True RMS means that an instrument calculates the root mean square (RMS) of the waveform it actually measures. RMS 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. An instrument that is not true RMS measures the average of the rectified signal and scales it as if the waveform were a sine wave, so its reading is right only for a sine wave.
This guide is part of the power fundamentals series. It gives the RMS formula, shows how far an average-responding meter is wrong on common waveforms, and explains why an RMS current reading is not a measurement of power or energy.
Distorted waveforms are measured as total harmonic distortion, which has its own guide with the THD and TDD limits.
The RMS value formula
IEC 60050-103 (IEV 103-02-03) defines the RMS value of a time-dependent quantity as the positive square root of the mean of its square over a given time interval. For a voltage or current x(t) over one period T:
XRMS = √( (1/T) × ∫ x(t)² dt ), integrated over the period
A digital meter works from samples. For N samples x₁ to xN taken over a whole number of cycles:
XRMS = √( (x₁² + x₂² + … + xN²) ÷ N )
Square each sample, calculate the mean of the squares, then take the square root. A sine wave without a DC component has a mean of zero over complete cycles, because its positive and negative half-cycles cancel. The squared samples are non-negative, so a non-zero waveform has a positive RMS value.
RMS of a sine wave
For a pure sine wave, RMS = peak ÷ √2 = 0.707 × peak. 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. The rectified mean of a sine wave is 2/π × peak = 0.637 × peak, which is 0.900 × RMS. Both ratios hold only for a sine wave.
RMS of a current with harmonics
A distorted current is the sum of its fundamental and its harmonics. Its RMS value is the square root of the sum of the squares of their RMS values:
IRMS = √( I₁² + I₂² + I₃² + … ) = I₁ × √(1 + THD²)
Take a current with an 8.0 A fundamental, a 4.8 A third harmonic and a 3.6 A fifth harmonic. The harmonic RMS is √(4.8² + 3.6²) = 6.0 A, so the current THD is 6.0 ÷ 8.0 = 75%, and the RMS current is √(8.0² + 6.0²) = 10.0 A. A meter that measures only the fundamental reads 8.0 A, while the cable heats as it does with 10 A. The THD and TDD calculator gives THD and TDD from the harmonic magnitudes.
True RMS vs average-responding meters
An average-responding instrument rectifies the signal, measures its average, and multiplies the result by 1.111. That factor is the form factor of a sine wave, so it 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:
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.
Form factor and crest factor
Two ratios describe the shape of a waveform. The form factor is the RMS value divided by the rectified mean. The crest factor is the peak value divided by the RMS value. An average-responding meter reads 1.111 divided by the form factor of the waveform, as a fraction of the true RMS value:
| Waveform | Crest factor (peak ÷ RMS) | Form factor (RMS ÷ rectified mean) | Average-responding reading |
|---|---|---|---|
| Sine wave | 1.414 | 1.111 | 100% of true RMS |
| Square wave | 1.000 | 1.000 | 111%, reads 11% high |
| Triangle wave | 1.732 | 1.155 | 96%, reads 4% low |
| Pulsed rectifier current in the figure above | 2.36 | about 1.76 | about 63%, reads 37% low |
The current of a linear load, such as a motor or a heater, on a clean supply is close to a sine wave. The current of a rectifier input, in IT loads, drives and LED drivers, often has a crest factor of 2 to 3.
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.
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 at power factor 1: current is proportional to voltage throughout the waveform. This includes a purely resistive load even when both waveforms are distorted.
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:
| Load | Power factor | Active power | Energy in 8 hours |
|---|---|---|---|
| Current in phase with the voltage | 1.00 | 2.30 kW | 18.4 kWh |
| Current lags the voltage by 60° | 0.50 | 1.15 kW | 9.2 kWh |
The two loads have the same RMS current, but one uses twice as much energy over eight hours. A current-only sensor cannot show that difference. 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:
| Requirement | What to ask for |
|---|---|
| Current trend or running state | True RMS current, and the current range of the sensor |
| Active power and energy (kW, kWh) | A voltage reference on each phase, with each current paired to its own phase voltage |
| Circuits with electronic loads | The bandwidth and the crest factor limit of the meter and its current sensors |
| Three-phase totals | The supported wiring modes (three-wire, four-wire) |
| Comparison with another system | The same quantity, units, averaging period and timestamps |
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:
- The quantity. RMS current, active power and apparent power are different values.
- 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.
- The instrument type. An average-responding clamp meter reads low on distorted current.
- 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.
Common questions
What does true RMS mean?
A true RMS instrument calculates the root mean square of the waveform that it measures: it squares the samples, averages the squares and takes the square root. The result is correct for sine waves and for distorted waveforms, within the instrument's bandwidth and crest factor limits.
What is the RMS value?
The RMS (root mean square) value of an alternating voltage or current is its effective value: the DC value that would deliver the same power into a resistor. It is the square root of the mean of the squared instantaneous values over a whole number of cycles. 230 V RMS heats a resistor exactly as 230 V DC does.
How do you calculate RMS from the peak value?
For a pure sine wave, divide the peak by √2, or multiply it by 0.707. A 325 V peak is 230 V RMS, and a 14.1 A peak is 10 A RMS. The rule holds only for a sine wave. For any other waveform, divide the peak by that waveform's crest factor, or calculate the RMS from samples.
What is the difference between true RMS and average-responding meters?
An average-responding meter rectifies the signal, measures its mean and multiplies by 1.111, the form factor of a sine wave. It is right only on a sine wave. A true RMS meter calculates the RMS from the waveform itself. On a square wave the average-responding meter reads 11% high, on a triangle wave 4% low, and on the pulsed current of a rectifier input it can read 40% low.
Do I need a true RMS meter?
Yes, for any circuit that feeds electronic loads: variable-speed drives, rectifiers, UPS systems, LED lighting and IT equipment. On these circuits an average-responding instrument can read the current tens of percent low.
Is RMS current the same as power?
No. RMS voltage multiplied by RMS current gives apparent power in VA. Active power in W also depends on the power factor, so two circuits with the same RMS current can use very different amounts of energy.
What is crest factor?
The peak value divided by the RMS value. A sine wave has a crest factor of 1.414. The pulsed current of a rectifier input can have a crest factor of 2 to 3. An instrument has a maximum crest factor at which its stated accuracy applies.
What is form factor?
The RMS value divided by the rectified mean value. A sine wave has a form factor of 1.111, a square wave 1.000 and a triangle wave 1.155. An average-responding meter is calibrated with the sine wave figure, so on another waveform it reads 1.111 divided by that waveform's form factor, as a fraction of the true RMS value.