Gear Ratio Calculator
This gear ratio calculator takes the tooth counts or diameters of the driving and driven wheels and returns the ratio, output speed and torque, also for a second stage.
Example: Driver (driving gear) 20 teeth / mm · Driven gear 60 teeth / mm · Input speed 1,500 rpm · Input torque (optional) 10 Nm → Ratio: Ratio 3 : 1, output speed 500 rpm. Source: Wikipedia – Übersetzung (Technik): i = z₂/z₁, speed and torque conversion. Updated: .
How it is calculated
A 20-tooth pinion driving a 60-tooth gear gives a ratio of 3 : 1: 1,500 rpm becomes 500 rpm. The gear ratio says how many times the driving wheel turns for one turn of the driven wheel.
How it is calculated
The ratio is the tooth count of the driven wheel divided by that of the driving wheel. For belt drives and friction wheels use the diameters; the result is the same. Output speed is input speed divided by the ratio, and ideal torque is input torque times the ratio. With a second stage on the intermediate shaft the two ratios multiply.
Good to know
- A ratio above 1 is a reduction: slower but stronger.
- A ratio below 1 is an overdrive, for example when driving an alternator.
- An idler gear in between changes the direction of rotation, not the ratio.
Frequently asked questions
How do you calculate a gear ratio?
Ratio = teeth of the driven gear / teeth of the driving gear. For pulleys the ratio of the diameters is enough.
How do you calculate output speed?
n₂ = n₁ / ratio. At a ratio of 3, the driven wheel turns three times slower than the driving wheel.
What happens to the torque?
In the ideal case it rises by the same factor as the speed falls: M₂ = M₁ · ratio. Friction losses reduce it in practice.
How do I calculate several stages?
Multiply the ratios of all stages. Enter the second stage in the calculator to do this.
Sources and legal basis
- Wikipedia – Übersetzung (Technik): i = z₂/z₁, speed and torque conversion
- Wikipedia – Gear train (Gear ratio, Drehmomentverhältnis)
As of: · Editorial policy
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