Gear Ratio Calculator

What is a gear ratio calculator?

A gear ratio calculator works out how a pair of meshing gears changes speed and torque from two numbers: the teeth on the driving (input) gear and the teeth on the driven (output) gear. It reports the ratio, tells you whether the pair is a reduction or an overdrive, and — if you supply an input speed — converts it into the resulting output RPM. Mechanics, machinists, robotics builders, cyclists and curious tinkerers use it to predict how fast a shaft will turn, how much torque a gearset multiplies, or which gear pairing hits a target speed.

A gear ratio is simply a comparison of how many times one gear turns for each turn of the other. The calculator does the arithmetic instantly and labels the result so you know at a glance whether your output will be slower and stronger or faster and lighter.

How the gear ratio formula works

The tool uses one core relationship and a follow-on for speed:

gear ratio = driven teeth ÷ driving teeth

output RPM = input RPM ÷ ratio

The first line divides the output gear’s teeth by the input gear’s teeth. The second line uses that ratio to scale speed: because the gears are coupled, multiplying the teeth count up means dividing the rotation speed down by the same factor. Here is what each term means and the unit it carries:

• driving gear teeth — the tooth count on the input gear that supplies the turning force. A whole number.
• driven gear teeth — the tooth count on the output gear that is turned. A whole number.
• gear ratio — a unitless number, usually written as “ratio:1” (for example 3:1). It is the driven count divided by the driving count.
• input RPM — the rotation speed fed into the driving gear, in revolutions per minute.
• output RPM — the resulting speed of the driven gear, in revolutions per minute.

Reading the ratio: reduction, overdrive or direct drive

The size of the ratio tells you what the gearset does:

Ratio	Name	What happens to output
Greater than 1 (e.g. 3:1)	Reduction	Slower output, more torque
Equal to 1 (1:1)	Direct drive	Same speed, same torque
Less than 1 (e.g. 0.5:1)	Overdrive	Faster output, less torque

A reduction trades speed for turning force; an overdrive does the reverse. Torque scales in the opposite direction to speed, so a 3:1 reduction roughly triples torque while cutting speed to a third (ignoring friction losses).

Examples

Every example below uses only the formula above, so you can reproduce each answer by typing the same values into the calculator.

Example 1 — a 3:1 reduction (the classic case)

A 12-tooth driving gear meshes with a 36-tooth driven gear.

ratio = driven ÷ driving = 36 ÷ 12 = 3:1

This is a reduction because the ratio is above 1. The small input gear must spin three times to turn the large output gear once. Now feed it 3,000 input RPM:

output RPM = input RPM ÷ ratio = 3,000 ÷ 3 = 1,000 RPM

The output shaft turns at 1,000 RPM, one third of the input, while delivering roughly three times the torque.

Example 2 — a 1:1 direct drive

A 24-tooth driving gear meshes with a 24-tooth driven gear.

ratio = 24 ÷ 24 = 1:1

Equal teeth give direct drive. At 3,000 input RPM:

output RPM = 3,000 ÷ 1 = 3,000 RPM

Speed and torque pass straight through unchanged — the gearset only transmits motion, it does not multiply it.

Example 3 — a 0.5:1 overdrive

A 40-tooth driving gear meshes with a 20-tooth driven gear.

ratio = driven ÷ driving = 20 ÷ 40 = 0.5:1

Because the ratio is under 1, this is an overdrive: the small output gear spins faster than the input. At 3,000 input RPM:

output RPM = 3,000 ÷ 0.5 = 6,000 RPM

The output runs at 6,000 RPM, double the input, but carries roughly half the torque. This is the trade-off overdrive gearing makes for higher speed.

Gear ratio reference: ratio, type and output speed

This chart shows common driving and driven tooth pairs, the ratio they produce, and the output speed at a 3,000 RPM input (output = 3,000 ÷ ratio). Use it to eyeball where a pairing lands.

Driving teeth	Driven teeth	Ratio	Type	Output at 3,000 RPM
40	20	0.5:1	Overdrive	6,000 RPM
30	20	0.67:1	Overdrive	4,500 RPM
24	24	1:1	Direct drive	3,000 RPM
12	24	2:1	Reduction	1,500 RPM
12	36	3:1	Reduction	1,000 RPM
10	40	4:1	Reduction	750 RPM

Higher reductions push output speed lower and torque higher; overdrives do the opposite.

Common uses

The gear ratio calculator earns its keep anywhere rotation is geared:

• Drivetrain and axle work — predict wheel or shaft speed for a chosen final-drive pairing.
• Robotics and RC builds — pick a motor-to-output ratio that delivers the torque or speed a project needs.
• Machine tools and conveyors — set spindle or roller speed by matching gear or sprocket teeth.
• Bicycles and chain drives — compare chainring and sprocket teeth, which follow the same driven-over-driving rule.
• Education — show why a small gear driving a big one slows things down and multiplies torque.
• Speed targeting — work backward from a desired output RPM to find the ratio, then the tooth counts.

Tips and common mistakes

• Driven over driving, not the other way around. Ratio is driven teeth ÷ driving teeth. Flipping it inverts every answer and turns a reduction into an overdrive.
• Identify input versus output first. The driving gear is the one supplying power; the driven gear is the one being turned. Mislabeling them flips the ratio.
• Speed and torque move oppositely. A reduction that slows the output multiplies torque by about the same factor, minus friction losses — you never get both more speed and more torque for free.
• A ratio under 1 is still valid. Values less than 1 mean overdrive, not an error; the output simply spins faster than the input.
• Use teeth, not diameter. Count actual teeth for an exact ratio. Pitch diameters are proportional but easier to misread.
• Idler gears do not change the ratio. A gear placed between input and output reverses direction but leaves the overall ratio set by the first and last gears unchanged.

Limitations and notes

This calculator returns the theoretical, ideal gear ratio and the speed it implies, computed purely from tooth counts. It assumes perfectly meshing gears with no slip, so it does not account for friction, backlash, gear efficiency losses, or the slight torque drop every real gearset suffers — measured output torque will be a little under the ideal multiple. It also models a single gear pair: in a multi-stage gearbox, multiply the individual stage ratios together to get the overall ratio, and remember an idler between two gears changes rotation direction but not the ratio. The output RPM figure is exact arithmetic from your inputs, rounded only for display. Everything runs privately in your browser: the tooth counts and RPM you type stay on your device and nothing is uploaded. Treat the result as an accurate design estimate, and confirm critical builds against the manufacturer’s gear specifications.

For related work, pair this ratio with the engine displacement calculator to size a powerplant, estimate output with the horsepower calculator, or check rolling distance using the tire size calculator — and find more in the automotive category.