Duty Cycle and RMS Load Formulas

Duty cycle formulas: the RMS current of a load that changes with time, the average current and the duty factor, for a motor or a heater on a cycle.

The formulas

Ii is the current in each part of the cycle and ti its duration (in any one unit). The heating in a motor or a cable goes with the square of the current, so the RMS value is the steady current that would give the same heat over the whole cycle. The RMS value is larger than the average value when the load varies. It should stay below the continuous rating of the motor or the cable, and the peak must still be within the overload and the torque limits. The cooling of a motor at rest is slower, which this page does not model. The cycle here is an example.

Worked example: 100 A for 10 s, 20 A for 30 s, off for 20 s

The cycle is 60 s.

1. Σ(I² × t) = 100² × 10 + 20² × 30 + 0 = 112,000, and divided by 60 it is 1,867
2. Irms = √1,867 = 43.2 A
3. Iav = (100 × 10 + 20 × 30) / 60 = 26.67 A, and the duty factor is 40 / 60 = 66.67%

Frequently asked questions

Why use the RMS value?

The heating goes with the current squared, so the RMS value gives the steady current with the same heating over the cycle.

Why is the RMS value higher than the average?

Squaring gives more weight to the large currents, so a varying load has an RMS value above its average.

Is the RMS check enough for a motor?

No. The motor must also handle the peak torque and the starts per hour, and its cooling at rest is poorer.

Does this apply to cables?

It gives a first estimate for a short cycle. For a long cycle the cable follows the thermal time constant, so use the cable maker's data.

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