Gear Ratio Calculator
Gear ratio from tooth counts, with output RPM, torque multiplication and mechanical advantage, and an optional second stage for compound gear trains.
Gear Ratio Calculator: with the default inputs, gear ratio is 3.5:1.
The input gear, on the motor or engine side. Also called the driver or pinion.
The output gear, on the load side.
Torque going into the driving gear.
Driven teeth ÷ driving teeth, written as N:1.
- Ratio (numeric)
- 3.5
- Simplified whole-number ratio
- 7 : 2
- Output speed (RPM)
- 400
- Output torque (N·m)
- 35
- Torque multiplication (×)
- 3.5
- Mechanical advantage
- 3.5
- Stage 1 ratio
- 3.5
- Stage 2 ratio
- 1
- What the train does
- Reduction — 3.5× slower, 3.5× more torque
Assumptions
- Ideal, lossless gears — no friction, backlash or windage.
- Ratios are taken from tooth counts; pulley diameters or sprocket teeth work identically.
- Mechanical advantage equals the gear ratio, which is only true when efficiency is 100%.
- Steady-state operation; inertia during acceleration is not included.
| Point | Speed (RPM) | Torque (N·m) | Power (W) |
|---|---|---|---|
| Input | 1,400 | 10 | 1,466.08 |
| Output | 400 | 35 | 1,466.08 |
Power is identical at every point because this is an ideal train. A real spur-gear stage is 96–99% efficient, a worm drive can be 50–90%, so multiply the output by the efficiency of each stage.
How this is worked out
The formula
Ratio = driven teeth ÷ driving teeth Compound train = ratio₁ × ratio₂ × … Output RPM = input RPM ÷ ratio Output torque = input torque × ratio Mechanical advantage = ratio (ideal, lossless) Power in = power out: τ_in × ω_in = τ_out × ω_out
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- Driving gear teeth
- The input gear, on the motor or engine side. Also called the driver or pinion.1 or more · whole numbers only · defaults to 20
- Driven gear teeth
- The output gear, on the load side.1 or more · whole numbers only · defaults to 70
- Input speed
- A number.0 or more · defaults to 1400
- Input torque
- Torque going into the driving gear.0 or more · defaults to 10
- Add a second stage(under More options)
- For a compound gear train, where the ratios multiply.defaults to off
- Stage 2 driving teeth(under More options)
- A number.1 or more · whole numbers only · defaults to 15
- Stage 2 driven teeth(under More options)
- A number.1 or more · whole numbers only · defaults to 45
What you get back
- Gear ratiomain answer
- Driven teeth ÷ driving teeth, written as N:1.
- Ratio (numeric)
- Simplified whole-number ratio
- Output speed (RPM)
- Output torque (N·m)
- Torque multiplication (×)
- Mechanical advantage
- Stage 1 ratio
- Stage 2 ratio
- What the train does
What this assumes
- Ideal, lossless gears — no friction, backlash or windage.
- Ratios are taken from tooth counts; pulley diameters or sprocket teeth work identically.
- Mechanical advantage equals the gear ratio, which is only true when efficiency is 100%.
- Steady-state operation; inertia during acceleration is not included.
About this calculator
A gear ratio is one division — driven teeth over driving teeth — and everything else follows from it. Enter the two tooth counts and an input speed and you get the ratio, the output speed, the torque at the output and the mechanical advantage. Turn on the second stage under More options for a compound train, where the stage ratios multiply.
Which gear is which
The driving (or driver, or input, or pinion) gear is the one connected to the power source. The driven gear is on the load side. Ratio = driven ÷ driving, so a 20-tooth pinion turning a 70-tooth wheel is 3.5:1 — the big gear turns once for every 3.5 turns of the small one. Getting these backwards inverts everything, so a good sanity check is that a reduction (ratio above 1) always means the output is slower and stronger.
The same arithmetic covers pulleys (use diameters) and chain sprockets (use teeth). A bicycle in a 50-tooth chainring and an 11-tooth cog is running 0.22:1 — a heavy overdrive, which is exactly what a top gear is.
Speed down, torque up, power constant
Gears do not create energy. They trade speed for torque at a fixed product: a 3.5:1 reduction gives exactly 3.5 times the torque at 1/3.5 of the speed, and the power at the output equals the power at the input. That trade is the whole reason gearboxes exist — an electric motor makes its power at 3,000 RPM and a winch drum wants 100 RPM and a lot of pull.
Mechanical advantage and torque multiplication are the same number seen from two angles: the ratio is how much the output torque exceeds the input torque, and equally how much force you gain at the cost of distance. In an ideal train it is exactly the gear ratio.
Compound trains
Two stages in series multiply: a 3.5:1 followed by a 3:1 is 10.5:1 overall, not 6.5:1. This is how gearboxes get to 60:1 without a gear the size of a dinner plate. It also multiplies the losses — each stage keeps 96–99% in spur gears, so a four-stage box loses roughly 10%.
An idler gear between two others changes the direction of rotation but not the ratio at all: it appears once as a driven gear and once as a driver, and cancels out.
Where the ideal model breaks
- Efficiency. Nothing here subtracts losses. Spur and helical gears are 96–99% per stage, bevel around 95%, and worm drives anywhere from 50% to 90% depending on lead angle — a worm gearbox's output torque can be far below ratio × input.
- Backlash and wind-up matter for positioning, not for steady drive.
- Common factors. If the tooth counts share a factor, the same pairs of teeth meet repeatedly and any single bad tooth wears one partner hard. Designers pick "hunting" ratios (no common factor) so wear spreads.
- Tooth count minimums. Below roughly 17 teeth at a 20° pressure angle, standard cutting undercuts the tooth root and weakens it, unless the gear is profile-shifted.
- Torque ratings. A ratio that works arithmetically may still shear the small gear. Check the gear's rated torque, not just the numbers.
Frequently asked questions
▸How do I calculate a gear ratio?
Divide the driven gear's tooth count by the driving gear's. A 20-tooth driver turning a 70-tooth driven gear is 70 ÷ 20 = 3.5:1.
▸Does a gear ratio multiply torque?
Yes, by exactly the ratio, at the cost of the same factor in speed. A 3.5:1 reduction turns 10 N·m into 35 N·m at 1/3.5 the RPM. Power in equals power out, minus friction.
▸How do compound gear trains work?
The stage ratios multiply. A 3.5:1 stage feeding a 3:1 stage gives 10.5:1 overall, which is how compact gearboxes reach very high reductions.
▸What does an idler gear do to the ratio?
Nothing. It reverses the direction of rotation, but because it is both a driven gear and a driver its tooth count cancels out of the overall ratio.
▸Is mechanical advantage the same as gear ratio?
For an ideal gear train, yes — the ratio is exactly how much the output torque exceeds the input torque. Real trains lose a few percent per stage to friction, and worm drives lose a lot more.
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Solve speed = distance ÷ time for any of the three, with hours-minutes-seconds input, km/h, mph or m/s output, running pace per km and per mile, and the steps shown.
Newton's second law solved for force, mass or acceleration, plus weight on any planet from NASA surface gravities — in newtons, pounds-force and kgf.
Power from work and time (P = W/t), force and speed (P = Fv) or voltage and current (P = VI) in watts, kW, horsepower and BTU/h, with energy use per hour and day.