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Gear Ratio and Gearmotor Torque Calculator

Work out the gear ratio, output speed, and output torque of an industrial gearmotor or speed reducer in one place. Enter the ratio directly, or from the tooth counts, or as a stack of stages, then give the tool the motor power or a known input torque, the input speed, the efficiency per stage, and a service factor. It returns the output speed at the gearbox shaft, the output torque in newton metres, kilogram-force metres, and pound feet side by side, the torque multiplication, and the gearbox rating you should size against once the service factor is folded in. It works in metric or imperial, and every number stays in your browser.

A reduction does two things at once, and they pull in opposite directions. It divides the speed by the ratio and multiplies the torque by the ratio, minus whatever the gears lose to friction along the way. That is the whole reason a small, fast motor can turn a slow, heavy load: the gearbox trades the speed you do not need for the torque you do. This calculator makes that trade explicit so you can pick a ratio from the speed and torque the load actually needs, then confirm the motor can supply the input torque at its rated speed. A gearmotor is the motor and reducer sold as one unit; a speed reducer is the gearbox on its own. The tool treats them the same way, because the gear maths is identical. Free, no sign-up, and built for sizing a real drive.

In short: the gear ratio is the input speed over the output speed, which equals the driven tooth count over the driver tooth count. Output speed is the input speed divided by the ratio, and output torque is the input torque times the ratio times the efficiency. When you know the power, the motor torque is 9,550 x kW / rpm in metric or 5,252 x HP / rpm in imperial. For a 4 kW motor at 1,450 rpm through a 20:1 reducer at 95 percent efficiency, the input torque is 26.34 N.m, the output speed drops to 72.5 rpm, and the output torque climbs to 500.6 N.m (51.0 kgf.m / 369 lb.ft), a 19.0 times gain. With a service factor of 1.25, size the gearbox for at least 626 N.m of rated torque, not the running 500.6 N.m.

Gear ratio

Motor and drive

Gearmotor result

501 N.moutput torque at the gearbox shaft

Gear ratio
20.00:1
Output speed
72.5 rpm
Output torque
500.5 N.m (51.0 kgf.m / 369 lb.ft)
Input (motor) torque
26.34 N.m
Torque multiplication
19.00 x
Required torque (with SF)
626 N.m (461 lb.ft)

A 20.00:1 reduction turns 26.3 N.m into 501 N.m at 72.5 rpm, a 19.0 times torque gain. With a service factor of 1.25, pick a gearbox rated for at least 626 N.m.

How the calculator works

The tool takes a drive train apart into its three linked numbers: the ratio, the speed, and the torque. You describe the ratio in whichever form you have it, then hand the tool the motor side, and it works the load side out. Give it the ratio directly if a catalogue lists it, or the driver and driven tooth counts if you are reading a gear pair, or a list of stage ratios if you are stacking reductions. Then set the input speed in rpm, tell it whether you know the motor power or the input torque, and give it the efficiency per stage and a service factor. The panel returns the output speed, the output torque in three units, the input torque, the torque multiplication, and the rated torque you should size the gearbox against.

The gear ratio is the first thing it settles. A reduction ratio of i to 1 means the input turns i times for every one turn of the output. That same i is the input speed divided by the output speed, and it is also the tooth count on the driven gear divided by the tooth count on the driver, because the teeth have to mesh one for one. When you enter a stack of stages, the tool multiplies the stage ratios together, since each stage reduces the output of the one before it. Three stages of 3 to 1 give an overall 27 to 1, not 9 to 1, because the reductions compound.

From the ratio the speed falls straight out. Output speed is the input speed divided by the ratio: n_out = n_in / i. A 1,450 rpm motor through a 20 to 1 reducer turns its output shaft at 72.5 rpm, because 1,450 divided by 20 is 72.5. Speed is the easy half of the trade, and it is exact, since gear teeth do not slip the way a belt can. The ratio you set is the speed division you get, and no efficiency term touches it. Efficiency only shows up on the torque side, where the friction lives.

Torque is where the reducer earns its keep. Output torque is the input torque times the ratio times the efficiency: T_out = T_in x i x eff. The ratio multiplies the torque by the same factor it divides the speed by, and the efficiency shaves a little off because the gear mesh loses some of the work to friction and heat. When you enter the power instead of a torque, the tool first finds the motor torque from the power and speed, using T = 9,550 x kW / rpm in metric or T = 5,252 x HP / rpm in imperial, then runs it through the ratio and efficiency. On the default 4 kW at 1,450 rpm, the motor torque is 26.34 N.m, and a 20 to 1 reducer at 95 percent turns that into 500.6 N.m, a 19.0 times gain rather than the full 20, because the 5 percent loss costs you the last bit.

The last number is the one that decides what you buy. The gearbox has to be rated for more than the running torque, because starts, jams, and long hours punish it beyond the steady load. The tool multiplies the output torque by the service factor to get the rated torque you should size against, so 500.6 N.m at a service factor of 1.25 asks for a gearbox rated to at least 626 N.m. Pick a unit whose catalogue rating clears that number and you have a drive that lasts. The output speed and torque also feed the wider machine-sizing work in the Industrial Automation silo, where the conveyor, pump, and fan tools take the shaft speed a gearmotor delivers and turn it into a line speed or a flow.

The gear ratio and how to get it

The gear ratio is the single number that sets everything else, so it is worth being precise about what it means. A ratio of i to 1 is a reduction: the fast input shaft turns i times for each slow turn of the output shaft. The bigger the i, the more the speed drops and the more the torque climbs. A 20 to 1 reducer is a deep reduction that turns a 1,450 rpm motor into a 72.5 rpm output, while a 4 to 1 reducer is a gentle one that only takes 1,750 rpm down to 437.5 rpm. Ratios below 1, where the output turns faster than the input, are overdrives or step-ups, and they divide torque instead of multiplying it, but industrial gearmotors are reductions almost every time.

There are three honest ways to get the ratio, and the tool accepts all three. The first is to read it off a catalogue or a nameplate, where the maker states it directly, and you type it in. The second is to count teeth. The ratio of a single gear pair is the driven tooth count over the driver tooth count, so a 15 tooth pinion driving a 60 tooth gear is 60 over 15, which is 4 to 1. This works because the teeth mesh one for one, so the small gear has to spin four times to walk the big gear round once. The third is to multiply stages, which the next paragraph covers.

The tooth count route is exact and it is the one to trust when you have the gears in front of you, because it does not depend on any rounding in a catalogue. It also tells you which shaft is which. The driver is the gear the motor turns, the driven is the gear that carries the load, and the ratio is always the driven over the driver for a reduction. If you flip them by mistake you get the reciprocal, an overdrive instead of a reduction, and the torque and speed come out backwards. When the tooth counts give an awkward number, such as 48 over 13, the ratio is simply 3.69 to 1, and the tool carries the full precision rather than rounding it to a tidy figure.

Output speed and output torque

Once the ratio is fixed, the speed is the simplest calculation on the page. Output speed is input speed divided by ratio, full stop. A 1,450 rpm motor and a 20 to 1 reducer give 72.5 rpm, a 1,750 rpm motor and a 4 to 1 reducer give 437.5 rpm, and a 1,460 rpm motor and a 27 to 1 stack give 54.1 rpm. There is no efficiency term and no loss, because gear teeth transmit rotation without slip. Whatever ratio you dial in is exactly the speed reduction you get at the output shaft, which is why a gearbox is the reliable way to set a precise output speed when a belt or a friction drive would creep.

Torque is the mirror image, and it is where the efficiency lives. A reduction multiplies torque by the ratio, so the same 20 to 1 that cuts 1,450 rpm to 72.5 rpm also lifts the torque roughly twenty-fold. It is not quite twenty-fold, because the gear mesh loses a few percent to friction, so the real multiplier is the ratio times the efficiency. At 95 percent, a 20 to 1 reducer gives 19.0 times the input torque, not 20.0. The tool reports both the raw ratio and the actual torque multiplication so you can see the size of the bite the efficiency takes. On a deep or multi-stage reduction that bite grows, because each stage loses its own slice.

The reason speed and torque trade so cleanly is that a gearbox conserves power, minus its losses. Power is torque times speed, so if the speed drops by twenty and the power stays nearly the same, the torque has to climb by nearly twenty to balance the equation. The small shortfall is exactly the friction loss, the power that leaves as heat rather than reaching the output shaft. That is why a highly efficient spur or helical reducer gives back almost the full ratio in torque, while a worm drive, which throws away far more to friction, gives back much less than its nominal ratio. The tool shows the output torque in newton metres, kilogram-force metres, and pound feet together, so a shop that thinks in any of the three can read the result without converting by hand.

Torque from the motor power

Most of the time you do not have the input torque to hand; you have the motor power off the nameplate. Converting between them needs only the speed. In metric, torque in newton metres is 9,550 times the power in kilowatts divided by the speed in rpm. In imperial, torque in pound feet is 5,252 times the power in horsepower divided by the speed in rpm. Those two constants, 9,550 and 5,252, are just unit-conversion numbers that fold in the 2 pi from rotation and the seconds and minutes, so you never have to carry the raw physics. Set the tool to take the power and it does this step first, before it touches the ratio.

The default shows it clearly. A 4 kW motor at 1,450 rpm makes 9,550 times 4 divided by 1,450, which is 26.34 N.m at the motor shaft. That is the input torque the reducer sees, and everything downstream flows from it. Run it through a 20 to 1 reducer at 95 percent and you get 500.6 N.m at the output. The same logic works in reverse: if you know the torque a load needs and the speed it needs it at, you can back out the power the motor must supply, which is the check you run to make sure the motor is not undersized for the job.

One thing to watch is which speed goes into the torque-from-power formula. The motor power and the motor speed belong together, so use the input rpm to get the input torque, then apply the ratio. If you accidentally put the output rpm into the formula you will get a torque that is already multiplied by the ratio, and then multiplying by the ratio again double-counts it. The tool keeps the two speeds straight for you, using the input speed for the power conversion and reporting the output speed separately, so the torque multiplication you read is the honest one and not an artefact of mixing the shafts up.

Efficiency and the gear type

Efficiency is the term that separates a good reducer from a lossy one, and it depends almost entirely on the gear type. A spur or helical stage runs about 95 to 98 percent efficient, so it gives back nearly all of the ratio as torque. A bevel stage is close, around 95 percent. A worm drive is the outlier: it can be anywhere from 40 to 90 percent, and it drops as the ratio climbs and the load rises, because a worm works by sliding one thread across another rather than rolling teeth, and sliding means friction. A high-ratio worm can turn half the input power into heat, which is why worm gearboxes often need the housing sized as a radiator.

When you stack stages, the efficiencies multiply, they do not average. Three spur stages at about 97 percent each give an overall efficiency near 0.97 cubed, which is roughly 91 percent, because the loss compounds the same way the ratio does. The tool applies the per-stage efficiency across the stages you enter, so a three-stage reducer at 97 percent per stage lands near the 91 percent overall that the third worked example uses. This is why a single-stage reducer, where it can reach the ratio you need, is often a touch more efficient than a multi-stage one for the same overall reduction, though the single stage may be physically larger.

The worm case deserves a warning of its own, because its efficiency can fall low enough to change how the drive behaves. Below about 50 percent efficiency a worm can become self-locking, meaning the output cannot back-drive the input, which is either a feature or a hazard depending on the machine. A hoist may want that holding behaviour, while a conveyor that needs to coast to a stop does not. The point for sizing is simpler: never assume the nominal ratio is the torque gain. A 40 to 1 worm at 70 percent gives only 28 times the input torque, not 40, so read the tool’s torque multiplication figure rather than the ratio when you check whether the drive can move the load.

The service factor and sizing the gearbox

The running torque is not the number you size against. A gearbox that is only rated for the steady load it carries in normal running will fail early, because real machines start, stop, jam, and run for long unbroken hours, and every one of those punishes the gears beyond the smooth running value. The service factor is the multiplier that bridges the gap. You take the output torque, multiply it by a service factor, and choose a gearbox whose catalogue rated torque clears the result. On the default, 500.6 N.m times 1.25 asks for at least 626 N.m of rated torque.

The size of the service factor depends on the duty, and the gear industry publishes tables for it. AGMA service factors and the NEMA MG-1 standard set out values by application, and they typically run from about 1.0 for a smooth, light-duty machine that runs a few hours a day up to 2.0 or more for a machine that takes heavy shock loads, runs around the clock, or starts frequently. A uniform load like a steady conveyor might sit at 1.25, while a rock crusher or a machine with a heavy flywheel that slams to a stop wants a much higher factor. Pick the factor from the kind of load the machine really carries, not from the smooth catalogue picture of it.

There is a second check the service factor does not fully cover, and it is worth doing by hand. The starting and peak torque a machine demands can spike far above the running value, especially if the load can jam or the motor can stall. A conveyor that seizes on a trapped object, or a mixer that starts in a set batch, can ask for two or three times the running torque for a moment. The service factor gives you headroom for the wear that long duty causes, but you should also confirm the gearbox and the motor can survive the momentary peak, because a single stall can strip teeth that years of steady running never would. Size for the running torque with a service factor, then sanity-check the peak.

Multi-stage reducers

A single gear pair can only reduce so far before the gears get awkwardly mismatched in size, so deep reductions are built in stages. Each stage takes the slow output of the one before it and reduces it again, and the ratios multiply. Two stages of 5 to 1 and 4 to 1 give 20 to 1 overall, three stages of 3 to 1 give 27 to 1, and so on. The tool’s multi-stage mode lets you type the stage ratios one per line and multiplies them for you, which saves the arithmetic and the chance of a slip when you are stacking three or four numbers.

The trade for a big ratio in several stages is that the efficiency compounds against you. Every stage takes its own small bite, so a three-stage spur reducer at 97 percent per stage lands near 91 percent overall, and the torque multiplication comes out a little below the raw ratio would suggest. The third worked example runs exactly this case: three stages of 3 to 1 for 27 to 1 overall, at 91 percent, turning a 7.5 kW motor into 1,205.4 N.m at 54.1 rpm, a 24.6 times gain rather than the full 27. The deeper the stack, the wider the gap between the nominal ratio and the real torque gain, so on multi-stage drives it pays to read the multiplication figure rather than trusting the ratio.

Staging also changes where the load sits. The first stage runs fast and light, the last stage runs slow and heavy, and the last stage carries the full output torque. This is why the final stage of a big reducer uses the largest gears and the sturdiest shaft: it sees the multiplied torque, while the input stage barely feels it. When you size a multi-stage gearbox you are really sizing that final stage for the output torque plus the service factor, and the tool’s rated-torque figure is exactly what that final stage has to survive. The compact planetary gearboxes common on servo and robotics drives are multi-stage reductions built to pack a high ratio into a short housing.

Reflected inertia and why it matters

There is a second thing a reducer does that the torque and speed numbers do not show, and it matters most on machines that start and stop quickly. A gearbox does not just change the torque and speed the motor feels; it also changes the inertia. The inertia of the load, reflected back through the reducer to the motor shaft, is the load inertia divided by the ratio squared: J_reflected = J_load / i squared. A 20 to 1 reducer cuts the inertia the motor feels by a factor of 400, because the ratio enters as a square, not just once.

That squared term is a large lever, and it is the reason gearboxes appear on servo drives even where the speed reduction is modest. A motor accelerating a heavy load directly would need enormous torque just to spin up the mass, but put a reducer in between and the reflected inertia collapses, so a small, fast motor can accelerate a big load crisply. The cost is that the reducer also multiplies the torque the motor must supply, so there is a sweet spot: too little ratio and the reflected inertia swamps the motor, too much and the torque demand does. Matching the reflected load inertia to the motor inertia, often to within a factor of a few, is the core of servo sizing.

This calculator gives you the ratio, the output torque, and the torque multiplication, which are the steady-state numbers, and it points you at the inertia relationship, but it does not run the full acceleration sum. Sizing a servo means adding the torque to accelerate the reflected inertia through the move profile on top of the torque to hold the load, which is a separate calculation. A dedicated servo and actuator sizing tool for this silo is on the way and will take the reflected inertia this reduction produces and finish that job. For now, use this tool to fix the ratio and confirm the steady torque, and treat the inertia note as the bridge to that next step.

Metric and imperial units

The tool works in either unit system and shows the torque in three units at once, so nobody has to convert by hand. Set it to metric and you enter kilowatts and read newton metres; set it to imperial and you enter horsepower and read pound feet, with the tool converting internally. The output torque always comes back three ways, in newton metres, kilogram-force metres, and pound feet, because a European shop, a torque-wrench-in-kilograms tradition, and a North American shop each read a different one, and lining them up removes the friction of translating a spec across a supply chain.

The conversions behind the scenes are the standard ones. One newton metre is 1 divided by 9.80665 kilogram-force metres, so you divide newton metres by 9.80665 to get kgf.m. One newton metre is 0.73756 pound feet, so you multiply to cross to imperial torque. On the power side, one horsepower is 0.7457 kilowatts, which is how the tool takes an imperial motor rating and runs it through the same metric core. The fifth worked example shows this end to end: a 10 HP motor entered in imperial comes back as 956.3 N.m, 97.5 kgf.m, and 705 lb.ft, all from the one input.

Five worked examples

Example 1: gearmotor from the motor power (the default)

This is the case the tool opens on. A 4 kW motor runs at 1,450 rpm through a 20 to 1 reducer at 95 percent efficiency, with a service factor of 1.25. The tool finds the motor torque first, 9,550 times 4 divided by 1,450, which is 26.34 N.m. Through the 20 to 1 reducer at 95 percent, the output shaft turns at 72.5 rpm and carries 500.6 N.m (51.0 kgf.m / 369 lb.ft), a torque multiplication of 19.0 times. With the 1.25 service factor, the required gearbox rating is about 626 N.m. The lesson: the reducer trades 1,450 rpm down to 72.5 rpm and turns 26 N.m into 500 N.m, which is the whole point of a gearmotor on a slow, heavy load.

Example 2: ratio from the tooth counts

Here you read the ratio off the gears. A 12 tooth driver meshes into a 48 tooth gear, so the ratio is 48 over 12, which is 4 to 1. The motor is 2.2 kW at 1,750 rpm, the efficiency is 96 percent, and the service factor is 1.0 for a smooth light-duty load. The motor torque is 12.01 N.m, the output turns at 437.5 rpm, and the output torque is 46.1 N.m (4.7 kgf.m / 34 lb.ft), a 3.8 times gain. The required rating with the 1.0 factor is about 46 N.m. The lesson: the ratio is just the tooth count of the driven gear over the driver, and a gentle 4 to 1 gives a gentle torque gain to match.

Example 3: a multi-stage reducer

Deep reductions stack. Three stages of 3 to 1 give 27 to 1 overall, at about 91 percent efficiency across the three spur stages. The motor is 7.5 kW at 1,460 rpm with a 1.25 service factor. The motor torque is 49.06 N.m, the output turns at 54.1 rpm, and the output torque is 1,205.4 N.m (122.9 kgf.m / 889 lb.ft), a 24.6 times gain rather than the full 27. The required rating is about 1,507 N.m. The lesson: stage ratios multiply, so three 3 to 1 stages give 27 to 1, not 9 to 1, and each stage takes a small efficiency bite that pulls the real torque gain below the nominal ratio.

Example 4: a worm drive

A worm gives a big ratio in one stage but pays for it in heat. A 40 to 1 worm runs at 70 percent efficiency, driven by a 1.5 kW motor at 1,750 rpm, with a 1.4 service factor for the sliding load. The motor torque is 8.19 N.m, the output turns at 43.8 rpm, and the output torque is 229.2 N.m (23.4 kgf.m / 169 lb.ft), a 28.0 times gain. The required rating is about 321 N.m. The lesson: a worm gives a 40 to 1 reduction in a single compact stage, but it wastes 30 percent of the power as heat, so its torque gain is 28 times, well below the ratio. Never read the nominal ratio as the torque gain on a worm.

Example 5: an imperial gearmotor entered in HP

A shop that thinks in horsepower can size the drive without converting anything by hand. A 10 HP motor at 1,750 rpm drives a 25 to 1 reducer at 94 percent efficiency with a 1.25 service factor. The tool converts internally and reports the motor torque as 40.69 N.m, the output speed as 70.0 rpm, and the output torque as 956.3 N.m (97.5 kgf.m / 705 lb.ft), a 23.5 times gain. The required rating is about 1,195 N.m. The lesson: enter the motor in HP and the tool still reports the output torque in newton metres, kilogram-force metres, and pound feet side by side, so the result reads cleanly whichever unit the rest of the drive is specified in.

Three expert tips

Pick the ratio from both the speed and the torque

A reduction divides the speed and multiplies the torque by the same factor, so the ratio is not a free choice, it is set by what the load needs at both ends. Start from the output speed the machine has to run at and the torque it has to deliver there, and the ratio that gives both is your answer. Then run the check back the other way: at that ratio, can the motor supply the input torque at its rated speed without stalling or overheating? A ratio that gives the right output torque is useless if the motor cannot make the input torque to feed it. Size from the load first, confirm the motor second, and the drive will hold.

The efficiency depends on the gear type, so never assume the ratio is the torque gain

Spur and helical stages run about 95 to 98 percent, so they give back almost the full ratio in torque, but a worm can sit anywhere from 40 to 90 percent and drops as the ratio and load climb. A high-ratio worm can turn half the power into heat, and below about 50 percent efficiency it may even self-lock so the output cannot back-drive. That changes both the torque you get and the way the drive behaves at rest. Read the tool’s torque multiplication figure rather than the nominal ratio, because on a worm the gap between the two is the difference between a drive that moves the load and one that stalls short.

Size against the service factor, not the running torque

The steady output torque is the number the drive carries on a good day; the service factor is what keeps it alive through the bad ones. Multiply the output torque by an AGMA or NEMA service factor, from about 1.25 for a uniform load up to 2.0 or more for shock loads, long hours, and frequent starts, and choose a gearbox whose rated torque clears that number. Then check the starting and peak torque separately, because a jam or a stall can spike far above the running value for a moment, and a single spike can strip teeth that years of steady duty never would. Rated torque with a service factor plus a peak-torque sanity check is the sizing that lasts.

Limits of the method

This calculator gives a sound first pass at a drive train, not a finished gearbox selection. It computes the ratio, the output speed, the output torque, the torque multiplication, and the rated torque against a service factor, which is most of what a sizing exercise needs to pick a unit from a catalogue. It applies a single efficiency figure per stage, treats the ratio as exact, and assumes the motor can supply the input torque you feed it at its rated speed. Those assumptions are close to reality for a well-matched industrial gearmotor running in its normal range.

What it does not do is the detail a full selection carries. It does not read a manufacturer’s thermal rating, so it will not tell you whether a worm gearbox can shed the heat it makes at a high ratio and a long duty, which can limit the drive well before the torque does. It does not run the acceleration sum that servo sizing needs, so it gives you the reflected inertia relationship as a note rather than a full move-profile torque. It does not model the starting and peak torque spikes, which you must check by hand, and it does not account for bearing life, shaft loads, or the mounting. Use the result to fix the ratio and size the steady torque, then confirm the thermal rating, the peak torque, and the mechanical loads against the manufacturer’s data and a qualified engineer before you commit to a unit.

Common mistakes to avoid

The first mistake is flipping the driver and the driven. The ratio for a reduction is the driven tooth count over the driver, and swapping them gives the reciprocal, an overdrive that divides torque instead of multiplying it. Always put the gear the motor turns as the driver and the gear that carries the load as the driven. The second is reading the nominal ratio as the torque gain on a lossy drive. A 40 to 1 worm at 70 percent gives only 28 times the torque, so trust the torque multiplication figure the tool reports, not the ratio, especially on worms and deep multi-stage stacks.

A third mistake is mixing the input and output speeds in the torque-from-power step. The motor power and the motor speed belong together, so use the input rpm to get the input torque, then apply the ratio; feeding the output rpm into the formula double-counts the ratio. A fourth is sizing against the running torque instead of the rated torque, which leaves no headroom for starts, jams, and long hours; always multiply by a service factor and clear the result. A fifth is treating stage ratios as additive, adding three 3 to 1 stages to get 9 to 1 when they multiply to 27 to 1. Keep the driver and driven straight, read the multiplication not the ratio, hold the two speeds apart, size against the service factor, and multiply the stages, and the numbers the tool gives will match the drive you build.

Where this calculator fits

It suits anyone specifying a gearmotor or a speed reducer without opening a full drive-train study. A machine builder choosing a gearbox for a new conveyor or mixer can fix the ratio from the output speed and torque the machine needs, then read the rated torque to pick a unit. A maintenance engineer replacing a failed reducer can confirm the ratio from the tooth counts and match the torque before ordering. A designer laying out a drive can test how the output speed and torque move as the ratio changes, in metric or imperial, and see the service factor headroom at a glance.

Because it separates the ratio, the speed, and the torque, it also builds intuition for the trade a gearbox makes. You can watch the torque climb and the speed fall as you deepen the ratio, see the efficiency bite grow as you stack stages, and watch a worm give back far less than its ratio while a helical stage gives back almost all of it. For the machines a gearmotor drives, the Conveyor Belt Speed and Motor Power Calculator turns the output shaft speed into a belt speed and the motor power a conveyor needs, the Pneumatic Cylinder Force and Air Consumption Calculator covers the air-powered actuators alongside a geared drive, the Air Receiver Tank Size and Compressed-Air Demand Calculator sizes the compressed-air storage behind a shop, and the VFD Energy Savings Calculator shows what slowing a pump or fan with a drive saves. A servo and actuator sizing tool, which takes the reflected inertia this reduction produces and finishes the acceleration sum, is on the way in this silo. For the energy a drive train uses, the Energy Management hub rolls the running cost into the plant-wide picture, and Lean Production carries tools for the flow around the machine.

Frequently asked questions

What does this gear ratio and gearmotor torque calculator do?

It works out the gear ratio, output speed, and output torque of an industrial gearmotor or speed reducer. You enter the ratio directly, from the driver and driven tooth counts, or as a stack of stages, then give the tool the motor power or a known input torque, the input speed in rpm, the efficiency per stage, and a service factor. It returns the output speed, the output torque in newton metres, kilogram-force metres, and pound feet, the input torque, the torque multiplication, and the rated torque you should size the gearbox against once the service factor is folded in. On the default 4 kW motor at 1,450 rpm through a 20:1 reducer at 95 percent, it reports 26.34 N.m input, 72.5 rpm output, 500.6 N.m output torque, a 19.0 times gain, and a required rating of about 626 N.m.

What is the gear ratio formula?

The gear ratio is the input speed divided by the output speed, which equals the tooth count on the driven gear divided by the tooth count on the driver. A ratio of i to 1 means the input turns i times for every one turn of the output. For a single gear pair, a 15 tooth driver into a 60 tooth gear is 60 over 15, which is 4 to 1. For a multi-stage reducer, the overall ratio is the product of the stage ratios, so three stages of 3 to 1 give 27 to 1, not 9 to 1, because the reductions compound. Always take the driven tooth count over the driver for a reduction; flipping them gives an overdrive that divides torque instead of multiplying it.

How do I get the output speed and output torque?

Output speed is the input speed divided by the ratio: a 1,450 rpm motor through a 20 to 1 reducer turns its output at 72.5 rpm. There is no efficiency term on the speed, because gear teeth do not slip. Output torque is the input torque times the ratio times the efficiency: T_out = T_in x i x eff. The ratio multiplies the torque by the same factor it divides the speed by, and the efficiency shaves off the friction loss, so a 20 to 1 reducer at 95 percent gives 19.0 times the input torque, not the full 20. On the default, 26.34 N.m of input torque becomes 500.6 N.m at the output shaft. The tool reports the torque in newton metres, kilogram-force metres, and pound feet together.

How do I find the torque from the motor power?

Use the speed. In metric, torque in newton metres is 9,550 times the power in kilowatts divided by the speed in rpm. In imperial, torque in pound feet is 5,252 times the power in horsepower divided by the speed in rpm. The constants 9,550 and 5,252 fold in the rotation and the unit conversions so you never handle the raw physics. On the default, a 4 kW motor at 1,450 rpm makes 9,550 times 4 divided by 1,450, which is 26.34 N.m at the motor shaft. Use the input speed with the motor power to get the input torque, then apply the ratio; feeding the output speed into the formula double-counts the ratio and inflates the torque.

Why is the torque gain less than the gear ratio?

Because the gear mesh loses some of the power to friction, and that loss comes off the torque. A gearbox conserves power minus its losses, so if the speed drops by the ratio and a few percent of the power leaves as heat, the torque climbs by the ratio times the efficiency rather than the full ratio. A 20 to 1 reducer at 95 percent gives 19.0 times the input torque, not 20.0. The bite grows on deep or multi-stage reductions, because each stage loses its own slice and the efficiencies multiply. On a worm drive the gap is large, since a 40 to 1 worm at 70 percent gives only 28 times the torque. The tool reports the actual torque multiplication so you do not have to assume the ratio is the gain.

What efficiency should I use for each gear type?

A spur or helical stage runs about 95 to 98 percent efficient, a bevel stage about 95 percent, and a worm drive anywhere from 40 to 90 percent, dropping as the ratio and load rise. The tool defaults to 95 percent per stage, a sensible middle for a helical reducer, and you should override it with the maker’s figure where you have it. When you stack stages the efficiencies multiply, not average, so three spur stages at 97 percent each land near 91 percent overall. A worm is the case to watch: it works by sliding rather than rolling, so it wastes far more as heat, and below about 50 percent efficiency it can self-lock, meaning the output cannot back-drive the input. Pick the efficiency from the gear type, and never assume a worm gives back its nominal ratio.

What is a service factor and how do I choose one?

The service factor is the multiplier that turns the running output torque into the rated torque you size the gearbox against, giving headroom for starts, jams, and long hours. You multiply the output torque by the factor and pick a gearbox whose catalogue rated torque clears the result, so 500.6 N.m at a factor of 1.25 asks for at least 626 N.m. The gear industry publishes the factors: AGMA service factors and the NEMA MG-1 standard set values by application, typically from about 1.0 for a smooth, light-duty machine up to 2.0 or more for heavy shock loads, around-the-clock running, or frequent starts. A steady conveyor might sit at 1.25, a rock crusher much higher. Choose the factor from the real duty of the machine, then also check the starting and peak torque separately.

How do multi-stage reducers work?

A multi-stage reducer builds a deep ratio by stacking gear pairs, and the stage ratios multiply. Two stages of 5 to 1 and 4 to 1 give 20 to 1, three stages of 3 to 1 give 27 to 1, because each stage reduces the output of the one before it. The tool’s multi-stage mode lets you enter the stage ratios one per line and multiplies them for you. The catch is that the efficiencies compound too, so three spur stages at 97 percent each land near 91 percent overall, and the torque multiplication comes out below the raw ratio. The final stage carries the full output torque, so it uses the largest gears and the sturdiest shaft, and it is the stage you size against the rated torque. Planetary gearboxes pack a high multi-stage ratio into a short housing.

What is reflected inertia and why does it matter?

Reflected inertia is the inertia of the load as the motor feels it through the reducer, and it is the load inertia divided by the ratio squared: J_reflected = J_load / i squared. A 20 to 1 reducer cuts the inertia the motor feels by a factor of 400, because the ratio enters as a square. That large lever is why gearboxes appear on servo drives even where the speed reduction is modest: a reducer lets a small, fast motor accelerate a heavy load crisply by collapsing the reflected inertia. The trade is that the reducer also multiplies the torque the motor must supply, so servo sizing looks for a ratio that matches the reflected load inertia to the motor inertia. This tool gives the ratio and the steady torque and points at the inertia relationship; a servo and actuator sizing tool, on the way in this silo, finishes the acceleration sum.

Can I enter the motor in horsepower instead of kilowatts?

Yes. Set the units to imperial and enter the motor in horsepower, and the tool converts internally, one HP is about 0.7457 kW, and reports the output torque in newton metres, kilogram-force metres, and pound feet like any other case. The fifth worked example does exactly this: a 10 HP motor at 1,750 rpm through a 25 to 1 reducer at 94 percent gives 40.69 N.m input, 70.0 rpm output, and 956.3 N.m (97.5 kgf.m / 705 lb.ft) output, a 23.5 times gain, with a required rating of about 1,195 N.m. In imperial the torque-from-power step uses 5,252 times HP divided by rpm instead of 9,550 times kW. The torque always comes back in all three units, so a shop that thinks in horsepower or pound feet reads the result without converting anything by hand.

What is the difference between a gearmotor and a speed reducer?

A gearmotor is the electric motor and the gear reducer built and sold as a single unit, with the reducer bolted straight to the motor shaft. A speed reducer, or gearbox, is the geared unit on its own, which you couple to a separately bought motor. The gear maths is identical either way: the ratio divides the speed and multiplies the torque, the efficiency depends on the gear type, and you size against the output torque times a service factor. This tool treats them the same, since it works from the ratio, the input speed, and the input torque or power regardless of whether the motor is integrated. Gearmotors are common where space is tight and the drive is a catalogue match; separate reducers suit custom drives where the motor is chosen independently.

How does a worm drive differ from a helical or spur reducer?

A worm drive uses a screw-like worm meshing with a wheel, which gives a high ratio in one compact stage but works by sliding one surface across another, so it loses far more to friction than a spur or helical reducer that rolls teeth. A worm can be 40 to 90 percent efficient and drops as the ratio and load climb, while a spur or helical stage runs 95 to 98 percent. That means a worm gives back much less than its nominal ratio in torque: a 40 to 1 worm at 70 percent gives 28 times, not 40. A worm also runs hot, so its thermal rating can limit the drive before the torque does, and below about 50 percent efficiency it can self-lock so the output cannot back-drive the input. Read the torque multiplication, not the ratio, and check the thermal rating on any high-ratio worm.

Is the calculator free, and does it store my data?

Yes, the tool is free with no sign-up, and every calculation runs in your browser. The numbers you enter are never sent to a server, stored, or shared. You can download a clean PDF or export a CSV of the result, and share a summary on WhatsApp, all from the numbers computed on your own device. The calculator is for planning and education, so confirm any figure that informs a gearbox purchase, a drive selection, or a machine design with a qualified engineer and the manufacturer’s data for the specific motor and reducer you intend to use. In particular, confirm the thermal rating on a high-ratio worm, the starting and peak torque the machine can demand, and the bearing and shaft loads, because this tool sizes the steady torque and the ratio, not the full mechanical and thermal duty of the unit.

More industrial automation calculators

Four sibling tools in the Industrial Automation silo are live now, with the servo sizing tool in build. Each links here as it goes live.

Servo sizingSoon
Servo and Actuator Sizing
Size a servo from the load inertia, the move profile, and the reflected torque this reduction produces through the gearbox.
Conveyor speedLive
Conveyor Belt Speed and Motor Power
Turn the output shaft speed into the belt speed and the motor power a conveyor needs from the load and the geometry.
VFD savingsLive
VFD Energy Savings
See what slowing a pump or fan with a variable frequency drive saves in energy, money, and carbon.

The four live siblings are the Conveyor Belt Speed and Motor Power Calculator, which turns the shaft speed a gearmotor delivers into a belt speed and motor power, the Pneumatic Cylinder Force and Air Consumption Calculator, the Air Receiver Tank Size and Compressed-Air Demand Calculator, and the VFD Energy Savings Calculator. The servo and actuator sizing tool, which takes the reflected inertia this reducer produces and finishes the acceleration sum, is still building. While it finishes, explore a live hub such as Energy Management, where the running cost of a drive train rolls up into the plant-wide picture, or Lean Production for tools you can use today.

Sources, disclaimer, and editorial transparency

The gear relationships used here follow standard drive-engineering practice. The ratio is the input speed over the output speed and the driven tooth count over the driver, the output speed is the input speed divided by the ratio, and the output torque is the input torque times the ratio times the efficiency. Torque from power is treated as 9,550 x kW / rpm in metric and 5,252 x HP / rpm in imperial, the reflected load inertia as the load inertia divided by the ratio squared, and the required gearbox rating as the output torque times a service factor drawn from AGMA service-factor guidance and the NEMA MG-1 standard. Efficiency by gear type follows recognized ranges: spur and helical about 95 to 98 percent per stage, bevel about 95 percent, and worm 40 to 90 percent and falling with ratio and load. Unit constants are 9.80665 for newton metres to kilogram-force metres, 0.73756 for newton metres to pound feet, and 0.7457 for horsepower to kilowatts. This calculator and guide are built and reviewed by the OpsCalculators team; see our Editorial Policy for how each tool is researched, built, and tested.

Results are accurate estimates for planning and education, not a substitute for a full drive-train selection or an engineering review. The method applies a single efficiency per stage, treats the ratio as exact, and sizes the steady output torque against a service factor, but it does not read a manufacturer’s thermal rating, does not run the acceleration sum that servo sizing needs, and does not model the starting and peak torque spikes a jam or a stall can produce. High-ratio worm drives in particular can be limited by heat before torque, and a momentary peak can strip teeth that steady running never would. Confirm the thermal rating, the peak torque, the bearing and shaft loads, and the final unit selection against the manufacturer’s data and a qualified engineer before you commit to a gearbox. See our full Disclaimer. OpsCalculators.com is operated by MAFHH INTERNATIONAL LTD. Your inputs are processed in your browser and are never stored; see our Privacy Policy.