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How to Calculate Electric Motor Torque

By Lauren Nagel

Published: 21-06-2022, Last updated 21-06-2022

Introduction

Torque is an important variable when considering electric motor performance. It can be used to calculate mechanical power and derive electrical power. For drones and electric aircraft, knowing your torque also allows you to calculate motor efficiency separately from the efficiency of the rest of the system.

In this article we will:

  • Use the electric motor torque formula to calculate the torque of a brushless motor 
  • Test our calculation experimentally using the Series 1580 test stand

series 1580 motor tester

Figure 1: Series 1580 test stand with brushless motor

So how can you calculate electric motor torque?

Let’s say we want to know the torque of our motor, the Xoar 2407. Here’s what we know:

  • Weight: 36 g
  • Kv: 2300 Kv
  • Stator dimensions: 24 x 7 x 0.15 mm
  • Config: 12N14P

Nothing here is immediately helpful for calculating torque, so let’s look at some background information.

Motor torque is related to several variables, but the most important one for calculating torque is current.

Electric Motor Torque Formula:

electric motor torque formula

‘Kt’ is the motor torque coefficient, whose units are N.m/A (Newton-meters per Amp). Kt is the ratio of torque:current, a relationship that is not perfectly linear.

By itself, this coefficient is not of much use to us, but we can use the assumption that Kt = 1/Kv, and Kv is a number that we do have.

Let’s say we want to deliver 20 A of current to our motor. We can use this number and our motor’s Kv to calculate the theoretical torque.

Motor Kv is generally given in RPM/V, but for it to work in our formula we need it in SI units, which is (Radians/ Second)/ Volt in this case. To make the conversion we will divide 2300 by 60 s and multiply it by 2π.

kv si unit conversion

For a more precise explanation of motor Kv see our article: How to Calculate Motor Kv

Now we can plug our SI Kv value into our motor torque formula:

electric motor torque calculation

This figure seems reasonable, but the nonlinearity caused by the ESC and the motor can mean that theoretical results do not necessarily reflect reality. We generally expect a difference of 10 - 50% between the theoretical value and the measured value.

Note that this equation works on the assumption that the relationship between torque and current is linear, which is not the case, so the torque calculated will not be perfectly accurate.

Let’s hook up the motor to our test stand and see how close we get to our theoretical value.

motor torque test

Figure 2: Series 1580 test stand with brushless motor and propeller

We used the test stand to run a simple step test, taking a measurement when the system reached 20 A. The results of that test are below.

electric motor torque vs. current graph

Figure 3: Torque vs. Current results

At 20 A, we measured 0.133 Nm of torque with the Series 1580, a 46% difference from what we calculated.

As you can see, contrary to what the formula suggests, the relationship between current and torque is not linear. This is due to losses from the ESC and the motor.

This data goes to show that torque calculations can only give us an estimate of the true torque produced by a motor. To obtain accurate torque data, you need a tool to measure it.

We’ve been aware of this dilemma for quite some time, which is why we developed our motor test stands to allow users to collect highly accurate motor data. In addition to measuring torque, our test stands also measure thrust, RPM, electrical power, mechanical power, motor and ESC efficiency, propeller efficiency, and overall system efficiency.

Further reading: Brushless Motor Power and Efficiency Analysis

If you have any further questions don’t hesitate to leave us a comment below.

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