Motor Speed

Formula

Description

A DC motor's speed is determined by the voltage across the back-EMF, which equals the supply voltage minus the resistive drop in the windings. The back-EMF constant Ke relates this voltage to rotational speed. At no load, current is minimal and the motor spins at nearly V/Ke. As mechanical load increases, more current flows, increasing the I×R drop and reducing speed. This natural speed regulation is a characteristic of DC motors. Speed control is typically achieved by varying the supply voltage using PWM, which effectively changes the average voltage seen by the motor.

Variables

• n — Rotational speed (rad/s, divide by 2π/60 to get RPM)
• V — Supply voltage (V)
• I — Armature current (A)
• R — Winding resistance (Ω)
• Ke — Back-EMF constant (V/(rad/s))

Practical Notes

At stall (n = 0), the current is V/R, which can be very high and may damage the motor or driver if sustained. Motor drivers often include current limiting for protection. For precise speed control, use encoder feedback with a PID controller. BLDC motor controllers (ESCs) use electronic commutation and can operate from the back-EMF for sensorless speed measurement.