How do you calculate a gear ratio?
Divide the teeth on the driven (output) gear by the teeth on the driver (input) gear. A 12-tooth gear driving a 48-tooth gear gives 48 ÷ 12 = 4, written 4:1. Output speed is the input speed divided by the ratio, and output torque is the input torque multiplied by it. The tooth counts are what matter — the physical sizes follow from them, because gears only mesh if their teeth are the same size.
Does a gear train create extra power?
No. It trades speed for torque and nothing else. Gear down by four and you get a quarter of the speed and about four times the torque; the product of the two — the power — is unchanged apart from friction losses. This is the single most useful thing to understand about gearing, and it is why the calculator shows power in and power out side by side.
What does an idler gear do?
It reverses the direction of rotation and can bridge a distance too great for two gears to span — but it changes the overall ratio not at all. In a simple train each middle gear appears once as a driven gear and once as a driver, so its tooth count cancels exactly. Put any size of idler you like between a 20-tooth and a 40-tooth gear and the output still turns at half the input speed.
Which way does the output gear turn?
Every external mesh reverses the direction, so it comes down to counting them. Two gears means one mesh and a reversed output. Three gears means two meshes and an output turning the same way as the input. In general, an even number of meshes preserves the direction and an odd number reverses it — which is the real reason an idler gets fitted when the ratio is already correct.
What is the difference between gearing up and gearing down?
Gearing down means a small driver turning a large driven gear: less speed, more torque, a ratio above 1:1. That is what a car does in first gear, and what every winch and hoist does. Gearing up, or overdrive, is the reverse — a large driver turning a small driven gear, giving more speed and less torque, as in a bicycle's highest gear or a car's top gear on the motorway.
How efficient are gears?
A well-made spur or helical gear mesh is about 97–99% efficient, so even a multi-stage box loses only a few percent. Bevel gears are similar. Worm drives are the exception at roughly 40–70%, because the worm slides against the wheel rather than rolling on it. Losses compound: three meshes at 98% each give 0.98³, about 94% overall.
Why is a worm drive so inefficient?
Because the worm's thread slides along the wheel's teeth instead of rolling across them, and sliding means friction. The trade is worth it for two reasons: a worm gives an enormous reduction in one compact step, often 40:1 or more, and it usually cannot be back-driven, so the load cannot turn the motor. That self-locking behaviour makes it a natural brake for hoists, gates and jacks.
What is the smallest number of teeth a gear can have?
Practically, around 17 for a standard 20° pressure angle. Below that the cutting tool removes material from the root of each tooth — called undercutting — which weakens it and makes engagement rougher. Smaller pinions are made, using profile shifting or a higher pressure angle, but a design that needs a 10-tooth pinion is usually better split into two gentler stages.
Why split a large reduction across several stages?
A single pair beyond about 6:1 forces either a very small, weak pinion or a very large, heavy wheel. Two stages of 5:1 give 25:1 in a package far smaller, lighter and stronger than one 25:1 pair, and usually quieter as well. The efficiency cost is one extra mesh, typically a couple of percent.
How does a gear ratio relate to torque and RPM in a car?
The engine produces its useful torque over a narrow band of revs, and the gearbox multiplies that torque to whatever the wheels need. First gear multiplies heavily — lots of torque, little speed — for pulling away. Top gear does the opposite, letting the engine turn slowly at motorway speed. The final drive ratio in the differential multiplies everything again.