How electric motors work

October 16, 2026

Electric motors turn electrical power into rotation. Almost everything that moves runs on them, from fans, pumps, drills and washing machines to drones, electric cars, robot joints and 3D printers, and motors use about 45% of the world's electricity. They're useful because they start instantly, can be controlled precisely in speed, torque and position, run quietly with no exhaust, and good ones turn 85–95% of their input power into shaft power.

Every motor works on the same two effects: a current in a magnetic field feels a force, and a wire moving through a magnetic field makes a voltage. Those two effects give two equations that predict how any motor behaves from its datasheet. The motor types differ only in where the magnetic field comes from and in how the motor switches its current so the force keeps pushing the same way as the shaft turns. Those two choices are why a 3D printer uses a stepper, a drone uses a brushless motor, and a factory pump uses an induction motor.

Every figure is live and starts slow so you can follow it, and the speed slider runs it faster. The numbers they show come from the same models that move the parts.

Two laws do all the work

Current in a magnetic field feels a force. A wire carrying current I across a field B feels a sideways force F = B·I·L, where L is its length. Put that wire on a rotor at radius r and the force becomes a torque. Add up all the wires and you get one number for the motor:

Torque is proportional to current. Kt, the torque constant, is in newton-metres per amp. It is set by the magnets, the number of turns, and the geometry, and it doesn't change while the motor runs.

A wire moving through a field makes a voltage. The same wire moving at speed v makes e = B·L·v. Spin the rotor and every motor is also a generator, pushing back against its supply:

Back-EMF is proportional to speed. It is why a motor doesn't draw infinite current: as it speeds up, it pushes back harder against the supply.

In SI units, Kt and Ke are the same number (N·m/A equals V·s/rad), because energy can't appear or vanish inside the motor. The electrical power going into the back-EMF, e·I, has to equal the mechanical power coming out, τ·ω, and writing both out gives Ke·ω·I = Kt·I·ω.

Each motor type below is a different answer to two design questions:

1. Where does the field come from? Permanent magnets, or currents the motor induces in itself.
2. How does the current keep switching? As the rotor turns, the force on a given wire would reverse. Something has to switch the current in step with the rotor: brushes, a driver following a step sequence, electronics reading a sensor, or the AC supply itself.

The motor equations

At steady speed, the supply voltage splits between the winding's resistance and the back-EMF:

Solve for speed and you get a straight line:

That one line describes the motor at every operating point: asking for more torque slows it down, and raising the voltage moves the whole line up in parallel. The motor's power, efficiency and heat all follow from it:

• Power peaks in the middle. Output power τ·ω is a parabola that peaks at half the stall torque and half the no-load speed: Pmax = τs·ω0 / 4.
• Efficiency peaks near no-load. Copper loss is I²R and grows with the square of torque, so a motor wastes the smallest share of its power when lightly loaded, near its no-load speed. Running at maximum power means running at under 50% efficiency.
• Torque costs heat. Copper loss is I²R = (τ/Kt)²·R. Define the motor constant Km = Kt/√R and that becomes (τ/Km)². Km is the motor's torque per square root of watt of heat, and it is the most honest measure of how strong a motor is.

With the defaults (24 V, 1 Ω, Kt = 0.05 N·m/A), stall torque is 1.2 N·m and no-load speed is 480 rad/s, about 4,600 rpm. Ask for 0.3 N·m and it draws about 6 A, runs near 3,400 rpm, puts out about 100 W, and makes about 40 W of heat in the winding.

The winding doesn't make a motor stronger. Rewind the same motor with half the turns and Kt halves, but R drops to a quarter (half the wire length, double the cross-section). Km = Kt/√R stays the same. The winding only matches the motor to your supply: few turns for low voltage and high current, many turns for high voltage and low current. How strong a motor is depends on its size, its magnets, and how well it gets rid of heat.

Continuous torque is a heat rating. A motor can make huge torque for a moment, limited by the drive's current and by saturating the iron. What it can make all day is whatever torque keeps the winding below its temperature limit. That is why datasheets give continuous and peak torque separately, and why a heatsink raises the same motor's continuous rating.

Kv, the number on hobby motors, is the same constant inverted: rpm per volt. Kv = 60/(2π·Ke), so Kt ≈ 9.55/Kv for a DC motor. A 100 Kv motor makes about 0.1 N·m per amp. (Brushless datasheets define their voltages differently, so expect that conversion to be off by 10–15%.)

Brushed DC

The brushed DC motor is the oldest and simplest motor. The magnets sit inside the outer can and the coils are on the rotor. A split ring on the shaft (the commutator) feeds the coils current through two spring-loaded carbon brushes. As the rotor turns, the commutator re-routes current into whichever coils are about to make forward torque, so the shaft does its own switching.

Load a brushed motor and it slows down on its own until the back-EMF has dropped enough to let in the current the load needs. No controller does this, which is why a brushed motor is the easiest motor to use: connect it to a battery and it runs, and swap the wires to run it backwards. Speed is set by voltage, usually by switching the supply on and off thousands of times a second (PWM).

What you give up:

• Brushes wear. They rub on the commutator and wear down. Small motors last hundreds to a few thousand hours.
• Sparks and noise. Every switch interrupts current in an inductor, which sparks and makes electrical noise.
• Heat is in the wrong place. The windings are on the spinning rotor, and the only way out for their heat is through the air gap, which limits continuous torque.
• Ripple. With only a few coils, torque rises and falls as the commutator switches. You can see the coil currents step on the scope. A 3-slot motor like this one ripples about 13%.

You find them in toys, car windows, pumps, cheap power tools, and inside hobby servos. Coreless versions, with the windings in a basket and no iron in the rotor, have very low inertia and no cogging. They're used in medical devices and precise instruments.

Brushless (BLDC and PMSM)

A brushless motor is a brushed motor turned inside out: the magnets are on the rotor and the coils are on the stator, the fixed part. The hot coils now sit on the frame where they're easy to cool, and nothing rubs. Electronics now switch the current in step with the rotor, so the drive has to know the rotor angle at every instant. It gets the angle from hall sensors, an encoder, or an estimate from the back-EMF, which fails at very low speed.

This one is a 12-slot, 14-magnet outrunner, a common layout for drone motors and for the pancake motors in robot joints. Things to see in it:

• Electrical angle. With 7 pairs of magnets, the current goes through a full cycle 7 times per turn. θelectrical = pole pairs × θmechanical, and the drive switches the phases by electrical angle.
• The field goes backwards. With this winding, the pattern of energised teeth turns 7 times faster than the can and in the opposite direction, which looks wrong but is correct.
• 6-step vs FOC. A simple drive switches each phase fully on, off, or reversed, six times per electrical cycle. That's what "BLDC" originally meant, and the torque ripples. Field-oriented control (FOC) drives all three phases with sine waves so that the stator field always sits 90 electrical degrees ahead of the magnets, and the torque comes out flat. A motor wound for sine-wave drive is usually called a PMSM (permanent magnet synchronous motor), though the physics is the same as a BLDC.
• Angle errors cost torque. If the drive's idea of the rotor angle is off, torque falls as the cosine of the error. At 90° electrical you get nothing, and past that it pushes the wrong way. Above rated speed, FOC drives deliberately add a negative d-axis current that weakens the magnets' field. That lowers the back-EMF and buys more speed at less torque ("field weakening").

Torque scales with the rotor's surface area times its radius: τ ≈ 2π·r²·L·σ. Here σ is the magnetic shear stress in the air gap, typically tens of kilopascals. Doubling the diameter quadruples the torque for the same length, which is why high-torque motors are fat pancakes and high-speed motors are long and thin.

Brushless motors turn 85–95% of their input into shaft power. They wear nothing but bearings, run at tens of thousands of rpm, and have the best torque for their weight. The cost is the drive: it needs a position sensor or a good estimator, current sensing, and firmware. They're in drones, EVs, hard drives, fans, power tools, and every serious robot.

Steppers

A stepper is a brushless motor built so that you can move it a known amount without measuring anything. The rotor has 50 teeth, 7.2° apart. The stator has 8 poles, 45° apart, and 45° is 6¼ teeth, not a whole number, so each pole sits a quarter of a tooth out of line with its neighbour. Energise one pair of coils and the nearest rotor teeth snap into line with that pair. Switch to the next pair and they snap a quarter tooth further. A quarter of 7.2° is 1.8°, so 200 steps per turn.

Near a step, the rotor behaves like a spring. With rotor teeth Nr and holding torque Th, the restoring torque for a small error Δθ is:

A 0.45 N·m NEMA 17 with 50 teeth has a stiffness of about 22 N·m/rad, so a 0.05 N·m disturbance moves the shaft about 0.13°. A spring with inertia rings, and the figure shows it ringing after every step.

The driver counts pulses and assumes the shaft followed. Jump straight to a high step rate from a standstill, without ramping up, and the field outruns the rotor. The rotor slips by whole electrical cycles (4 full steps at a time), and nothing in the system knows, because an open-loop driver has no sensor to check. Its other limits:

• Torque falls with speed. Each step has to push current through the winding's inductance, with time constant L/R. At high step rates the current never reaches its target before the next step. This is why stepper drivers run at 24–48 V and limit the current by chopping: the higher voltage gets the current up faster.
• Microstepping is smoothness, not accuracy. At 1/16 the driver sets sixteen current ratios per step. But the extra torque from one microstep is only Th·sin(90°/16) ≈ 10% of holding torque, so a little friction or load eats the resolution.
• They burn power holding still. Full current flows even when nothing moves, so a stepper at rest is at its hottest.
• Resonance. At some step rates the ringing adds up from step to step, and the motor can stall in the middle of its speed range.

Steppers are cheap, simple, have great torque at low speed, and hold position without a sensor. They're the motor in 3D printers, hobby CNC machines, camera sliders, and valves. Bolt an encoder on ("closed-loop stepper") and you fix the silent step loss, but not the falling torque curve.

Induction motors

The induction motor is the common motor with no magnets, and it drives most of the world's pumps, fans and compressors.

Its stator makes a rotating magnetic field from the supply alone, with no electronics. Three coils 120° apart, fed three-phase currents 120° apart in time, add up to a field of constant strength that turns around the motor in step with the supply frequency:

A 2-pole motor on 50 Hz turns its field at 3,000 rpm. A 4-pole motor on 60 Hz turns it at 1,800 rpm.

The rotor is a cage of aluminium or copper bars shorted at both ends, with no connections at all. If the rotor spins at the same speed as the field, the bars see no change, the field induces no current, and there is no torque. So the rotor always runs a little slower than the field. The field slips past the bars, induces current in them, and that current in the field makes torque. The relative speed is the slip, s = (ns − n)/ns, typically 2–5% at full load.

Torque against slip is roughly the Kloss curve:

Near synchronous speed, torque rises almost linearly with slip, so speed sags a little as load rises. Torque peaks at the breakdown slip sk, and loading the motor past that peak stalls it. Starting from rest (s = 1) it gives less torque than at its peak, and draws 5–8 times its rated current.

To vary the speed, you vary the frequency. A variable-frequency drive (VFD) does that, and it raises the voltage in proportion to the frequency (constant V/f) to keep the field strength constant. Modern drives use vector control, the same field-oriented idea as FOC, and get servo-like performance out of an induction motor.

Induction motors are cheap and rugged, have no magnets, and run straight off the grid. They waste power heating their rotor bars, so they lose a few percentage points more than permanent-magnet motors. They are also heavier, and the slip means the speed depends on the load. The first Tesla Model S used one, as does nearly every industrial fan.

A servo is a loop, not a motor

A servo is any motor with a sensor and a controller that keeps correcting it toward a target, rather than a type of motor. A hobby servo packs the whole idea into a matchbox-sized case: a small brushed motor at over 10,000 rpm, a 200:1 gear train, and a potentiometer on the output. The chip compares the pot with the commanded pulse width (1 ms is one end, 2 ms is the other) and drives the motor in proportion to the error.

Watch the scope: a big error drives the motor flat out, and the drive tapers off as the horn closes in. Push on the horn and it pushes back, but only after you've pushed it off target a little. A purely proportional controller needs some error to make any effort at all. Real controllers add an integral term to remove that steady lean, and a derivative term to damp overshoot, which together make a PID (proportional, integral, derivative) controller.

An industrial servo is the same idea with better parts. It has a brushless motor and an encoder with hundreds of thousands to millions of counts per turn. Its drive runs three loops nested inside each other:

1. Current (torque) loop, innermost, at tens of kilohertz. It makes the motor produce the torque it's asked for.
2. Velocity loop, around that, at a few kilohertz.
3. Position loop, outermost.

Each loop has to be several times faster than the one around it. How well a servo rejects disturbances comes down to how high you can push those loops' bandwidth before they go unstable.

The rest, briefly

• Universal motor. A brushed motor whose field comes from a coil in series with the rotor instead of magnets, so it runs on AC or DC. It spins at 20,000 rpm or more and it's loud, and it's used in vacuum cleaners, blenders and older drills.
• Interior permanent magnet (IPM). Magnets buried inside the rotor iron, so the motor makes torque from the magnets and also from the rotor's shape pulling toward the field (reluctance torque). Most EV traction motors work this way.
• Switched and synchronous reluctance. Rotors with no magnets and no windings, just shaped iron that pulls toward whichever stator poles carry current. Cheap and rugged, but switched reluctance is noisy, with lots of torque ripple.
• Voice coil. A coil in a magnet gap, with limited travel, that makes force directly: no cogging, no backlash, and moves settled in milliseconds, used in speaker cones and hard drive heads.
• Linear motors. A permanent magnet motor unrolled flat, so it pushes along a line instead of turning, used in pick-and-place machines and precision stages.
• Piezo and ultrasonic. Crystals that flex nanometres per volt, vibrated to walk a rotor along, used in camera autofocus and microscope stages.

Choosing one

All the numbers are typical ranges, and small motors sit at the low end of every efficiency range.

When you read a datasheet, these are the lines that matter:

• Kt, Kv, R and L. The four constants of the motor equations. Check whether R is per phase or phase-to-phase.
• Continuous torque (and the cooling the maker assumed for it) and peak torque.
• No-load speed at rated voltage, and the speed-torque curve if they give one.
• Rotor inertia. It matters as soon as you add a gearbox, because it gets multiplied by the ratio squared.
• Thermal resistance and thermal time constant. How quickly it heats, and how long it can stay at peak torque.
• Cogging torque. The lumpiness you feel turning it by hand with no power, from magnets pulling on teeth.

To size a motor for a job:

1. Write down the motion. Torque and speed over a full cycle, including the torque spent accelerating the load (τ = J·α).
2. Check peak. The highest torque in the cycle has to be under the motor's peak torque, at the speed where it happens.
3. Check heat. The RMS torque over the cycle, √(Σ τᵢ²·tᵢ / T), has to be under the continuous rating, because heat goes as torque squared.
4. Check voltage. At top speed, the back-EMF plus the I·R drop at that torque has to fit under the supply.
5. Then pick a gearbox, which changes all four; How gear reductions work covers that.