What is a gear ratio?

It is the number of teeth on the driven gear divided by the number on the driving gear. A three to one ratio means the output shaft turns once for every three turns of the input, running three times slower with three times the torque before losses. The ratio is fixed by geometry, so it is the one part of a drive that does not vary with load or speed.

Does gearing create extra power?

No. Power is torque multiplied by angular speed, and gearing multiplies one while dividing the other, so the product is unchanged apart from the friction loss. A reduction gives more torque and proportionally less speed. That is why a gearbox can never make a small motor into a big one, only make it useful at a different speed.

What efficiency should I assume for a gear mesh?

Ninety seven to ninety nine per cent per stage for well lubricated spur and helical gears, a little lower for bevel gears, and dramatically lower for worm drives, which commonly sit between forty and seventy per cent depending on lead angle and lubrication. If you do not know, ninety seven per cent per stage is a defensible starting assumption for parallel shaft gearing.

How do I calculate the ratio of a multi-stage gearbox?

Multiply the individual stage ratios together. Three stages of three to one give twenty seven to one overall. The efficiencies multiply too, so three stages at ninety seven per cent deliver about ninety one per cent of the input power, and the difference leaves the casing as heat that has to be designed for.

Why do designers avoid whole number gear ratios?

Because in a whole number ratio the same teeth always mesh with each other, so any imperfection on one tooth wears the same handful of partner teeth for the life of the drive. Choosing counts that share no common factor, a hunting tooth arrangement, makes every tooth eventually meet every other and spreads wear and noise evenly.

Can I use this for chain and belt drives?

Yes. Sprockets and toothed pulleys follow exactly the same arithmetic, with the driven sprocket tooth count divided by the driving one giving the ratio. Chain drives are typically ninety eight per cent efficient when properly tensioned and lubricated, and toothed belt drives are similar, so the default efficiency here suits both.

Gear Ratio Calculator

Works anywhere

Works out the ratio of a gear pair from the tooth counts, then converts input speed and torque into output speed and torque including the friction loss at the mesh. A 20 tooth pinion driving a 60 tooth gear is 3.000:1, turning 1,000 RPM into 333 RPM and 50 Nm into 145.5 Nm.

Results

Worked example. Edit the values and press Calculate

Gear ratio

3.000:1

A reduction: slower and stronger at the output.

Output speed
333 RPM
Output torque (ideal)
150.0 Nm
Before friction, which no real mesh escapes.
Output torque after losses
145.5 Nm
Output speed as a share of input
33.33%
Torque multiplication
3.00x
Input power
5.24 kW
Output power
5.08 kW
Power lost at the mesh
157 W
This leaves as heat and is what a gearbox casing has to shed.

Why use this calculator

A gear pair trades speed for torque at an exact, fixed rate, and almost every drive design problem is a question about where to sit on that trade. Electric motors and internal combustion engines both produce useful power in a narrow speed band that rarely matches what the load wants, so the gearbox exists to move between them.

What the arithmetic alone hides is the loss. Every mesh gives away a few per cent of the power as heat, spur and helical gears keep ninety seven to ninety nine per cent per stage and worm drives can keep less than half, so a three stage reduction is measurably weaker than the ideal ratio suggests.

This calculator gives the ideal output and the real one side by side, plus the power that has to leave the casing as heat.

How to use it

Count the teeth on the driving gear, the one attached to the motor or engine, and enter that first, remembering that on a belt or chain drive the sprocket tooth counts work identically.
Enter the driven gear tooth count next, which is the one connected to the load.
Take the input speed from the motor nameplate, the engine specification or a tachometer reading at the operating point you care about, since torque and speed both vary across an engine's range.
Enter the input torque in newton metres from the same source, converting from pound feet by multiplying by 1.356 if your data sheet is imperial.
Finally set the mesh efficiency: ninety seven per cent is a safe default for a single spur or helical stage, and a worm drive needs a much lower figure.

What each result means

Gear ratio: Driven teeth divided by driving teeth. Above one is a reduction, below one an overdrive, and exactly one is direct drive.
Output speed: The driven shaft speed in revolutions per minute, which falls by exactly the ratio.
Output torque (ideal): Torque at the output assuming no friction at all, which is the theoretical maximum and never achieved.
Output torque after losses: The realistic torque available at the output shaft once mesh efficiency is applied. Size your load against this.
Output speed as a share of input: The output speed expressed as a percentage of input speed, a quick sanity check on the direction of the ratio.
Torque multiplication: How many times the input torque appears at the output before losses. It equals the ratio exactly.
Input power: Mechanical power entering the gear pair, calculated from input torque and speed. Compare it against the motor rating.
Output power: Power available at the driven shaft after the mesh loss. Power, not torque, is what the motor must actually supply.
Power lost at the mesh: The difference between input and output power, which becomes heat in the gears, bearings and oil.

The formula

The ratio

R = Td ÷ Tp

Where Td is the driven gear tooth count and Tp the driving gear tooth count, so the ratio is above one for a reduction.

Output speed

No = Ni ÷ R

Where Ni is the input speed in revolutions per minute.

Ideal output torque

To = Ti × R

Where Ti is the input torque, and the real figure is To × η, where η is the mesh efficiency as a decimal.

Transmitted power in watts

P = T × 2πN ÷ 60, which is why halving speed and doubling torque leaves power unchanged

How this number is used in practice

Gearing is the reason a small motor can move a heavy load, and the reason it takes longer to do it. A cordless drill running a 20,000 RPM motor through a fifty to one planetary set produces around four hundred RPM at the chuck and roughly fifty times the motor's torque, minus losses.

An electric vehicle usually needs only a single fixed reduction of about eight or nine to one, because an electric motor makes full torque from zero speed and pulls cleanly to very high revolutions, which is exactly why it does not need the multi-speed gearbox a petrol engine cannot do without.

Efficiency is where ideal ratios and real hardware separate. A well made spur or helical stage keeps ninety seven to ninety nine per cent of the power, so a three stage reduction at ninety seven per cent still delivers about ninety one per cent. A worm drive keeps far less, frequently between forty and seventy per cent depending on lead angle and lubrication, and it converts the difference into heat that has to leave the casing.

That is the trade a designer accepts for compactness, high reduction in one stage, and in many cases self-locking behaviour under back drive.

Tooth count choice carries a subtlety beyond the ratio. Designers avoid whole number ratios wherever possible, preferring a hunting tooth arrangement where the two counts share no common factor, so every tooth on one gear eventually meets every tooth on the other and wear distributes evenly.

A twenty to sixty pair is exactly three to one, which means tooth one always meets the same three teeth for the life of the drive. Changing the pair to twenty one and sixty two gives almost the same ratio and a far better wear pattern.

Worked examples

20 tooth pinion driving a 60 tooth gear at 1,000 RPM and 50 Nm
3.000:1, output 333 RPM, ideal torque 150.0 Nm and 145.5 Nm after a 97% mesh, transmitting 5.24 kW in.
An overdrive: 40 tooth driving a 20 tooth at 3,000 RPM and 200 Nm
0.500:1, output 6,000 RPM, and torque falls to 97.0 Nm after losses.
A winch reduction: 12 tooth driving 84 tooth at 1,750 RPM and 8 Nm
7.000:1, output 250 RPM and 54.3 Nm at the drum after a 97% mesh.
A worm drive at 40% efficiency: 1 tooth start driving a 40 tooth wheel
40.000:1 with torque multiplied forty times but only 16.0 Nm delivered from 1 Nm in, the rest lost as heat.

When people use it

Selecting a gearbox ratio to match a motor's speed band to a load's requirement
Checking whether a drive will deliver enough torque at the output once losses are counted
Sizing a chain or belt drive by sprocket tooth counts, which follow identical arithmetic
Estimating the heat a gearbox casing must shed from the power lost at each mesh
Comparing a compact worm drive against a multi-stage spur reduction on efficiency

Tips

Ratio above one is a reduction, below one an overdrive. Reversing the tooth counts inverts the ratio and the whole behaviour of the drive.
Multi-stage ratios multiply and so do the losses. Three stages at 97% deliver about 91% of the input power, not 97%.
Avoid whole number ratios where you can. Tooth counts sharing no common factor spread wear evenly across every tooth.
Worm drives buy compactness and high single-stage reduction at a serious efficiency cost, frequently below 70% and sometimes below 50%.
Torque is not power. Gearing multiplies torque and divides speed, so the power available never rises, it only falls by the losses.
Chain and belt drives use the same arithmetic with sprocket or pulley tooth counts, so this calculator works for them unchanged.
Convert pound feet to newton metres by multiplying by 1.356 before entering an imperial data sheet figure.

What it assumes, and where it stops being accurate

A single gear pair. Multi-stage gearboxes multiply the ratios and compound the losses, so run each stage separately.
Mesh efficiency covers gear tooth friction only. Bearing drag, oil churning and seal friction sit on top and grow with speed.
Steady state operation. Start-up, shock loading and reversal all produce torques well above the calculated figure.
It is not a strength calculation. It says nothing about whether the teeth, shafts or bearings can carry the load they are given.
Backlash, tooth profile, module and face width are ignored, and all of them matter for a real design.
Input torque is assumed constant with speed, which is true for many electric motors and false for internal combustion engines.

Terms used on this page

Pinion: The smaller gear in a pair, usually the driving gear in a reduction drive.
Reduction: A gear arrangement where the output turns slower than the input and torque is multiplied.
Overdrive: The opposite arrangement, where the output turns faster than the input and torque is divided.
Hunting tooth: A tooth count pairing with no common factor, so wear distributes evenly across every tooth.
Mesh efficiency: The proportion of input power that survives one gear engagement, the rest becoming heat.

Questions people ask

What is a gear ratio?: It is the number of teeth on the driven gear divided by the number on the driving gear. A three to one ratio means the output shaft turns once for every three turns of the input, running three times slower with three times the torque before losses. The ratio is fixed by geometry, so it is the one part of a drive that does not vary with load or speed.
Does gearing create extra power?: No. Power is torque multiplied by angular speed, and gearing multiplies one while dividing the other, so the product is unchanged apart from the friction loss. A reduction gives more torque and proportionally less speed. That is why a gearbox can never make a small motor into a big one, only make it useful at a different speed.
What efficiency should I assume for a gear mesh?: Ninety seven to ninety nine per cent per stage for well lubricated spur and helical gears, a little lower for bevel gears, and dramatically lower for worm drives, which commonly sit between forty and seventy per cent depending on lead angle and lubrication. If you do not know, ninety seven per cent per stage is a defensible starting assumption for parallel shaft gearing.
How do I calculate the ratio of a multi-stage gearbox?: Multiply the individual stage ratios together. Three stages of three to one give twenty seven to one overall. The efficiencies multiply too, so three stages at ninety seven per cent deliver about ninety one per cent of the input power, and the difference leaves the casing as heat that has to be designed for.
Why do designers avoid whole number gear ratios?: Because in a whole number ratio the same teeth always mesh with each other, so any imperfection on one tooth wears the same handful of partner teeth for the life of the drive. Choosing counts that share no common factor, a hunting tooth arrangement, makes every tooth eventually meet every other and spreads wear and noise evenly.
Can I use this for chain and belt drives?: Yes. Sprockets and toothed pulleys follow exactly the same arithmetic, with the driven sprocket tooth count divided by the driving one giving the ratio. Chain drives are typically ninety eight per cent efficient when properly tensioned and lubricated, and toothed belt drives are similar, so the default efficiency here suits both.

Use this with

Gear Ratio Calculator answers one part of the question. These pick up where it stops: Ohm's Law Calculator, Speed Distance Time Calculator, Ratio Calculator and Fuel Efficiency Calculator.

Where these figures come from

Works anywhereLast reviewed 2026-09·How we build and check calculators

This calculation is jurisdiction-neutral arithmetic. No country-specific rules are applied.

American Gear Manufacturers Association. Gear rating, efficiency and nomenclature standards
American Society of Mechanical Engineers. Power transmission and mechanical design references
International Organization for Standardization. ISO 6336 and related gear load capacity standards

Gear Ratio Calculator produces an estimate for general information. It is not financial, tax, medical, legal or engineering advice. read the full disclaimer. Spotted a wrong number? Report it and it gets fixed. The form picks up this calculator and the inputs you used.