Electric Motor Torque Density and Power Density: The Reference Guide

What Torque Density and Power Density Mean

Neither metric is a property of a motor topology in the abstract; both are properties of a specific design, at a specific size, built with specific materials, measured against a specific basis. That last part — the basis — is what most published figures leave out, and it's the subject of most of the rest of this page.

Torque density is torque divided by a reference mass or volume — Nm/kg gravimetrically, Nm/L volumetrically. Power density is the same idea for power — kW/kg or kW/L. Both are the site's own long-standing shorthand, "torque per gram" and "power-to-weight ratio," made precise enough to actually compare.

The everyday analogy is strength-to-weight versus speed-to-weight. A strong-for-its-size motor delivers a lot of turning force per kilogram — that's torque density. A fast-for-its-size motor delivers a lot of shaft power per kilogram at whatever speed it runs — that's power density. A motor can be excellent on one and unremarkable on the other, and which one matters depends entirely on what the motor has to do.

Both figures come in gravimetric and volumetric form, and the two don't always favour the same design. A motor optimised purely for Nm/kg wants mass out of the design wherever it doesn't contribute torque; a motor optimised purely for Nm/L wants the active material packed as tightly as the thermal design allows, even if that costs some mass elsewhere. Most real designs sit somewhere between the two, because both the vehicle's weight budget and its available envelope are usually fixed at the same time, not traded off against each other freely.

Which basis dominates the decision depends on what's actually constrained. A quadcopter arm cares about gravimetric density first — every gram not spent on the motor is a gram available elsewhere on the airframe, and there's usually room to make the motor slightly larger if it stays light. A robot joint or an in-wheel drive is often the opposite: the envelope is fixed by the mechanical design around it, so volumetric density decides whether the motor fits at all, and mass is the secondary concern once it does.

Torque Density vs Power Density

This is the single most common confusion in torque and power density search results, so it's worth stating precisely, early, and in terms of the one equation that governs it:

P = T · ω

Power equals torque times angular speed. Because speed is a free variable in that equation and mass isn't tied to it the same way, power density rises with speed while torque density does not. A small, fast, geared motor and a larger, slower, direct-drive motor can be specified to produce exactly the same kW/kg — and differ several-fold in Nm/kg, because the geared motor reaches its power target mostly through speed, and the direct-drive motor reaches the same power mostly through torque, at a fraction of the RPM.

Which figure to optimise for depends on where the gearbox lives, not on which number looks better. If a gearbox is already part of the design, power density is the more honest comparison, because the gearbox will convert the motor's speed into whatever torque the application actually needs. If the application is direct-drive — no gearbox between motor and load — torque density is what determines whether the motor can do the job at all, because there's no downstream stage left to make up a torque shortfall. The direct-drive-vs-geared-motor question should be answered before either density figure is used to compare two motors.

This is also why a "highest power density" claim can be true and still be the wrong motor for a direct-drive application. A high-speed, low-torque motor paired with an external gearbox can post an excellent kW/kg figure on the motor alone, while the gearbox — which the density figure doesn't include — adds mass, mechanical losses, backlash, and a wear item that the motor's own datasheet says nothing about. The system-level density, motor plus gearbox together, is what a direct-drive design is implicitly being compared against, even when only the motor's number is quoted.

Where Torque Comes From: Air-Gap Shear Stress

Every density figure ultimately traces back to one physical quantity: the tangential force per unit area developed at the air gap, called shear stress and measured in kPa. Shear stress is the product of electric loading (how much current-carrying copper surface faces the gap) and magnetic loading (how strong the field crossing the gap is). It's the same quantity in every motor topology — what differs between designs is how much rotor surface area that shear stress gets to act over, and at what radius.

For a cylindrical rotor, torque is approximately shear stress multiplied by the rotor's surface area multiplied by its radius — a surface that scales with radius times axial length, acting at that same radius. That means every improvement in torque density is, underneath, one of exactly three things: a higher achievable shear stress (better magnets, thinner effective air gap, better cooling to allow more current), more rotor surface area for the same mass, or that surface area sitting at a larger radius for the same mass. There is no fourth lever. Section 6 shows how axial flux geometry pulls on the third one particularly hard.

Electric loading and magnetic loading are each bounded by something physical, not just by design ambition. Electric loading is set by how much current-carrying copper can be packed along the gap and how much current density that copper can sustain without overheating — which is exactly the thermal-ceiling argument in section 7, arriving from a different direction. Magnetic loading is set by magnet grade, magnet thickness, and how effectively the magnetic circuit concentrates flux across the gap, which is where the coreless-vs-iron-core choice in section 9 has its electromagnetic effect. Shear stress is where those two independently-bounded quantities meet, which is why it's the single number worth tracking across very different motor designs.

The Thermal Ceiling: Continuous vs Peak Torque Density

Shear stress isn't free to push arbitrarily high — it's limited by current density in the winding, and current density is limited by how fast the resulting heat can be removed before the winding's temperature exceeds what the insulation and magnets can tolerate. Continuous density, in other words, is fundamentally a heat-removal problem, not an electromagnetic one — the electromagnetics would happily sustain much higher shear stress if the heat had somewhere to go.

This is why cooling method changes the achievable continuous density directly, and changes the ratio between continuous and peak density along with it. A motor that can only shed heat by natural convection has a low continuous ceiling and a large gap to its peak capability, because peak operation only has to be sustained for the short time it takes the windings to heat up, not indefinitely. Better cooling — forced air, a liquid jacket, or direct fluid contact — raises the continuous ceiling toward the peak, narrowing that gap.

This is also why a peak torque or power density figure, quoted without a duration, tells you almost nothing. Every motor can produce a large peak for a short enough pulse — the winding's thermal mass absorbs the heat faster than it can raise the temperature meaningfully. What differs between motors is how long that peak can be sustained before the continuous ceiling is the only thing left standing, and that duration is the number that actually belongs next to any peak figure.

Cooling method sets where the continuous ceiling sits, roughly in this order from lowest to highest achievable continuous density: natural convection, where heat leaves only through still air and the housing's own surface area; forced-air cooling, where a fan multiplies the effective heat transfer coefficient at the housing surface; liquid cooling, where a jacket or channel removes heat close to its source rather than waiting for it to conduct out to the housing; and direct immersion or wet-rotor construction, where the coolant contacts the winding or stator directly with no intervening housing wall at all. Each step generally narrows the gap between continuous and peak density, because each one raises how much continuous shear stress the thermal design can actually sustain — while doing nothing to change what the electromagnetics could theoretically produce for a brief pulse.

This is precisely the trade the sealed motor thermal design decision makes explicit: a sealed motor's heat has to cross a boundary it wouldn't otherwise have, which typically lowers its continuous ceiling relative to an unsealed design with the same active parts, while a canned motor's rotor and stator can sit in direct contact with a coolant, at the cost of the can losses and lifespan trade-offs covered there.

Removing Iron: The Coreless Contribution to Density

Stator iron is mass that produces no torque of its own. It concentrates flux and lowers the magnetic circuit's reluctance, which lets the magnets and copper produce more torque than they could unassisted — but the iron itself never carries current and never sees a Lorentz force. Every kilogram of it is pure overhead relative to the shear-stress argument in section 5, paid for with a compact air gap rather than with active torque-producing material.

Iron earned its place in motor design for a good reason: a low-reluctance path lets a modest magnet produce a strong field across a small air gap, which historically mattered more than it costs in mass when magnet materials were weak and expensive. Modern rare-earth magnets shift that balance — they're strong enough, in the right geometry, to bridge a larger effective gap without iron's help, which is precisely what makes removing the iron a density gain rather than a step backward.

A coreless axial flux motor removes that mass entirely, at a cost: without iron to concentrate flux, the effective air gap grows, which demands stronger magnets (usually in a Halbach array) to reach useful shear stress, and the windings sit fully exposed to the time-varying field, which raises AC copper losses at high frequency. The density gain is real and the trade-offs are real; neither cancels the other out, which is exactly why the full trade-off deserves its own treatment rather than a one-line summary here.

The net effect on density is still favourable for most applications this site's density claims are aimed at, because the mass removed is pure overhead relative to torque production, while the cost is paid in AC losses and magnet spend rather than in mass. A design that's thermally constrained rather than mass-constrained gets less benefit from going coreless, since removing core loss doesn't help a design that was never limited by it in the first place — another reminder that density gains and efficiency gains are related but distinct arguments, developed fully in section 11.

Motor Constant Km and the Density-Efficiency Trade

Density figures say how hard a design is being driven, not how efficiently it converts current into torque. The honest companion metric is the motor constant:

K_m = T ⁄ √P_loss

Torque per square root of resistive loss, quoted at a specific winding temperature since copper resistance — and therefore loss for a given current — changes with it. Km is basis-independent of cooling: unlike a continuous density figure, it doesn't change if you bolt on a better heatsink, because it describes the winding's own electromagnetic efficiency at converting current into torque, not how much heat the surrounding design can carry away.

The square root isn't an arbitrary choice of exponent. Torque scales roughly linearly with current, while resistive loss scales with current squared, so torque divided by the square root of loss is the ratio that stays constant as current changes for a fixed winding design — it captures something about the winding's geometry and material, not about the operating point chosen when the figure was measured. That's what makes Km comparable across motors driven at different current levels, in a way that a torque or loss figure alone isn't.

This is why two motors can share an impressive density figure and differ sharply in practice: a high-density design pushed hard on current density can have a mediocre Km, meaning it's paying for that density in efficiency and heat rather than winning it for free. Density and efficiency are related but not the same trade — a motor optimised purely for density, without regard to Km, is a motor optimised to run hot.

How Turncircles Quotes Density

Turncircles quotes torque and power density on continuous operation, active-part mass — magnets, copper, and back-iron where present, excluding housing and bearings — with peak figures always stated separately and never blended into the same number. Volumetric density is quoted against the outer envelope, since that's the figure that actually answers a packaging question.

The reasoning follows directly from how the motors are built. Turncircles designs custom motors around each application, which means housing and bearings are themselves application-dependent — a naked motor built into a drone arm and the same active electromagnetic design housed for a sealed pump application would report wildly different complete-motor density figures despite being electromagnetically identical. A complete-motor figure would be a fact about someone else's mechanical integration, not about the motor design itself. Active-part mass is the part Turncircles' design process actually targets a density figure against, so it's the only basis that stays meaningful across every application the same electromagnetic design gets built into.

Peak figures are never blended into the headline continuous number, and are always paired with the duration they were verified over, per the thermal-ceiling argument in section 7. This is the same discipline the checklist in section 12 asks any supplier to apply — the basis Turncircles commits to here is simply that checklist, answered once, in writing, rather than answered case by case when asked.

To see this basis applied to your own torque, speed, and envelope requirements, configure a motor and review the simulated density figures directly, quoted on exactly the basis described above.