Explainer: How to Calculate Motor Torque from Power

What determines the required torque

Torque is the turning force that moves a mechanical load. In electric motor applications, it is the force generated at the shaft. The relationship between torque, power, and speed is fixed by physics. Power is the rate of doing work. Speed is how fast the shaft rotates. Torque is the force needed to maintain that rotation against resistance.

Engineers often confuse these three variables. They treat power as a standalone metric without considering the speed at which it is delivered. A motor rated at a certain kilowatt value can produce very different torque levels depending on its rotational speed. A slow turning pump requires high torque at low speed. A high-speed fan requires lower torque at high speed. Both may demand the same power output, but their torque requirements are different.

The core task in torque sizing is to determine the exact force needed at the shaft. This figure dictates the frame size and the selection of the drive. If the calculated torque exceeds the motor capability, the machine stalls or overheats. If it is significantly lower, the system is oversized. Both outcomes affect capital costs and operational efficiency.

The standard torque calculation formula

The direct way to find the required torque is to use the standard equation. This torque calculation formula relates power, speed, and torque. It works for both AC and DC machines, as well as synchronous and induction types.

The formula is derived from the definition of mechanical power. Power equals torque multiplied by angular velocity. To solve for torque, you divide power by angular velocity. The most common form uses rotational speed in revolutions per minute. The constant 9549 converts the units from watts and rpm to newton-metres.

The equation looks like this:

Torque (N.m) = Power (W) / (2 * pi * Speed (rpm))

Alternatively, using the standard constant:

Torque (N.m) = (Power (kW) * 9549) / Speed (rpm)

This relationship is linear. If speed doubles, the required torque halves for the same power. If power doubles, the required torque doubles. This inverse relationship is critical when specifying variable speed drives. A VFD changes the speed, which changes the torque demand at that specific operating point.

How speed affects torque sizing

Speed is the second major variable in the torque calculation formula. It is not just a number on a nameplate. It represents the mechanical reality of the load.

Consider a conveyor belt. The belt speed is set by the production line requirement. A high-speed line requires a smaller motor to achieve the same power transfer than a slow line. The torque requirement drops as speed increases. This allows for a smaller frame size, which saves space and reduces weight.

However, starting conditions change the picture. Many industrial loads have high breakaway torque. A heavy pump or a dense material conveyor needs significantly more torque at zero speed to get moving. Once the load is up to speed, the torque demand drops to a steady-state value.

This distinction drives the selection process. You must size for the peak torque, not just the running torque. The torque sizing process must account for the worst-case scenario. This often means looking at the starting current and the thermal limits of the winding.

A worked example in plain words

Imagine a production line using a horizontal mixer. The motor drives the mixing drum. The load requires 10 kilowatts of power to operate at full speed. The drum is designed to rotate at 1,500 rpm.

To find the required torque, use the formula. Multiply the power in kilowatts by 9549. Then divide that result by the speed in rpm.

The calculation is (10 * 9549) / 1500.

The result is approximately 63.7 newton-metres.

This is the running torque. The motor must be able to produce at least this amount during normal operation. However, the mixer has a heavy load. The starting torque requirement is higher. If the load needs 150% of the running torque to start, the peak torque requirement is about 95.5 newton-metres.

You would then select a motor with a nameplate torque that meets or exceeds 63.7 newton-metres. More importantly, you would verify that the starting torque capability, often provided in the technical data sheet, meets the 95.5 newton-metres requirement. This ensures the machine starts reliably without stalling.

Key factors in torque sizing decisions

The calculation gives a baseline number. The final selection involves context. Several factors influence how that number is applied.

Duty cycle is the first factor. A motor running 24/7 has different thermal limits than one running in short bursts. Continuous duty requires a lower torque density to keep temperatures down. Intermittent duty allows for higher torque peaks, as the machine has time to cool.

The type of load matters. A fan or pump has a torque curve that follows a specific pattern with speed. A constant torque load, like a conveyor, needs a different profile. A variable torque load, like a compressor, requires a different drive configuration. The torque sizing must match the load curve.

Acceleration time is another variable. If the load must reach speed quickly, the torque must be high during that ramp-up period. Slow acceleration allows for lower peak torque. The torque calculation formula gives the steady-state value. You must add the acceleration torque component. This is calculated based on the load inertia and the desired acceleration rate.

Common mistakes in torque sizing

Engineers and buyers make specific errors in this process. These mistakes lead to failed installations or wasted capital.

The first mistake is using average speed instead of operating speed. If a VFD changes the speed, the torque changes. You must calculate the torque at the specific speed where the load is running. Do not use the base motor speed if the application runs at a different point.

The second mistake is ignoring the starting torque. Many loads require more than 100% of rated torque to start. If the motor is selected based only on the running torque, it may not start. This causes high current draw and potential damage to the motor windings.

The third mistake is unit errors. Power is often in kilowatts, but the formula expects watts or requires a specific constant. Speed is in rpm, but the formula expects radians per second. Mixing these up creates massive errors. Always check the units before calculating.

A fourth mistake is ignoring the gearbox. If the motor drives a gearbox, the torque at the motor shaft is different from the torque at the load. You must account for the gear ratio. The torque at the load is the motor torque multiplied by the ratio and efficiency. You must calculate the motor torque required to produce the load torque.

Verifying the selection

The calculated torque is a starting point. It is not the final answer. You must verify it against the equipment specifications.

Check the manufacturer’s data sheet. Look for the rated torque at the rated speed. Compare it to your calculated running torque. Check the starting torque or torque at breakdown. Compare it to your peak torque requirement.

Review the nameplate. It lists the power and speed. It may list the torque. If it does not, calculate it using the formula. Ensure the calculated value matches the data sheet value.

Check the thermal design. High torque at low speed generates heat. The insulation class and cooling method must handle the heat generated during the duty cycle. A motor that meets the torque requirement but overheats is a failed selection.

Torque sizing is a precise calculation. It requires accurate load data and a clear understanding of the operating conditions. Use the standard formula. Account for starting and acceleration demands. Verify the result against the manufacturer’s data. This process ensures the motor is correctly matched to the load. It avoids oversizing and underperformance. It leads to a reliable and efficient drive system.

Reference data for calculation

The table below shows the relationship between power, speed, and torque. It helps to see how the variables interact. The values are calculated using the standard formula. They illustrate the inverse relationship between speed and torque for a constant power output.

Power (kW)	Speed (rpm)	Torque (N.m)
5	1450	32.8
5	1000	47.7
5	500	95.5
10	1450	65.6
10	1000	95.5
10	500	191.0

The numbers show that halving the speed doubles the torque. Doubling the power doubles the torque. This is the core principle of torque sizing. Use this table to cross-check your own calculations. If your numbers are far from these, check your units or your input values.

The process is straightforward. Define the load power. Define the operating speed. Apply the formula. Add the starting and acceleration components. Select the motor. Verify with the data sheet. This method is reliable and widely accepted in the industry. It forms the basis of every motor selection project.