A motor nameplate gives power and speed, but the thing a machine actually needs is torque. A conveyor has to overcome a resisting moment, a pump has to turn against a head, a hoist has to hold a load. Power on its own says nothing about whether a motor can do any of those, because power is torque multiplied by rotational speed, and the same power can be delivered as a large torque turning slowly or a small torque spinning fast. Converting between them is a single division, and it is one of the most consequential divisions in machine design.
This motor torque calculator from Arb Digital does that conversion and then continues into the electrical side, working out the input power the motor draws, the apparent power the supply has to provide, and the resulting full-load current for a single-phase, three-phase or DC machine. It is an engineering and teaching tool. It does not size conductors or protective devices, it publishes no ampacity table, and it is not a substitute for a qualified electrician working to the wiring rules that apply where the motor is installed.
What This Motor Torque Calculator Does
The first half is pure mechanics. Rated output power divided by angular velocity gives shaft torque, reported in newton metres and pound-feet. This is the full-load torque: the torque the motor produces at its rated speed while delivering rated power continuously. It is not the starting torque, not the pull-up torque and not the breakdown torque, all of which are larger and all of which are defined separately by design class.
The second half is electrical. Rated power is what leaves the shaft; the motor draws more than that from the supply, and the ratio is its efficiency. Dividing output by efficiency gives real input power in kilowatts. Dividing that by the power factor gives apparent power in kilovolt-amperes, which is what the supply, the cable and the transformer actually have to carry. Current then follows from apparent power and voltage, with a factor of the square root of three for a three-phase supply.
The bar breakdown makes the losses visible. Of the electrical power going in, one part becomes useful shaft power and the rest becomes heat in the windings, the iron and the bearings. On a small motor that loss fraction is often a fifth of everything you pay for, which is why efficiency classes exist and why replacing an old motor can pay for itself.
How to Use It
- Take the power and speed from the nameplate. Rated output power is what the motor delivers, not what it consumes. Confusing the two overstates the torque by the reciprocal of the efficiency.
- Use the full-load speed, not the synchronous speed. A four-pole motor on 50 Hz has a synchronous speed of 1,500 RPM but runs at perhaps 1,455 under load. Using 1,500 understates the torque by around three per cent.
- Choose the supply type. Three-phase brings in the root-three factor, single-phase does not, and a DC supply ignores power factor entirely.
- Enter efficiency and power factor at full load. Both fall away sharply on a lightly loaded motor, so nameplate values only describe the rated operating point.
- Treat the current as an estimate, not a design figure. The nameplate full-load amps is the number to use for anything that matters, and code tables govern circuit sizing.
The Formulas and a Worked Example
Torque is power divided by angular velocity: T = P / ω, with ω = 2π × RPM / 60 in radians per second. Combining the constants gives the shortcut most engineers carry in their heads, T = 9,549 × P(kW) / RPM in newton metres, or T = 5,252 × hp / RPM in pound-feet. This calculator uses the exact expression rather than the rounded constant. On the electrical side, input power is Pᵢₙ = Pₒᵤₜ / η, apparent power is S = Pᵢₙ / cosφ, and current is S / (√3 × V) for three-phase or S / V for single-phase and DC. The relation P = τω is derived in the OpenStax section on work and power for rotational motion.
Work the default. A 15 kW motor at 1,460 RPM has an angular velocity of 2π × 1,460 / 60 = 152.89 rad/s, so the shaft torque is 15,000 / 152.89 = 98.11 N·m, which is 72.36 lb-ft. At 91 per cent efficiency the input power is 15 / 0.91 = 16.48 kW. At a power factor of 0.85 the apparent power is 16.48 / 0.85 = 19.39 kVA, and on a 400 V three-phase supply the current is 19,392 / (1.732 × 400) = 27.99 A. Note that the 2.6 kW difference between input and output is not lost bookkeeping — it is heat the motor has to shed, and it is why the frame gets hot.
Full-Load Torque Is the Smallest Torque on the Curve
The number this page produces is one point on a speed-torque curve that spans from standstill to synchronous speed, and it is close to the lowest useful value on that curve. Locked-rotor torque is what the motor produces at zero speed, typically one and a half to three times full-load torque depending on design class. Pull-up torque is the minimum during acceleration, which is the value that determines whether a high-inertia load ever gets moving. Breakdown torque is the peak, usually two to three and a half times full load, beyond which the motor stalls rather than producing more.
Those multiples are set by the motor's design class rather than being free parameters, and the classes are defined in NEMA MG 1, the standard for motors and generators, with equivalent designations elsewhere in IEC 60034. Design B is the general-purpose workhorse, Design C offers higher starting torque for hard-to-start loads such as loaded conveyors, and Design D trades speed regulation for very high starting torque in punch presses and hoists. Selecting on full-load torque alone, without checking that the accelerating torque exceeds the load torque at every speed, is how motors end up stalled and burning.
Why the Current Here Is Not the Nameplate FLA
This calculator derives current from power, efficiency, power factor and voltage. Those four numbers are exactly what a motor manufacturer uses to publish full-load amps, so the result usually lands within a few per cent of the nameplate. It is nevertheless the wrong number to design a circuit with, for three separate reasons.
First, nameplate efficiency and power factor are rounded and are stated at rated load on rated voltage, so a calculated current inherits the rounding of both. Second, the real machine is not the catalogue machine: manufacturing tolerance, supply voltage that sits low, and an unbalanced three-phase supply all shift the actual draw. Third, and decisively, wiring rules do not use the calculated value or even always the nameplate value. Conductor and overload sizing in most jurisdictions is based on tabulated full-load current values for the motor's horsepower and voltage, deliberately not on the individual nameplate, so that a replacement motor does not require the circuit to be rebuilt.
For that reason this page publishes no ampacity table, no conductor size and no protective device rating, following the same precedent as the live breaker size calculator, which explains at length why those figures belong in the code book rather than on a web page. Use the wire size calculator and the voltage drop calculator for the arithmetic that supports a design, and have the design itself done by a qualified electrician against the edition of the wiring rules in force locally.
Speed, Gearing and the Torque You Actually Get
Because torque is inversely proportional to speed at constant power, gearing is the cheapest torque multiplier there is. A reducer with a ratio of 20 to 1 turns 98 N·m at 1,460 RPM into roughly 1,860 N·m at 73 RPM, less whatever the gearbox loses, typically two to five per cent per stage. That is why a slow, high-torque application almost always uses a fast motor and a reduction rather than a large slow motor, which would be enormous and expensive. The gear ratio calculator handles the ratio arithmetic.
The other route is a variable frequency drive, and it behaves differently in two regions. Below the base frequency, the drive holds the volts-per-hertz ratio constant, the magnetic flux stays constant and the motor produces approximately constant torque at any speed, though cooling suffers on a shaft-mounted fan at low speed. Above base frequency the voltage cannot rise any further, so flux falls and the motor moves into a constant-power region where torque drops off inversely with speed. Feeding a constant-torque load into that region is a common and expensive misapplication.
How This Differs From the Adjacent Arb Digital Tools
This page starts from a motor's power and speed rating and works in both directions, mechanical and electrical, in one pass. The torque calculator works from force and lever arm, which is a statics problem rather than a rotating-machine one. The torque converter only rescales a torque value between units and does no physics. The horsepower calculator goes the other way, from work done to power. The electrical power calculator and the power factor calculator handle the supply-side relations without any shaft involved, and the kVA calculator covers apparent power for general loads rather than motors specifically.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Entering input power instead of rated output — the nameplate kW or hp is shaft output. Using the electrical draw inflates the torque by the reciprocal of the efficiency.
- Using synchronous speed — an induction motor never reaches it. The full-load speed is a few per cent lower, and the torque is correspondingly higher.
- Mixing metric and electrical horsepower — mechanical horsepower is 745.7 W and metric horsepower is 735.5 W. The one per cent gap propagates straight into the torque.
- Treating full-load torque as starting torque — the starting value is one and a half to three times higher and is set by design class. Sizing a hard-starting load on full-load torque leaves it stalled.
- Using the calculated current to size a circuit — code tables and the nameplate govern, not a derived figure, and the design belongs to a qualified electrician.
Related Free Tools From Arb Digital
For statics rather than rotation use the torque calculator, and for unit changes the torque converter. Power relationships are covered by the horsepower calculator, the electrical power calculator and the kVA calculator, while supply quality is handled by the power factor calculator and the voltage drop calculator. Drivetrain arithmetic lives in the gear ratio calculator, and the stored energy of a spinning rotor in the rotational kinetic energy calculator. The full free online tools hub lists everything Arb Digital has published.
Frequently Asked Questions
Divide the rated output power in watts by the angular velocity in radians per second, where angular velocity is two pi times RPM divided by sixty. The common shortcut is torque in newton metres equals 9,549 times the power in kilowatts divided by the speed in RPM.
Full-load speed, which is the figure on the nameplate. An induction motor must run slower than synchronous speed to produce torque at all, and using the synchronous value understates the torque by roughly the slip, typically two to four per cent.
Because the nameplate rating is mechanical output at the shaft, and the motor also has resistive losses in the windings, magnetic losses in the iron, and friction and windage. Input power equals output divided by efficiency, and the difference leaves as heat.
It relates line-to-line voltage to the per-phase voltage in a balanced three-phase system. Total three-phase power equals root three times line voltage times line current times power factor, so current carries that factor when you rearrange for it.
Usually close, because manufacturers derive the nameplate figure the same way, but not identical. Rounded efficiency and power factor, supply voltage variation and manufacturing tolerance all shift it, and circuit design uses code tables and the nameplate rather than a calculated value.
More than full-load torque, typically one and a half to three times as much depending on design class, and the peak breakdown torque can be higher still. Those multiples are defined by the motor standard, not by this calculation, which gives only the full-load point.
Below base frequency it holds volts per hertz constant, so torque stays roughly constant while power falls with speed. Above base frequency the voltage cannot rise further, flux falls, and torque drops off inversely with speed in a constant-power region.
This tool is provided for educational and preliminary engineering use. It does not size conductors, overloads or protective devices, publishes no ampacity values, and is not a substitute for a qualified electrician or engineer working to the wiring rules and motor standards in force in your jurisdiction.
