Torque Constant⚠ unverified
Electrical / Motors · Return the motor torque constant
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| Kt | Kt | N.m/A | 1.0 | Torque constant |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | Kt | N.m/A | Torque constant, in newton-metres per ampere (N.m/A) |
The science & history
Understanding the Parameters
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$K_t$ — how much torque each amp of current produces; set by magnetic flux and winding geometry. A motor's torque is then $T = K_t I$ (before friction losses).
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Its twin is the back‑EMF constant $K_e$ (volts per rad/s, see Back Emf); the two are the same physical machine constant seen from the two sides of the energy conversion.
Derivation (the $K_t = K_e$ identity)
An ideal (loss‑free) motor converts all electrical power crossing the back‑EMF into mechanical power. The electrical power delivered to the back‑EMF is $E\,I$, and the mechanical power produced is $T\omega$; equating them,
$$E\,I = T\,\omega.$$
Substituting the back‑EMF $E = K_e\,\omega$ and the torque $T = K_t\,I$:
$$K_e\,\omega\,I = K_t\,I\,\omega \quad\Rightarrow\quad \boxed{K_t = K_e}.$$
So the same constant governs both "volts per speed" and "torque per amp" — they cannot be chosen independently. (In non‑SI unit systems a numerical conversion factor appears, but the underlying equality is exact.)
History
The equality $K_t = K_e$ is a textbook consequence of energy conservation in electromechanical energy conversion, formalised as electric machines matured in the late 19th and early 20th centuries. It is the reason a single "motor constant" characterises both the driving and generating behaviour of a machine.
Related Concepts: Back Emf, Speed Constant, Motor Torque, Motor Current
Notes: Registry calculator torque-constant is a definitional pass‑through (it returns the supplied
$K_t$). The physics is the relation $T = K_t I$ and the identity $K_t = K_e$ (SI).