True RMS measurement in energy metering

RMS (root mean square) is the effective value of an alternating voltage or current. An RMS current of 10 A heats a resistor by the same amount as a steady 10 A DC current. A true RMS instrument calculates this value from the real waveform. It does not assume that the waveform is a sine wave.

This guide is part of the power fundamentals series. It explains when the difference matters, and why an RMS current reading is not a measurement of power or energy.

How RMS is calculated

For a sampled waveform, square each sample, calculate the mean of the squares, then take the square root. The mean of an alternating current is zero, because the positive and negative half-cycles cancel. The squares are all positive, so the RMS value is not zero.

For a pure sine wave, RMS = peak ÷ √2. A sine wave with a peak of 14.14 A has an RMS value of 10 A. On a 230 V supply, the voltage peak is about 325 V.

True RMS and average-responding instruments

An average-responding instrument rectifies the signal, measures its average, and multiplies the result by 1.11. That factor is correct only for a sine wave. Fluke gives the error on distorted waveforms as up to 40% low or 10% high.

A true RMS instrument calculates the RMS value directly, so it is correct for both waveforms below:

Swipe to see the whole drawing

The pulsed current is typical of equipment with a rectifier input: switch-mode power supplies, variable-speed drives, UPS systems and LED drivers. The rectifier draws current only near the peak of the voltage, so the current flows in short, tall pulses. In this example the peak is 2.4 times the RMS value. An average-responding clamp meter on this circuit reads about 6.3 A, and the cable carries 10 A.

Crest factor

Crest factor is the peak value divided by the RMS value:

A high crest factor tells you that the current is distorted. Harmonic current adds to the RMS current, and it heats cables, transformers and neutral conductors. On a three-phase four-wire circuit with many single-phase electronic loads, the third harmonic currents of the three phases add in the neutral. Measure the neutral current on these boards. A change in a machine's current waveform over time can also be an early sign of a fault; the condition monitoring guide explains what electrical data can show. The THD and TDD calculator gives THD and TDD from harmonic magnitudes.

RMS current is not kW

RMS voltage multiplied by RMS current gives apparent power in volt-amperes (VA). Active power in watts (W) is the mean of the instantaneous product of voltage and current. The two are equal only when the voltage and the current are in phase and undistorted.

Two single-phase loads show the difference. Both draw 10 A RMS at 230 V RMS, so both have an apparent power of 2.3 kVA:

The current trends of the two loads are identical, and the energy differs by a factor of two. A current-only sensor cannot show this. The power factor guide explains the ratio, and the kW vs kWh guide explains the step from power to energy.

What to specify

Ask for the quantity that the project needs, and for the evidence that the instrument measures it:

The current sensor must match the meter input. A CT with a current output, a CT with a voltage output and a Rogowski coil are not interchangeable. The CT selection guide explains the choice.

When two readings disagree

A clamp meter and a monitoring system often disagree for valid reasons. Check these points in order:

1. The quantity. RMS current, active power and apparent power are different values.
2. The time. A clamp meter updates its display several times per second. A monitoring system often reports an average over a minute or longer. Take both readings at the same time on a steady load.
3. The instrument type. An average-responding clamp meter reads low on distorted current.
4. The limits. Check the range, the bandwidth and the crest factor limit of each instrument.

If the difference remains, record both instrument models, their settings, the raw values and the circuit. Only qualified people may open electrical panels or fit reference instruments, and they must follow the site safety procedure.

True RMS with a ZEM

The ZEM electricity monitor samples the voltage and current of each phase and reports RMS voltage, RMS current, power factor, kWh and kVAh for each three-phase circuit. Its current sensors are calibrated to the meter, so its Class 0.5S accuracy applies to the meter and sensors together. The readings go over the Zigbee mesh to a Gateway, where Edge stores them. See the three-phase power guide for how the meter adds the phase powers.