Motor Speed
n = (V − I×R) / Ke
Quick answer
This calculator solves n = (V - I×R) / Ke for n. With Supply Voltage 12 mV, Current 2 mA, Winding Resistance 0.47 Ω, Back-EMF Constant 1 × 10⁻⁵ V/(rad/s), the result is 1106 rad/s.
Calculator
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.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| V | Supply Voltage | V | pV, nV, µV, mV, V, kV |
| I | Current | A | pA, nA, µA, mA, A, kA |
| R | Winding Resistance | Ω | mΩ, Ω, kΩ, MΩ |
| Ke | Back-EMF Constant | V/(rad/s) | V/(rad/s) |
Step by step
- 1. What you know: Supply Voltage 12 mV, Current 2 mA, Winding Resistance 0.47 Ω, Back-EMF Constant 1 × 10⁻⁵ V/(rad/s)
- 2. The relation: n = (V - I×R) / Ke
- 3. Substitute: V = 12 mV, I = 2 mA, R = 0.47 Ω, Ke = 1 × 10⁻⁵ V/(rad/s)
- 4. Result: n = 1106 rad/s
Related quantities from the same inputs
- P = V × I = 24 µW
Worked examples
Minimum range
Given: Supply Voltage 0.33 V, Current 2 mA, Winding Resistance 1 Ω, Back-EMF Constant 1 × 10⁻⁴ V/(rad/s)
Result: n = 3280 rad/s
Low range
Given: Supply Voltage 3.3 V, Current 20 mA, Winding Resistance 10 Ω, Back-EMF Constant 0.001 V/(rad/s)
Result: n = 3100 rad/s
Typical
Given: Supply Voltage 12 mV, Current 2 mA, Winding Resistance 0.47 Ω, Back-EMF Constant 1 × 10⁻⁵ V/(rad/s)
Result: n = 1106 rad/s
High range
Given: Supply Voltage 0.23 mV, Current 100 µA, Winding Resistance 4.7 mΩ, Back-EMF Constant 1 × 10⁻⁷ V/(rad/s)
Result: n = 2295 rad/s
Maximum range
Given: Supply Voltage 2.3 mV, Current 1 mA, Winding Resistance 47 mΩ, Back-EMF Constant 1 × 10⁻⁶ V/(rad/s)
Result: n = 2253 rad/s
How n changes with Supply Voltage
| Supply Voltage (input) | n (result) |
|---|---|
| 1.2 mV | 26 rad/s |
| 3 mV | 206 rad/s |
| 6 mV | 506 rad/s |
| 9 mV | 806 rad/s |
| 12 mV | 1106 rad/s |
| 18 mV | 1706 rad/s |
| 24 mV | 2306 rad/s |
| 48 mV | 4706 rad/s |
| 84 mV | 8306 rad/s |
| 120 mV | 11910 rad/s |
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<p><a href="https://vbatpower.com/formulas/motor-speed/">Motor Speed</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Motor Speed?
Use n = (V - I×R) / Ke. With Supply Voltage 12 mV, Current 2 mA, Winding Resistance 0.47 Ω, Back-EMF Constant 1 × 10⁻⁵ V/(rad/s), n works out to 1106 rad/s.
What is the formula for Motor Speed?
The formula is n = (V - I×R) / Ke. 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.
Related Concepts
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