, alternatively called the back EMF constant) are values used to describe characteristics of electrical motors.
In SI units, the motor constant is expressed in newton metres per square root watt (
): where The motor constant is winding independent (as long as the same conductive material is used for wires); e.g., winding a motor with 6 turns with 2 parallel wires instead of 12 turns single wire will double the velocity constant,
and torque work in tandem, with rigidly connected shafts, the
of the system is still the same assuming a parallel electrical connection.
Alternatively, the system could run at the same torque as before, with torque and current split equally across the two motors, which halves the resistive losses.
The table below provides conversions between common SI units
is the motor velocity, or motor speed,[2] constant (not to be confused with kV, the symbol for kilovolt), measured in revolutions per minute (RPM) per volt or radians per volt second, rad/V·s:[3] The
rating of a brushless motor is the ratio of the motor's unloaded rotational speed (measured in RPM) to the peak (not RMS) voltage on the wires connected to the coils (the back EMF).
= 5,700 rpm/V supplied with 11.1 V will run at a nominal speed of 63,270 rpm (= 5,700 rpm/V × 11.1 V).
The motor may not reach this theoretical speed because there are non-linear mechanical losses.
On the other hand, if the motor is driven as a generator, the no-load voltage between terminals is perfectly proportional to the RPM and true to the
is often expressed in SI units volt–seconds per radian (V⋅s/rad), thus it is an inverse measure of
[7] Sometimes it is expressed in non SI units volts per kilorevolution per minute (V/krpm).
[8] The field flux may also be integrated into the formula:[9] where
By Lenz's law, a running motor generates a back-EMF proportional to the speed.
Once the motor's rotational velocity is such that the back-EMF is equal to the battery voltage (also called DC line voltage), the motor reaches its limit speed.
is the torque produced divided by armature current.
is the armature current of the machine (SI unit: ampere).
is primarily used to calculate the armature current for a given torque demand: The SI units for the torque constant are newton meters per ampere (N·m/A).
is not intuitive, to the point that many people simply assert that torque and
An analogy with a hypothetical linear motor can help to convince that it is true.
of 2 (m/s)/V, that is, the linear actuator generates one volt of back-EMF when moved (or driven) at a rate of 2 m/s.
The inverse relationship between force per unit current and
To translate this model to a rotating motor, one can simply attribute an arbitrary diameter to the motor armature e.g. 2 m and assume for simplicity that all force is applied at the outer perimeter of the rotor, giving 1 m of leverage.
(angular speed per unit voltage) of the motor is 3600 rpm/V, it can be translated to "linear" by multiplying by 2π m (the perimeter of the rotor) and dividing by 60, since angular speed is per minute.
Now, if this motor is fed with current of 2 A and assuming that back-EMF is exactly 2 V, it is rotating at 7200 rpm and the mechanical power is 4 W, and the force on rotor is
N or 0.0053 N. The torque on shaft is 0.0053 N⋅m at 2 A because of the assumed radius of the rotor (exactly 1 m).
Assuming a different radius would change the linear
will generate 0.00265 N⋅m of torque per ampere of current, regardless of its size or other characteristics.