Gear Ratio Calculator

Find a gear ratio from tooth counts and see how it changes speed and torque between input and output.

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How to use the Gear Ratio Calculator

  1. Enter the driving gear teeth (input / pinion).
  2. Enter the driven gear teeth (output / ring).
  3. Enter the input speed.
  4. Enter the input torque and pick its unit.
  5. Enter the gear efficiency.
  6. Press Calculate. The result updates automatically as you type, and you can switch the result unit at any time.

About the Gear Ratio Calculator

A gear ratio describes how many turns the input makes for one turn of the output. When a small gear drives a larger one, speed drops and torque rises by the same factor, minus a little friction. That trade-off is the reason vehicles need multiple gears: low ratios multiply torque to get moving, and tall ratios keep engine RPM down at cruising speed.

The same math applies to chain sprockets on motorcycles and bicycles and to belt pulleys, using tooth counts or pulley diameters. Spur and helical gears are typically 97–99% efficient per mesh, and a hypoid ring and pinion is around 90–95%, so set efficiency below 100% for a more realistic torque figure.

Formula

Gear ratio = Driven teeth ÷ Driving teeth
Output RPM = Input RPM ÷ Ratio
Output torque = Input torque × Ratio × Efficiency

Example: a 41-tooth ring gear driven by an 11-tooth pinion gives 41 ÷ 11 = 3.727, the common "3.73" axle ratio. 3,000 rpm in becomes about 805 rpm out, and 300 lb-ft becomes about 1,118 lb-ft before losses.

Example calculation

Using the default values:

  • Driving gear teeth (input / pinion) = 11
  • Driven gear teeth (output / ring) = 41
  • Input speed = 3000 rpm
  • Input torque = 300 lb·ft
  • Gear efficiency = 100%

the calculator returns:

  • Gear ratio: 3.727 : 1
  • Output speed: 804.9 rpm
  • Output torque: 1,118.2 lb·ft
  • Type: Reduction (output slower, more torque)

Frequently asked questions

How do I calculate gear ratio from teeth?

Divide the number of teeth on the driven (output) gear by the teeth on the driving (input) gear. 39 ÷ 10 = 3.90:1.

Is a higher gear ratio faster?

A numerically higher ratio (like 4.10) gives quicker acceleration but lower top speed and higher cruising RPM. A numerically lower ratio (like 3.08) is better for fuel economy at highway speed.

How do I calculate ratio for multiple gear pairs?

Multiply the individual ratios. A 2.5:1 stage followed by a 4:1 stage gives 10:1 overall.

Last updated: · Category: Automotive calculators

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