SizingKitFree gear ratio rpm calculator
A gear ratio is a pair of whole numbers
Enter the tooth counts of each mesh and this returns the output speed, the output torque and the overall ratio for a train of up to four stages, with speed and torque printed leaving every stage rather than only at the end. It then runs the relation backwards: give it the ratio you want and it lists the integer pairs that come closest, how far each one misses in rev/min, and the center distance each forces at your pitch. Free, no account, and every figure computed in the browser.
- 100% free
- No signup
- Up to 4 meshes
- Tooth pairs ranked
- lbf·ft and N·m
The motor or engine end. 1,750 is a 4-pole induction motor under load.
Leave it as it is if you only want speeds — the ratio does not depend on it.
A compound train is stages multiplied, not added. Two 6:1 stages are 36:1, and each one only has to be a pair you can actually cut.
| Mesh | Driving teeth | Driven teeth | Ratio |
|---|---|---|---|
| 1 | 3.000:1 | ||
| 2 | 2.250:1 |
Default 97% — The middle of the 94–99% band that enclosed spur and helical drives are rated across. It is not a standard's number and there is no standard's number to have — AGMA 6034 gives the method for rating a real gearbox, not a constant to reuse.
10 DP is module 2.540 mm, which is 1.6% off the standard 2.5 module — near enough to look right on a drawing and far enough that the two will not mesh.
OUTPUT SPEED
259
rev/min · 27.15 rad/s · turning the same way as the input
OUTPUT TORQUE
286 lbf·ft
387 N·m
- Overall ratio
- 6.7500:1 reduction
- Torque multiplied by
- 6.351×
- Power in
- 15 hp / 11.2 kW
- Power out
- 14.1 hp / 10.5 kW
| Leaving mesh | rev/min | lbf·ft | N·m | Center distance |
|---|---|---|---|---|
| 1 — 18T to 54T | 583 | 131 | 178 | 3.600 in / 91.44 mm |
| 2 — 20T to 45T | 259 | 286 | 387 | 3.250 in / 82.55 mm |
Only one number above is soft. Teeth are integers, so 6.7500:1 is exact arithmetic and the output speed inherits nothing but the accuracy of the speed you typed. The torque is the one that carries an assumption: it has been through 2 meshes at 97.0% each, so 5.9% of the input power is leaving as heat in this calculation and the rest of it is at the output shaft. With an even number of external meshes the output turns the same way as the input, which is why a two-stage box needs no idler to keep its original direction.
Tooth pairs that give 4.710:1, and what each one costs
Every pair between 18 and 120 teeth, ranked by how close it lands. The floor is not a preference: 18 teeth is where a 20° full-depth tooth stops being undercut by its own cutter.
what a stock gear catalog means when it does not say
| Driving | Driven | Ratio | Off by | Output rev/min | Center distance | Tooth contact |
|---|---|---|---|---|---|---|
| 24T | 113T | 4.7083 | -0.035% | 372 | 6.850 in / 174.0 mm | hunting — every tooth meets every tooth |
| 21T | 99T | 4.7143 | 0.091% | 371 | 6.000 in / 152.4 mm | common factor 3 — each tooth meets 33 of the 99 |
| 20T | 94T | 4.7000 | -0.212% | 372 | 5.700 in / 144.8 mm | common factor 2 — each tooth meets 47 of the 94 |
| 25T | 118T | 4.7200 | 0.212% | 371 | 7.150 in / 181.6 mm | hunting — every tooth meets every tooth |
| 18T | 85T | 4.7222 | 0.259% | 371 | 5.150 in / 130.8 mm | hunting — every tooth meets every tooth |
| 23T | 108T | 4.6957 | -0.305% | 373 | 6.550 in / 166.4 mm | hunting — every tooth meets every tooth |
| 22T | 104T | 4.7273 | 0.367% | 370 | 6.300 in / 160.0 mm | common factor 2 — each tooth meets 52 of the 104 |
| 19T | 89T | 4.6842 | -0.548% | 374 | 5.400 in / 137.2 mm | hunting — every tooth meets every tooth |
Center distance is (N₁ + N₂) ÷ (2 × DP) at 10 DP, which is the definition of diametral pitch rearranged rather than a table. Full-depth involute geometry, N = 2k ÷ sin²φ with k = 1 for a full-depth tooth; nomenclature per ANSI/AGMA 1012. Fewer teeth than this and the cutter removes part of the flank near the root — a gear that still runs, with less tooth left to carry the load. Nothing in this range is exact, which is normal — a ratio you picked as a decimal usually is not a ratio of two small whole numbers.
How to work a gear train from one end to the other
Three inputs and one decision — and the decision is which pair of whole numbers you can actually get hold of.
Put in what goes into the train
The speed of the driving shaft and, if you care about what comes out of the far end, the torque it is turning under. A 4-pole induction motor on a 60 Hz supply is somewhere near 1,750 rev/min at full load, and the nameplate torque is its rated power divided by that speed rather than by the 1,800 it would turn at with no load on it.
Enter each mesh as two tooth counts
Driving gear first, driven gear second, one row per mesh. Stages multiply rather than add, so a 3:1 followed by a 4:1 is 12:1 overall, and each of those two is a pair that exists in a catalog while a single 12:1 spur pair usually is not. An idler between two gears is left out entirely — it cancels itself, and the panel has a line explaining why.
Take the ratio you can cut, not the one you asked for
The sheet under the answer runs the whole thing backwards: type the ratio you want and it lists every integer pair inside your tooth limits, ranked by how close each lands, with the output speed it gives and the center distance it forces at the diametral pitch you selected. Print that and you have the shortlist to check against what is on the shelf.
Technical specifications
| Meshes handled | 1 to 4 in series, each entered as a driving and a driven tooth count, ratios multiplied not added |
|---|---|
| Tooth range | 6 to 400 teeth per gear, whole numbers only — a fractional entry is refused rather than rounded |
| Undercut floor | Generated from N = 2k ÷ sin²φ: 31.9 at 14.5°, 17.1 at 20°, 11.2 at 25°, rounded up to the next whole tooth |
| Candidate search | Every integer pair from the undercut floor to your ceiling, ranked by error, the best 8 listed with error to three decimal places |
| Center distance | (N₁ + N₂) ÷ (2 × DP) at any of the 12 standard pitches from 3 to 48 DP, printed in inches and millimeters |
| Pitch cross-check | Each DP shown with its module: 10 DP is 2.54 mm, 1.6% off the standard 2.5 module and not interchangeable with it |
| Efficiency default | 97% per mesh, editable — the middle of the 94–99% band, and the only figure on the page that is not exact arithmetic |
| Runs offline | The search runs on the page with no request of any kind, so tooth counts you are trying out never leave the tab |
Frequently asked questions
Does a gear ratio multiply torque as exactly as it divides speed?
It divides speed exactly and multiplies torque very nearly. Speed is pure kinematics — a 54-tooth gear driven by an 18-tooth pinion turns exactly one third as fast, with no allowance for anything, because teeth cannot slip past each other. Torque is the same ratio minus whatever the mesh loses to sliding friction, oil churning and bearing drag, which is 1 to 2% for a well-lubricated spur or helical pair and dramatically more for a worm set. That is why the efficiency on this page is a field rather than a constant: everything else here is arithmetic on whole numbers, and this is the one place a real gearbox departs from it.
What is the smallest pinion I can use before the teeth get undercut?
Eighteen teeth for the 20° full-depth system that stock gears are cut to, and the figure is generated rather than looked up: N = 2k ÷ sin²φ with k = 1 gives 17.1 at 20°, so 18 is the first whole tooth clear of it. The same formula gives 31.9 at 14.5°, which is why old machine-tool gearing runs such large pinions, and 11.2 at 25°. Below the limit the generating cutter sweeps into the flank near the root and removes part of the involute, leaving a gear that meshes but has a thinner tooth root and less contact ratio. A profile-shifted pinion gets under the number legitimately, but that is a drawing change rather than a catalog part.
The candidate list says hunting or repeating. What is the difference?
Whether the same two teeth meet again before every tooth has met every other one. When the counts share no common factor — 19 on 68, say — the pair is a hunting ratio and each tooth touches all of the others in turn, spreading wear and any single damaged tooth's effect across the whole mate. With 20 on 70 the common factor of 10 means each pinion tooth only ever meets seven of the wheel's teeth, so a nick on one tooth hammers the same seven for the life of the drive. It is the reason gear catalogs are full of prime-ish numbers like 19, 23 and 37 that look arbitrary until you factor them.
The ratio I need is not a ratio of two whole numbers. What do I do?
Take the closest pair and read the error in rev/min rather than in percent, because rev/min is the form it will show up in. A 4.71:1 target on a 1,750 rev/min input wants 371.5 rev/min at the output; inside an 18 to 90 tooth window the closest single pair is 18 on 85, which is 4.7222 and lands at 370.6, one rev/min low. Whether that matters depends entirely on whether the output drives a timing function or a fan. Where it does, splitting the ratio over two meshes gets far closer — 21 on 57 followed by 34 on 59 is 4.7101, eight thousandths of a percent out — because the products of two rational numbers land much more densely than either one alone.
Does putting an idler gear in change the ratio?
No — an idler changes the direction and the center distance, and nothing else. Its tooth count appears once as a driven gear and once as a driving gear, so it cancels out of the product exactly, which is why this panel asks only for meshes that change the ratio. What the idler buys you is a reversal, since every external pair reverses rotation and an odd number of them leaves the output turning backwards, and the ability to span a distance without an enormous pair of gears. It carries full tooth load while doing it, so it is not a free part.
Will a 10 DP gear run against a module 2.5 gear?
No, and this is the trap the pitch selector is here to make visible. Ten diametral pitch is a module of 25.4 ÷ 10 = 2.54 mm, which is 1.6% away from the standard 2.5 module — close enough that the two gears will go together on a shaft centers apart and look plausible, and far enough that the teeth do not share a common tooth thickness or a common tooth spacing. They will run rough, load unevenly across the face and wear fast. The two series are separate systems that happen to be near each other around 10 DP, not the same system in two units.
Can I get the ratio from pitch diameters instead of counting teeth?
Yes, provided both gears are the same pitch and you are using the pitch diameter rather than the outside diameter. Two gears only mesh if they share a diametral pitch, and at a shared pitch the pitch diameter is simply the tooth count divided by that pitch, so the diameter ratio and the tooth ratio are the same number. The gotcha is measuring: what a caliper reaches on a spur gear is the outside diameter, which for a full-depth tooth is (N + 2) ÷ P, two whole addendums larger than the pitch circle. Counting teeth takes ten seconds and cannot be wrong.
About gear ratios, and why the decimal is the last thing to decide
A ratio is not a quantity you specify, it is a quantity you discover after choosing two tooth counts, and almost every mistake in gear selection starts by forgetting that direction of travel. The counts have to be whole numbers, they have to be large enough not to be undercut by their own cutter, they have to be small enough to fit the housing, and their sum together with the diametral pitch fixes the center distance to a hard number the bearings then have to sit at. Four constraints, two integers, and the decimal ratio falls out of whichever pair survives. That is why this page reports the ratio to four places but ranks the tooth pairs: the four places are the consequence, and the pair is the decision.
The trade the whole thing exists to make is speed for torque, and it is worth being precise about what is conserved. Power is, near enough — a reduction that divides speed by six multiplies torque by six and leaves the product where it was, minus a percent or two per mesh into heat. Nothing about that changes what a motor can do; it changes what it can do it at. A machine that needs 400 lbf·ft at 60 rev/min is asking for 4.6 hp, which a 5 hp motor already makes at 1,750 rev/min as 15 lbf·ft — what is missing is not a bigger motor but the 29:1 in between, and the same shaft power arrives at the far end either way. If the shaft power itself is what you are converting, the torque-to-horsepower page is where the constant behind it is derived, and where a belt drive would do the same job without cutting anything, the two-pulley geometry gets you the ratio from two diameters instead of two tooth counts.
Two things this page will not do. It does not rate a gear: bending and contact stress for a real tooth need the face width, the material, the quality number, the misalignment and a service factor, which is AGMA 2001 territory and a design calculation rather than a look-up. And it does not size the shaft that carries the reaction, which matters more than people expect, because a mesh pushes the two gears apart with a radial force of roughly the tangential load times the tangent of the pressure angle — the reason a 25° pinion is stronger in bending and harder on its bearings at the same time. What resists that push is the shaft's own section, and the section properties page is where that starts. Where the output of the train is a machine spindle, the number you are ultimately chasing is usually not rev/min at all but surface speed at the cutter, which changes with every tool you put in the holder while the back gear stays where it is.
What happens to the tooth counts you type
Every number on this page is worked out by JavaScript running in the tab you are reading it in. Nothing you type — loads, lengths, nameplate ratings, the rates your utility charges you — is uploaded, logged or kept, which is also why the calculators carry on working in a mechanical room with no signal.
The candidate search runs over a few hundred integer pairs every time you change a field, which is fast enough to feel instant and small enough that there would be no reason to do it anywhere but on your own device. Nothing about the ratio you are chasing is transmitted, so a design you have not published yet stays that way.