Back-EMF Constant (Ke) vs Torque Constant (Kt)

Introduction

Open three motor datasheets and you will often see two constants, Ke and Kt, listed with different symbols, different units, and sometimes different numbers. That mismatch trips up a lot of engineers who are sizing a motor and driver.
The back-EMF constant (Ke) links rotor speed to the voltage the motor generates, while the torque constant (Kt) links current to the torque the motor makes. In SI units they are numerically equal, because they are two views of the same electromechanical coupling.

The Two Constants at a Glance

Before the details, here is the side-by-side view. Both constants describe how the same motor converts between the electrical and the mechanical world, just measured from opposite ends.

Back-EMF Constant (Ke)

Definition and Units

The back-EMF constant tells you how much voltage the spinning motor produces for each unit of speed. In SI units that is V·s/rad, so multiplying Ke by the angular speed in rad/s gives the back-EMF voltage. Datasheets often use friendlier units like V/krpm or V per 1000 rpm, which is the same idea scaled for readability.
A quick example. If Ke is 0.05 V·s/rad and the rotor spins at 300 rad/s, the back-EMF is about 15 V. The number grows in direct proportion to speed.

What It Tells You

Ke sets your voltage headroom. The faster the motor turns, the more voltage it pushes back against the supply. Once the back-EMF approaches the bus voltage, the driver can no longer force more current, so the motor reaches its top speed for that bus. A higher Ke means a lower top speed at the same voltage, and a lower Ke means more speed but less torque per amp.
This article covers the constant, not the physics. For how back-EMF is generated, why it rises with speed, and how it is measured, see our article on back-EMF.
Takeaway: Use Ke to predict the voltage a motor needs and the top speed a given bus voltage allows.

Torque Constant (Kt)

Definition and Units

The torque constant tells you how much torque the motor makes per amp of current. Its SI unit is N·m/A, so multiplying Kt by the current gives the torque. For a motor under field-oriented control, the relevant current is the torque-producing component, often written Iq, and torque is close to Kt times Iq.
If Kt is 0.05 N·m/A and you push 10 A, you get about 0.5 N·m. The link is linear until the motor starts to saturate at high current.

What It Tells You

Kt drives your driver sizing. Once you know the torque your load needs, Kt tells you the current the driver must deliver. A motor with a high Kt makes more torque per amp, which keeps currents and copper losses lower for the same torque. That matters for the thermal budget of both the motor and the controller.
Kt is also the constant you tune against when you set up torque control. For how a controller regulates that torque in practice, see our overview of torque control.

Why Ke = Kt (in SI Units)

The two constants are equal because of energy conservation. The electrical power a motor takes in equals the mechanical power it puts out, minus losses. Write that balance for an ideal machine and the speed-to-voltage term and the current-to-torque term fall out with the exact same value. This is the electromechanical reciprocity at the heart of every motor.

• Units. Ke in V/krpm and Kt in N·m/A look different until you convert both to SI. Convert first, then compare.
• RMS vs peak. A constant quoted against peak phase current differs from one quoted against RMS current by a factor of the square root of two.
• Line-to-line vs phase. Voltage measured between two phases differs from the per-phase value, which shifts Ke.
• The 3/2 factor. Some three-phase torque equations carry a 3/2 scaling from the Clarke and Park transforms, which can be folded into Kt or kept separate.

Ke, Kt and Kv (the Velocity Constant)

A third symbol shows up on hobby, drone, and RC motors: Kv, the velocity constant. Kv is the inverse of Ke. It tells you how many rpm the motor turns per volt, so a “1000 KV” motor spins about 1000 rpm for each volt applied, ignoring load.
The quick conversions:

• A high Kv means a low Ke, so high speed and low torque per amp.
• A low Kv means a high Ke, so lower speed and more torque per amp.
• To go from Kv in rpm/V to Ke in V·s/rad, take the reciprocal and convert rpm to rad/s.

So the same motor can be described three ways. Ke from the voltage side, Kt from the torque side, and Kv as the speed-per-volt shorthand. They are not three properties, just three labels for one coupling.
Takeaway: Kv is roughly 1/Ke; a high-KV motor trades torque per amp for speed.

Using Ke and Kt in Motor Selection

These constants are how you match a motor, a controller, and a bus voltage to each other. Start from the job. Your peak torque requirement, divided by Kt, gives the peak current the driver must supply without overheating. Your top speed requirement, multiplied by Ke, gives the back-EMF the bus voltage has to exceed.
Pick a motor whose Kt keeps the current inside what your controller can handle, and whose Ke leaves voltage headroom at your top speed. If the current runs too high, look for a higher-Kt winding. If the motor cannot reach speed, you need either a lower Ke or a higher bus voltage. A controller with motor controllers that span a wide current and voltage range gives you room to make that match.
Takeaway: Size current from torque and Kt, then check speed against Ke and your bus voltage.

How SOLO Uses Ke and Kt

SOLO controllers identify the motor’s electrical constants during automatic motor identification, so the torque and speed loops are set up against the real Ke and Kt of your motor. That lets the drive convert a torque command into the right current across the range. You can run it on any of our motor controllers.

Conclusion

Ke and Kt describe the same motor from two sides. Ke links speed to generated voltage and sets your top speed at a given bus voltage. Kt links current to torque and sets the current your driver must supply. In SI units the two values are equal, because they are two views of one electromechanical coupling, and most datasheet mismatches come from units or measurement conventions. Knowing both lets you match motor, controller, and voltage with confidence, and a controller that identifies these constants for you, like a SOLO motor controller, removes most of the guesswork.

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