Gear Ratio: Speed for Torque, With the Math
Engineering · 5 min read · Last updated September 2026
The core formulas
Output RPM = input RPM ÷ ratio
Ideal torque multiplication = ratio
Worked example: 20 T pinion at 1,500 rpm → 40 T gear. Ratio = 40 ÷ 20 = 2:1. Output = 1,500 ÷ 2 = 750 rpm. The output shaft turns half as fast with (ideally) twice the torque — power stays constant, which is the whole point.
Chaining stages
Multi-stage ratios multiply: a 20:40 stage then a 20:30 stage then a 20:25 stage gives 0.5 × 0.667 × 0.8 = 0.267 — a 3.75:1 overall reduction. Input 1,500 rpm → 400 rpm out. Each mesh adds friction losses (typically a few percent), so real output torque is slightly under the ideal figure.
Reading a ratio in the real world
Ratios below 1 (overdrive, e.g. 0.8:1) raise output speed and cut torque — that is your car's highway gear. Ratios above 1 (reduction) are climbing gears and gearboxes. Bicycle gearing, conveyor speeds and drill chucks all follow the same two-formula logic; the Gear Ratio Calculator handles the arithmetic for any teeth counts.
Try the calculators
Ratio table: teeth in, RPM out
The ratio sets the output speed on its own — output is input ÷ ratio. With a 1,500 rpm input the table reads:
| Driver → driven | Ratio | Output at 1,500 rpm |
|---|---|---|
| 20 T → 60 T | 3.00 | 500 rpm |
| 20 T → 40 T | 2.00 | 750 rpm |
| 30 T → 45 T | 1.50 | 1,000 rpm |
| 40 T → 40 T | 1.00 | 1,500 rpm |
| 40 T → 30 T | 0.75 | 2,000 rpm |
| 45 T → 30 T | 0.667 | 2,250 rpm |
A ratio below 1 always speeds the output up and a ratio above 1 always slows it down, so the same table is an overdrive chart read from the bottom up.
Working backwards to a target speed
Driven teeth = required ratio × driver teeth — round to a whole tooth, then recompute
To turn 1,500 rpm into 400 rpm the required ratio is 1,500 ÷ 400 = 3.75. One 20-tooth driver would need 75 teeth, which most single-stage housings will not hold, so split it: 20 T → 40 T gives 2.00, then 16 T → 30 T gives 1.875, and 2.00 × 1.875 = 3.75. Output is 1,500 ÷ 3.75 = 400 rpm. Teeth counts are whole numbers, so always recompute the output from the teeth you actually fit rather than trusting the target.
Where the ideal torque figure leaks away
A spur-gear mesh is roughly 98% efficient, so a nominal 2:1 stage multiplies torque by about 1.96 rather than 2. Run three stages and the efficiency multiplies out to 0.98 × 0.98 × 0.98 ≈ 0.94 — about 6% of the torque gone as heat and noise before the output shaft turns. Helical gears trade a little more loss for quieter running, and wear, lubrication and bearing drag add further on top. Gears still exchange speed for torque, but they never hand the ideal figure back.
Worked example: Gear Ratio Calculator at its default inputs
Open Gear Ratio Calculator and press calculate without editing a field. What comes back is the table and result below, so the gear-ratio numbers here are checkable in one click.
| Input | Default |
|---|---|
| Driver Teeth | 20 |
| Driven Teeth | 60 |
Result: Gear Ratio: 3.00:1
The steps behind that answer
- Formula: Gear Ratio = Driven Teeth / Driver Teeth
- Step 1: Ratio = 60 / 20
- Step 2: Ratio = 3.00:1
- Step 3: Speed reduction = 1/3.00 = 0.333
Driver Teeth: half, as given, and half again
Same calculator, same fields, one change: driver teeth.
| Driver Teeth | Result |
|---|---|
| 10 | Gear Ratio: 6.00:1 |
| 20 | Gear Ratio: 3.00:1 |
| 30 | Gear Ratio: 2.00:1 |
The middle row is the default. The outer two show how far the answer drifts when driver teeth is wrong by half or by a half in the other direction.
Related guides
The ratio is a trade, not a free gain
Gear ratio is driven teeth divided by drive teeth. A higher ratio multiplies torque at the wheel and lowers speed for the same engine rpm; a lower ratio does the opposite. Energy is conserved, so the extra pull is paid for in revolutions.
Output rpm is input rpm divided by the ratio, and torque is input torque multiplied by it, minus losses. That is why a low first gear feels strong and why top gear feels weak at low speed.
Tyres and wheels change the real gearing
The final drive ratio is only half of it: a larger rolling radius lowers the effective ratio, so bigger tyres make the vehicle longer-legged and slower to accelerate. A tyre size change can undo a sprocket change entirely.
Road speed follows from engine rpm, overall ratio and rolling circumference. If you are chasing a specific cruise rpm, calculate all three together rather than changing one and testing.
Where the ratio matters most
Off-road and towing use low ratios for control at low speed; highway economy uses tall ratios to keep rpm down. Racing sits in between and is decided by where the engine makes power, not by a single optimum number.
Peak torque and peak power occur at different rpm, so the useful question is what the ratio does across the rev range you actually use. A ratio that is perfect at peak power can be unpleasant everywhere else.
Frequently asked questions
How do I calculate gear ratio?
Divide the driven gear’s tooth count by the driver’s. A 20-tooth driver turning a 40-tooth gear is a 2:1 reduction — output speed halves.
Does a higher gear ratio mean more speed or more torque?
More torque, less speed, when the ratio is above 1 (reduction). Below 1 it is an overdrive: more speed, less torque. Power stays roughly constant either way.
How do multiple gear stages combine?
Multiply the stage ratios. Stages of 0.5, 0.667 and 0.8 combine to 0.267 — an overall 3.75:1 reduction.
Why is real output torque lower than the ideal number?
Friction. Every gear mesh loses a few percent to sliding contact and lubrication drag, so a 2:1 stage multiplies torque by slightly less than 2.
How do I get exactly 400 rpm from a 1,500 rpm motor?
The required ratio is 1,500 ÷ 400 = 3.75. One route is a 20 T → 40 T pair (2.00) followed by 16 T → 30 T (1.875), because 2.00 × 1.875 = 3.75 gives 400 rpm at the output. Whole-tooth counts rarely hit a ratio exactly, so recompute the output from the teeth you fit.
How much power is lost passing through a gear train?
Roughly 1–2% per spur-gear mesh: about 2% for a single 2:1 pair, and around 6% across three stages because 0.98 × 0.98 × 0.98 ≈ 0.94. Helical gears, wear and under-lubrication all lose more, and bearings and seals add a further amount.
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