Back-EMF Voltage

Q: How do you calculate Back-EMF Voltage?

Use the formula Vemf = Ke × ω. A spinning motor generates a voltage (back-EMF) proportional to its rotational speed due to Faraday's law of electromagnetic induction. Enter the values you know in the calculator above and it solves for the remaining variable.

Q: What is the formula for Back-EMF Voltage?

The Back-EMF Voltage formula is Vemf = Ke × ω, where Vemf—Back-EMF voltage (V); Ke—Back-EMF constant (V/(rad/s)); ω—Angular velocity (rad/s).

Vemf = Ke × ω

Quick answer

This calculator solves Vemf = Ke × ω for Back-EMF Voltage. With Back-EMF Constant 0.5 V/(rad/s), Angular Velocity 300 rad/s, the result is 150 V. It solves in 3 directions, so you can enter the values you have and get the one you need.

Calculator

Back-EMF Constant

Angular Velocity

Back-EMF Voltage (V)

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Formula

Vemf = Ke × ω

Description

A spinning motor generates a voltage (back-EMF) proportional to its rotational speed due to Faraday's law of electromagnetic induction. The back-EMF constant Ke has the same numerical value as the torque constant Kt when both are expressed in SI units (V/(rad/s) and N·m/A respectively). Back-EMF opposes the applied voltage and limits the motor current at speed. At no load, the motor spins at a speed where back-EMF nearly equals the supply voltage. Back-EMF detection is used in sensorless BLDC motor control to determine rotor position without Hall sensors.

Variables

Vemf — Back-EMF voltage (V)
Ke — Back-EMF constant (V/(rad/s))
ω — Angular velocity (rad/s)

Practical Notes

Back-EMF can be used as a tachometer for speed measurement. During regenerative braking, the motor acts as a generator and the back-EMF drives current back to the source. BLDC sensorless control algorithms detect back-EMF zero-crossings on the undriven phase to commutate the motor. Ke is often specified in V/kRPM in datasheets; convert by dividing by 1000 × 2π/60.

Symbols and units

Symbol	Meaning	Default unit	Accepted units
Vemf	Back-EMF Voltage	V	pV, nV, µV, mV, V, kV
Ke	Back-EMF Constant	—	V/(rad/s)
omega	Angular Velocity	rad/s	rad/s, RPM

Step by step

1. What you know: Back-EMF Constant 0.5 V/(rad/s), Angular Velocity 300 rad/s
2. The relation: Vemf = Ke × ω
3. Substitute: Ke = 0.5 V/(rad/s), omega = 300 rad/s
4. Result: Back-EMF Voltage = 150 V

Worked examples

Minimum range

Given: Back-EMF Constant 0.025 V/(rad/s), Angular Velocity 9.549 RPM

Result: Back-EMF Voltage = 25 mV

Low range

Given: Back-EMF Constant 0.25 V/(rad/s), Angular Velocity 10 rad/s

Result: Back-EMF Voltage = 2.5 V

Typical

Given: Back-EMF Constant 0.5 V/(rad/s), Angular Velocity 300 rad/s

Result: Back-EMF Voltage = 150 V

High range

Given: Back-EMF Constant 0.8 V/(rad/s), Angular Velocity 3000 rad/s

Result: Back-EMF Voltage = 2.4 kV

Maximum range

Given: Back-EMF Constant 8 V/(rad/s), Angular Velocity 30000 rad/s

Result: Back-EMF Voltage = 240 kV

Solving for each variable

Solve for Back-EMF Voltage

Back-EMF Constant 0.025 V/(rad/s), Angular Velocity 9.549 RPM → 25 mV

Solve for Back-EMF Constant

Back-EMF Voltage 0.33 V, Angular Velocity 9.549 RPM → 0.33 V/(rad/s)

Solve for Angular Velocity

Back-EMF Voltage 0.33 V, Back-EMF Constant 0.025 V/(rad/s) → 13.2 rad/s

How Back-EMF Voltage changes with Back-EMF Constant

Back-EMF Constant (input)	Back-EMF Voltage (result)
0.05 V/(rad/s)	15 V
0.125 V/(rad/s)	37.5 V
0.25 V/(rad/s)	75 V
0.375 V/(rad/s)	112.5 V
0.5 V/(rad/s)	150 V
0.75 V/(rad/s)	0.225 kV
1 V/(rad/s)	0.3 kV
2 V/(rad/s)	0.6 kV
3.5 V/(rad/s)	1.05 kV
5 V/(rad/s)	1.5 kV

The same result in other units

Unit	Value
mV	150000
V	150
kV	0.15

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Frequently asked questions

How do you calculate Back-EMF Voltage?

Use Vemf = Ke × ω. With Back-EMF Constant 0.5 V/(rad/s), Angular Velocity 300 rad/s, Back-EMF Voltage works out to 150 V.

What is the formula for Back-EMF Voltage?

The formula is Vemf = Ke × ω. A spinning motor generates a voltage (back-EMF) proportional to its rotational speed due to Faraday's law of electromagnetic induction.

How do you find Back-EMF Constant when you know the other values?

Rearrange for Back-EMF Constant: with Back-EMF Voltage 0.33 V, Angular Velocity 9.549 RPM, Back-EMF Constant is 0.33 V/(rad/s).

How do you find Angular Velocity when you know the other values?

Rearrange for Angular Velocity: with Back-EMF Voltage 0.33 V, Back-EMF Constant 0.025 V/(rad/s), Angular Velocity is 13.2 rad/s.

What units does Back-EMF Voltage use?

Back-EMF Voltage is shown in mV, V, kV. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

Related Concepts

All Motors & Mechanical formulas →

Motor Mechanical Power Motor Torque Motor Speed Gear Ratio Output Torque Back-EMF Voltage Motor Efficiency Rotational Dynamics Stepper Motor Step Angle

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