Gear and Pulley Ratio Calculator

Gears, chains and belts: one stage or two, plus belt length and road speed

Every rotary drive asks the same question in different hardware: how much speed do I trade, and for how much torque? This calculator answers it for gear or chain stages (count teeth) and belt pulleys (measure diameters), one stage or two stages multiplied for compound drives. Add an input speed for output rpm, a torque and efficiency for real output torque, a centre distance for open belt length, and a tyre diameter to turn final rpm into vehicle speed. Direction reversals (every external gear mesh flips direction; open belts and chains do not) are stated in the reading section, because the ratio alone never mentions them.

Applies to torque only; speed ratio is set by geometry.
Enables the open-belt length result.
Turns the final output rpm into vehicle speed.

Disclaimer: This calculator gives estimates for general information only. It is not financial, medical or other professional advice. Real drives lose speed to belt slip and teeth to design limits this page does not check; verify load-critical drives with the component makers’ data.

What this calculator does

A stage ratio is driven divided by driver: in teeth for gears and chains (where the count is exact), in diameters for belts (where pitch diameter is the honest measure). Two stages multiply, which is how modest pairs build deep reductions: 2:1 after 3:1 is 6:1 overall, not an average of anything. Output speed is input divided by the total ratio. Output torque is input torque times the total ratio, discounted by the efficiency you supply, and that pair of facts is the entire economy of gearing: speed and torque trade against each other, power (minus losses) is conserved. Belt mode adds the two belt-only quantities: belt speed at the driver, and the open-belt length from your centre distance.

How to use it

  • Teeth are exact; pulley diameters should be pitch diameters. A belt rides partway into its groove, so the outside diameter overstates the working diameter slightly; for timing belts, count teeth and use gear mode instead.
  • Compound means the driven of stage 1 shares a shaft with the driver of stage 2. If your two stages are separate drives in sequence the same multiplication applies to the overall speed; if they are alternative ratios (a gearbox’s gears) it does not, and each should be run separately.
  • Efficiency belongs to the whole drive. Each gear mesh or belt stage typically keeps 95 to 99% of power; the torque row uses your single overall figure because published per-stage figures vary by type, lubrication and load.
  • Road speed needs effective diameter. A loaded tyre squashes, so its rolling diameter is a little less than the static one; the vehicle-speed row is an estimate from the figure you give, and the Tire Size Calculator decodes what any sidewall code claims.

The formulas

  • Stage ratio = driven / driver (teeth or diameters). Total ratio = stage 1 × stage 2 (stages multiply).
  • Output speed = input speed / total ratio. Output torque = input torque × total ratio × efficiency.
  • Belt speed = π × driver diameter × input rpm. Open belt length ≈ 2 × centre distance + π × (D + d) / 2 + (D – d)² / (4 × centre distance).
  • Vehicle speed = output rpm × π × tyre diameter, converted (tyre in inches: mph = rpm × π × diameter × 60 / 63,360).

Worked examples

A simple gear pair. 20 teeth driving 40, at 3,000 rpm with 50 units of input torque: ratio 2.00:1, output 1,500.00 rpm, ideal output torque 100.00, and at 95% overall efficiency 95.00. Note what did not happen: power did not double. The output turns at half speed with (nearly) twice the torque, which is the trade every gearbox sells.

A compound reduction. Add a second stage, 15 driving 45, behind the pair above: stages of 2.00 and 3.00 multiply to 6.00:1, and 3,000 rpm becomes 500.00 rpm. This is how winches, mixers and mill drives reach deep reduction without a single enormous gear, and the stage-by-stage reading shows which pair contributes what.

A belt drive, with its belt. A 100 mm driver turning a 200 mm pulley at 1,450 rpm: ratio 2.00:1, output 725.00 rpm, belt speed 7.59 m/s. With 500 mm between centres the open belt length is 1,476.24 mm, the figure a belt order is written from (before tensioning allowance, which the limitations note).

Reading your results

Ratios above 1 are reductions (slower, stronger); below 1 are overdrives (faster, weaker), and the calculator reports the plain number both ways deserve. Direction: each external gear mesh reverses rotation, chains and open belts preserve it, crossed belts reverse it, so a two-mesh compound gear drive ends turning the input’s way. And read the torque row with its efficiency attached: an ideal figure is a promise no hardware keeps, which is why the efficiency field exists and why the results print it.

Limitations

  • Belt slip and creep are real. Friction belts typically lose 1 to 3% of speed to slip under load; the ratio here is the geometric ideal, and synchronous (toothed) belts are the fix when the loss matters, counted as gears.
  • No strength or life checks. Tooth bending, contact stress, belt tension ratings, minimum wrap angles and bearing loads decide whether a drive survives, and none of them is assessed here.
  • Belt length is the geometric open-belt figure. Installation and tensioning allowances, idlers and crossed-belt geometry change the orderable length; makers’ catalogues finish that job.
  • Internal gears and planetaries differ. Ring-gear and planetary arrangements follow their own ratio rules (and do not reverse like external meshes); this page covers external stages and pulleys only.

Frequently asked questions

Why do compound ratios multiply instead of adding?

Because each stage acts on what the previous stage produced: the first pair halves the speed, the second thirds what is left, and a third of a half is a sixth of the original. Addition would describe stages acting on the original speed independently, which is not the machine anyone built. The same logic in reverse explains overdrive chains, and it is why gearbox overall ratios, from bicycle cassettes to mill drives, are always quoted as products of their stages.

Does a bigger ratio always mean more pulling power?

More torque at the shaft, yes; more power, no. Power out is power in minus losses, always. What the ratio buys is the ability to deliver that power at a speed the load can use: a winch needs torque at near-zero speed, a fan needs speed at modest torque, and the right ratio matches the engine’s comfortable operating point to the load’s demand. The confused version of this idea, that gearing creates energy, is the one claim the torque row’s efficiency figure exists to correct.

Chain or belt: which ratio should I trust?

Chains, like gears, are exact: sprocket teeth fix the ratio regardless of load, which is why timing and indexing drives use them. Friction belts are nominal: load, tension, wear and contamination all move the real ratio by a percent or two through slip, and the drift grows exactly when the drive works hardest. For a pump or compressor that hardly matters; for anything synchronised it decides the technology before it decides the numbers.

How do I get vehicle speed from gearing?

Multiply the engine speed down through every ratio between crank and wheel (gearbox, transfer case, final drive, each a stage here), then convert wheel rpm to road speed with the tyre’s circumference, which the optional tyre field does in one step: at 500 wheel rpm on a 26 inch tyre the speed is 38.67 mph. The Tire Size Calculator supplies honest diameters from sidewall codes, and its speedometer-error section covers the same ground from the other direction.

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Method: stage ratios from teeth or pitch diameters, stages multiplied, torque discounted by user efficiency, standard open-belt length formula. Last reviewed: 14 October 2026.