DC Motor

Every robot and gadget has one. See how a DC motor spins up to speed and how its steady speed trades off against load along the speed-torque line.

DC MotorLive

step response & speed-torque

Controls

Presets

Voltage (V)

Armature resistance (Ω)

Load torque (N·m)

Motor constant Kt (N·m/A)

A DC motor speeds up until back-EMF balances the applied voltage, giving a first-order step response. Its steady speed drops linearly with load along the speed-torque line: maximum speed at no load, maximum (stall) torque at zero speed. The green dot is the operating point where motor and load torque match.

▶ Run in Python

Data Inspector

No-load speed240 rad/s

Steady speed224 rad/s

Stall torque0.30 N·m

Current draw0.4 A

Reading this result: Light load: speed stays close to the no-load value, since only a small back-EMF drop is needed to supply the torque.

Governing equation

ω = \frac{V - I R}{k _{e}} = \frac{12 - 0.4 \cdot 2}{0.05} = 224 rad/s, τ = k_{t} I = 0.020 N\cdotm

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

or unlock everything with Pro →

★ Sign in to save this setup

Save your tuned setup, or drop this simulation into your own site, docs, or course page.

How it works

A DC motor accelerates until its back-EMF balances the applied voltage, following a first-order step response set by its mechanical time constant. Its steady speed falls linearly as load torque rises — full speed at no load, maximum stall torque at zero speed. The operating point is where the motor and load torque curves meet.

✦

Ask the AI about this model

The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.

More Robotics simulations

Forward Kinematics Inverse Kinematics Differential Drive Cart-Pole Balance Quadcopter Control RRT Path Planning Kalman Filter PID Controller Tuner

Frequently asked questions

Is this DC motor speed torque simulator tool really free?▾

Yes. DC Motor runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.

Do I need to install anything?▾

No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.

Can I save or share my simulation?▾

Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.

How accurate are the results?▾

The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.