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DC Motor Simulator: Torque, Speed & Back-EMF

Spin a permanent-magnet DC motor against a load, watch it settle onto its torque-speed curve, and see it stall if the load is too heavy.

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Raise the load torque and watch the rotor slow down; push it past the motor's stall torque and see the current spike.

Stalled: load torque exceeds what the motor can deliver. Current is now limited only by armature resistance — this is how motors burn out.

DC Motor Simulator: Torque, Speed & Back-EMFAZRS Sims

Speed–

Armature current–

Back-EMF–

Developed torque–

Load torque–

Output power–

Input power–

Efficiency–

About the DC Motor Simulator: Torque, Speed & Back-EMF

Free dc motor simulator: torque, speed & back-emf. Spin a permanent-magnet DC motor against a load, watch it settle onto its torque-speed curve, and see it stall if the load is too heavy. Drag, change the sliders and see the result live. No sign-up, works on phone and computer. Built for engineering, the dc motor simulator: torque, speed & back-emf runs instantly in your browser: change a setting or drag an object and the result updates at once, so you learn by trying things out rather than only reading about them.

Spin a permanent-magnet DC motor against a load, watch it settle onto its torque-speed curve, and see it stall if the load is too heavy. Use it to explore engineering ideas at your own pace, then check what you found against the key ideas further down this page.

How to use the DC Motor Simulator: Torque, Speed & Back-EMF

Use the controls to change Supply voltage V, Armature resistance Ra, Torque constant Kt (= Ke), Load torque, Rotor inertia J. The simulation reacts instantly.
Press "No load", "Rated load", "Stall it" to start, reset or change what is happening.
Where you see a glowing handle, object, weight or atom, drag it with your mouse or finger. Everything responds in real time.
Watch the readouts and graphs update as you experiment, and compare what you see with the key ideas below.

Things to try

Set the load torque to zero and see how close the rotor gets to the theoretical no-load speed V/Ke.
Slowly raise the load torque and watch the operating point slide down the torque-speed line while current climbs.
Use the Stall it preset and read the current warning — compare it with the running current at rated load.
Double the supply voltage and see the whole torque-speed line shift outward, roughly doubling the no-load speed.

Key ideas you can learn

Back-EMF Eb = Ke×ω grows as the rotor speeds up, and it opposes the supply voltage.
Armature current Ia = (V − Eb) / Ra, so current is highest the instant the motor starts (Eb = 0) and falls as it speeds up.
Developed torque T = Kt×Ia, and Kt and Ke are the same constant in SI units.
A DC motor's torque-speed relationship is a straight line: torque is highest at standstill (stall) and falls to zero at the no-load speed.
At steady state the developed torque exactly balances the load torque plus friction, which is what fixes the operating speed.
If the load torque is larger than the motor's stall torque, the rotor cannot turn: Eb stays zero and current is limited only by Ra, which is how motors overheat when jammed.

Back-EMF: E_b = K_e·ω

Armature current: I_a = (V − E_b) / R_a (while starting, R_a+R_start is used instead)

Developed torque: T = K_t·I_a

Equation of motion: J·dω/dt = T − T_load − b·ω (small viscous friction b keeps no-load speed finite)

Steady state: when T = T_load the speed stops changing, giving the operating point on the torque-speed line.

Mechanical power: P = T·ω — zero at stall (ω=0) and zero at no-load (T=0), peaking halfway between them at ω = V/(2K_e). This is the motor's maximum power point.

Why a starter is needed: at standstill E_b=0, so inrush current is V/R_a — often 10-20× rated current. A series R_start, shorted out once the motor is up to speed, limits this inrush.

Where this is used in the real world

Permanent-magnet DC motors like this one drive cordless power tools, small robots, electric window and seat motors in cars, toy and hobby motors, and the fans and pumps in countless appliances.

Who is this simulation for?

Engineering and technology students, makers, robotics clubs and teachers of design and technology. It gives a hands-on feel for how machines behave before you build a real one.

For teachers: project it on the board, let students predict what will happen, then run it together. For students: change one thing at a time and write down what changes.

Frequently asked questions

Why does current spike when a motor first starts or stalls?

At zero speed there is no back-EMF to oppose the supply, so the only thing limiting current is the armature resistance, which is usually small — that is why starting and stall currents can be many times the running current.

What is the difference between Kt and Ke?

They describe the same physical constant of the motor. Ke relates speed to back-EMF (volts per rad/s) and Kt relates current to torque (newton-metres per amp); in consistent SI units they have the same numeric value.

Why is the torque-speed curve a straight line?

Because Ia = (V − Keω)/Ra is linear in ω, and T = Kt×Ia, so T is a linear (decreasing) function of speed — maximum torque at standstill, zero torque at the free-running speed.

Is the DC Motor Simulator: Torque, Speed & Back-EMF free to use?

Yes. It is completely free, with no signup, no download and no ads inside the simulation. It runs in your web browser.

Does the DC Motor Simulator: Torque, Speed & Back-EMF work on a phone or tablet?

Yes. It uses touch as well as the mouse, so you can drag objects with your finger. A larger screen makes the controls easier to see.