Maps for Math

What is a DC motor's torque-speed curve?

At a fixed voltage, a brushed DC motor slows in a straight line as the load grows, from no-load speed down to zero at stall torque. Current rises in a straight line too. Power, torque times speed, is a parabola that peaks at half the stall torque. Peak efficiency comes at a much lighter load.

continuousoverheats over timespeedcurrent (20 A at stall)power (21.2 W peak)efficiency (22% peak)stall85.5 rpm, 4.03 W
Speed at this load
85.5 rpm
Mechanical power out
4.03 W
Current drawn
2.43 A
Efficiency
13.8%
Peak power (at half stall torque)
21.2 W

Challenge: Stay inside the continuous rating while getting at least half the motor's peak power.

%
From the motor’s datasheet. Pick an example above to fill all of these in.
More settings
The most it can carry without overheating. Often a quarter to a third of stall.

Play

Pick the cordless drill, then sweep the load from 0% to past stall.

Challenge: Stay inside the continuous rating while getting at least half the motor's peak power. The box under the picture turns green when you get it.

Stuck? Pick one of the examples from the “Try an example” menu, or press “New example.”

Understand

n=n0(1−TTs)n = n_0\left(1 - \frac{T}{T_s}\right)

Load a brushed DC motor at a fixed voltage and its speed falls in a straight line:

n=n0(1−TTs)n = n_0\left(1 - \frac{T}{T_s}\right)

Current rises in a straight line from its no-load value to its stall value. Power is torque times speed, so it's a parabola, zero at both ends and highest at Ts/2T_s/2. Efficiency peaks at a light load, far left of peak power.

All four curves share one scale, as a percent of their maximums. The first shaded zone is where the motor can run all day. The next one overheats it over time.

Use

Every input has a unit menu, so you can type values in the units you already have. Results follow your units.

Show the work

  1. Speed falls in a straight line from no-load to stalln = 90\left(1 - \frac{0.45}{9}\right) = 85.5\ \text{rpm}
  2. Current rises in a straight line with torqueI = I_0 + (I_s - I_0)\frac{T}{T_s} = 1.5 + 18.5 \times 0.05 = 2.425\ \text{A}
  3. Power = torque × angular speed, a parabola in TP = T\,\omega = 0.45 \times \frac{2\pi \times 85.5}{60} = 4.029\ \text{W}
  4. The parabola peaks halfway, at T = Tₛ/2 and n = n₀/2P_{\max} = \frac{T_s\,\omega_0}{4} = 21.21\ \text{W}
  5. Efficiency: power out ÷ power in\eta = \frac{P}{VI} = \frac{4.029}{12 \times 2.425} = 13.85\%

Export

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Pick a motor, then move the load. The motor numbers are in the boxes below, so you can type in your own datasheet.

  • Real motors deviate a little from the straight line. Friction, heating, and battery sag all shave off torque.
  • Many controllers limit current, which caps torque below stall. That's left out here.

For learning and estimation. Verify with applicable codes, standards, and a qualified professional before using in design, construction, or safety-critical work.

Cheat card

n=n0(1−TTs)n = n_0\left(1 - \frac{T}{T_s}\right)
I=I0+(Is−I0)TTsI = I_0 + (I_s - I_0)\frac{T}{T_s}
P=Tω,Pmax⁡=Ts ω04P = T\omega,\quad P_{\max} = \frac{T_s\,\omega_0}{4}
η=PVI\eta = \frac{P}{VI}
SymbolMeaningUnit
TsT_sstall torqueN·m
n0n_0no-load speedrpm
IsI_sstall currentA
TcT_ccontinuous torque ratingN·m
  • Two datasheet numbers draw the whole speed line, stall torque and no-load speed.
  • Running at peak power usually overheats a motor. Most designs run near peak efficiency.
  • A gearbox trades speed for torque. It moves the operating point left on this chart.

Print this card

Where it’s used

  • Electrical & Electronics
    Engineers pick motors and gear ratios so the working load sits near peak efficiency.
  • Mechanical
    Robot and actuator designers check that the load stays inside the continuous zone.
  • Hobbies & Crafts
    RC cars, robots, and drills all live on this line. A stalled motor gets hot fast.

Questions people ask

What is stall torque?

The torque that stops the motor completely. It draws its highest current there and turns it all into heat, so stalling for long can burn out the windings.

Where does a DC motor make the most power?

At half its stall torque and half its no-load speed. Power is torque times speed, and the product of a falling line peaks in the middle.

Why is the continuous rating so much lower than stall?

Heat. Losses grow with the square of current, and the motor can only shed so much. Above its continuous rating it overheats, often within minutes.

Sample LIN-0013 · rev 1 · model LIN-M13 · Level 4 · advanced algebra · updated 2026-09-27