Gear Ratio Calculator
Speed, torque and teeth across the mesh: ratio, output rpm and honest torque after the efficiency tax — spur, worm or planetary.
Gear Ratio Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Single mesh; compound trains multiply manually
- Efficiency entered, not derived
In short: A 20-tooth pinion driving a 60-tooth wheel is a 3:1 reduction: 1,800 rpm in becomes 600 rpm out, and 10 N·m at the pinion becomes 30 N·m ideal — 28.500000 N·m at 95% efficiency. The tax is the lesson: spur meshes keep 90–99% per stage, worm gears surrender up to half in sliding friction, and every lost percent leaves as heat the housing must drink.
Formula
ratio = Nₙᵣᵢᵛₑn / Nₓ · rpmₒᵤₜ = rpmᵢₙ / ratio · Tₒᵤₜ = Tᵢₙ × ratio × η
A gear mesh is a lever that turns: tooth counts set the trade, speed divided is torque multiplied — then efficiency takes its cut. The arithmetic is conservation dressed in involute teeth; the efficiency is friction's receipt, and worm sets pay the largest because their teeth slide rather than roll.
Worked Example
- Count the driver and driven teeth.
- Enter the input speed and torque.
- Set the efficiency for the mesh type.
- Read ratio, output rpm and taxed torque.
Defaults: 20→60 teeth, 1,800 rpm, 10 N·m, 95% → ratio 3, output 600 rpm, torque 28.500000 N·m. The overdrive check: swap the tooth counts — ratio 1/3, output 5,400 rpm, torque 3.166667 N·m. Speed and torque always trade through the same ratio.
Strengths & Limits Of This Model
Where this engine is strong
- Speed and torque priced together
- Efficiency tax explicit
Where it stops
- No tooth-strength checks
- No backlash or wear model
Practical Use Cases
Drive selection
motor to machine matching
Gearbox specs
speed vs torque budget
Teaching
the conservation with a tax
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Gear Ratio Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why does torque multiply with the SAME ratio that divides speed?
Because power is the conserved quantity, not either factor: power equals torque times speed, so if the mesh cuts speed by three it must multiply torque by three just to break even — and by slightly less than three because friction collects the difference. A gearbox is a torque transformer, never an amplifier; any ratio that raised power would be printing energy.
Which gear is 'driven' — and does it matter which I call that?
The driven gear is the one whose shaft does the useful work; the driver is where the motor attaches. Naming them matters because the ratio is driven÷driver — more driven teeth means reduction (slower, stronger), more driver teeth means overdrive (faster, weaker). Swap the labels and the same mesh trades speed back for torque, which is exactly what reversing a gearbox does.
Why are worm efficiencies so much lower?
Because the worm's tooth slides along the wheel's face rather than rolling — the same reason a screw holds: friction is the mechanism, and at high ratios it approaches self-locking, where backdriving stalls entirely. Spur and helical teeth roll, so they lose a few percent; worm sets routinely lose forty or more. The page's efficiency input is where that physics is declared, not discovered.
Does idler gear count change the ratio?
No — an idler between driver and driven cancels its own teeth: it reverses direction and shares the load but leaves the overall ratio untouched. Compound trains differ: two gears on ONE shaft form a compound pair and their ratios multiply. The page prices the simple mesh; chains of meshes multiply their ratios and divide their efficiencies.
What is the efficiency tax in numbers?
Each spur stage keeps roughly 90–99% depending on lubrication and wear; a three-stage box at 98% per stage delivers about 94% overall. A worm set at a typical 50–75% can lose nearly half the input power as heat — which is why worm housings have fins and oil considerations that spur boxes rarely face. Every lost percent becomes heat the housing must reject.
Why does gear ratio use tooth counts instead of diameters?
Because meshing gears share the same pitch — teeth must be the same size to interlock — so the tooth count IS the circumference in pitch units, and the count ratio equals the diameter ratio exactly. Counting teeth is also the only measurement that is exact: diameters wear and measure with error, teeth are integers. The formula's integers are the involute's mercy.
Can the output torque exceed the motor's rating safely?
The mesh multiplies torque, not capacity — the driven SHAFT and gear teeth must still be sized for the multiplied load, and the motor may stall if the machine demands more than the nameplate. Reduction buys mechanical advantage at the cost of speed, and every element downstream prices the new torque in its own metal. The page gives the number; the shaft design pays for it.
How does backlash or tooth wear show up in the numbers?
It does not — the ratio arithmetic is kinematic ideal, while backlash steals motion at reversal and wear steals profile, raising noise and eventually the efficiency input's honesty. That is why the efficiency field doubles as a health gauge: a spur mesh that drops from 97% to 90% is telling you about misalignment or starvation before the teeth visibly complain.