then multiplied. Counting only the first mesh gives a wrong output speed.

Another mistake is expecting the output torque to increase exactly by the ratio. That only happens in an ideal loss-free machine. Real gears lose energy through friction and sliding. Worm gears, small plastic gears, dry gears, and poorly aligned shafts can have much lower efficiency than precision spur gears. Tooth strength is also separate from ratio. A gear pair may produce the desired speed but fail because the teeth, shaft, keys, bearings, or housing cannot carry the load.

Use this calculator for early layout and mechanical understanding. For final gear design, check module or diametral pitch, pressure angle, face width, center distance, backlash, contact ratio, lubrication, material strength, bearing loads, shaft deflection, noise, and heat. For safety-critical lifting, vehicles, presses, or machinery, gear design should follow recognized standards and be reviewed by a mechanical engineer. A ratio calculator tells you speed and torque relationships; it does not prove that the gears are strong enough to survive.

Common questions

  • The driver gear is the gear receiving input power. The driven gear is the gear being turned by the driver.
  • A 3:1 ratio means the input turns three times for one output turn in a reduction. Output speed is lower, and ideal output torque is higher.
  • Calculate each mesh as driven teeth divided by driver teeth, then multiply all stage ratios together.
  • A simple idler gear between driver and driven gears usually changes direction but not the ratio, unless it is part of a compound stage on a shared shaft.
  • Efficiency accounts for power loss. Without it, torque estimates look too high because real gears lose energy through friction and other losses.
  • Use the result as an estimating and checking tool only. Final engineering decisions should be checked against the correct code, manufacturer data, site conditions, and a qualified professional review when safety, compliance, or expensive equipment is involved.
  • The calculator converts units internally and rounds the displayed values for readability. Keep extra digits during design work, and round only at the end when selecting a real product, tool setting, or equipment size.
  • The most common mistake is mixing units or entering a value in the wrong field. Read the unit label beside each input, especially when switching between inch, metric, pressure, flow, temperature, and speed units.