How to use the Gear Ratio Calculator
- 1. Pick the trainSimple (gears in a line, with idlers) or compound (pairs on shafts).
- 2. Enter teethDriver first. For compound trains, one stage per line: driver driven.
- 3. Add speed and powerGet output rpm, ratio, direction and, with power, the output torque.
Gear ratio formulas
For two meshing gears, N1 × T1 = N2 × T2, so the speed ratio is N1 / N2 = T2 / T1. In a simple train, idler gears cancel out: ratio = Tlast / Tfirst, and each extra idler only reverses the direction.
In a compound train, two gears share a shaft, so the ratio is the product of (driven / driver) for every stage. Torque goes up by the ratio and down by the efficiency: Tout = Tin × ratio × η. Input torque from power: T = 9549.3 × P(kW) / N(rpm) N·m.
Worked example and tips
A compound train has stages 20→60 and 15→45 with a 1440 rpm motor. Ratio = (60/20) × (45/15) = 9. Output speed = 1440 / 9 = 160 rpm. With two external meshes, the output turns the same way as the input.
- Odd number of gears in a simple train: output turns the same way as the input.
- A ratio above 1 means speed reduction and more torque.
- Internal (ring) gears do not reverse direction, so adjust for them.
Frequently asked questions
What does an idler gear do?
It fills a gap between two gears and changes the output direction, but it does not change the overall speed ratio.
Why use a compound train?
To get a large ratio in a small space. One big single reduction would need a very large gear.
Is efficiency per mesh important?
Each mesh loses a little power, often 1 to 2% for good spur gears. The tool multiplies the efficiency for every mesh.
Is this calculator free?
Yes. You enter your name and WhatsApp number once to see your result, and all other Uncodemy tools then open without the form. Everything is calculated in your browser.