Total harmonic distortion is the single number that measures how far an AC voltage or current waveform departs from a pure sine wave. Adjust the 3rd to 11th harmonic amplitudes and watch the THD, RMS factor, distortion factor and crest factor update in real time, and see exactly how waveform distortion is born.
Parameters
3rd harmonic
%
Amplitude of the 3rd harmonic relative to the fundamental
5th harmonic
%
Amplitude of the 5th harmonic relative to the fundamental
7th harmonic
%
Amplitude of the 7th harmonic relative to the fundamental
9th harmonic
%
Amplitude of the 9th harmonic (a triplen harmonic)
11th harmonic
%
Amplitude of the 11th harmonic relative to the fundamental
Results
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Total harmonic distortion THD (%)
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RMS of distorted wave (vs fund. ×)
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Distortion factor
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Crest factor
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Dominant harmonic
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IEEE 519 verdict
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Waveform comparison — pure sine vs distorted (animation)
The thin line is the pure fundamental sine wave; the bold line is the distorted composite of all harmonics. The gap between them is the distortion itself. Faint lines show individual harmonic components.
Total harmonic distortion THD (the RMS of all harmonics divided by the fundamental V1) and the distortion factor PF_dist. The harmonic amplitudes here are given relative to the fundamental (%).
Composite waveform v(t): the fundamental plus each odd harmonic of amplitude h_n, where h_n is a fraction of the fundamental.
What is Total Harmonic Distortion?
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I always assumed the electricity from a wall socket was a nice clean sine curve. What does it mean for a waveform to be "distorted"?
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An ideal AC supply really is a clean 50 Hz or 60 Hz sine wave. But real currents and voltages get pushed into jagged, non-sinusoidal shapes by all the equipment on the line. By Fourier's theorem, that distorted wave can be written as the sum of the "fundamental" (50/60 Hz) plus waves at integer multiples of it — the "harmonics". The 3rd harmonic is three times the fundamental frequency, the 5th is five times, and so on. THD bundles all those harmonics into one number: how much of them there is, relative to the fundamental.
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I see. When I raise the 3rd-harmonic slider on the left, the waveform warps. What actually causes that in real life?
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Almost always "non-linear loads". Diode rectifiers, switch-mode power supplies like the chargers in your laptop and phone, variable-frequency drives, LED lighting — they all pull current in sharp pulses near the voltage peaks. They do not draw current smoothly in proportion to the voltage. Run a Fourier analysis on those spiky currents and harmonics always pop out. In power systems the odd harmonics dominate, especially the 3rd, 5th and 7th, which is exactly why this tool only handles odd orders.
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If harmonics build up, what specific trouble does that cause?
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It is fairly serious. Harmonic currents heat transformers and motors more than they should, cutting efficiency and life. The nastiest case is the neutral conductor of a three-phase four-wire system. Normally, if the three phases are balanced, the neutral current is zero. But multiples of three — the 3rd, 9th and so on, called triplen harmonics — are in phase across all three lines, so instead of cancelling in the neutral they add up. The neutral current can end up larger than the phase currents, and overheated neutrals have caused real fires.
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That sounds scary. How much distortion is actually allowed? Is there a rule of thumb?
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The well-known international standard IEEE 519 asks that voltage THD be kept to roughly 5% or less. So this tool flags THD above 5% as "slightly over" and above 8% as "well over". With the default values, the THD is about 24.6% — nearly five times the limit, a clear fail. And on a real factory bus with lots of variable-frequency drives, numbers like that turn up all the time.
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So how do you bring the distortion back down?
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Three big approaches. First, harmonic filters — a passive filter that soaks up specific orders, or an active filter that injects an opposite-phase current to cancel them. Second, multi-pulse rectification: a 12-pulse or 18-pulse rectifier instead of a 6-pulse one makes the low-order harmonics cancel out neatly. Third, active PFC — power-factor correction — which forces the input current to follow a sine wave. It is now almost standard in modern server power supplies and EV chargers. Honestly, choosing low-THD equipment from the start is the easiest route.
Frequently Asked Questions
Voltage THD is defined as the ratio of the RMS of all harmonics to the fundamental V1: THD = √(V3²+V5²+V7²+…) / V1. This tool takes each harmonic amplitude as a percentage of the fundamental, so it converts them to fractions (h3 = V3/V1, etc.), computes THD = √(h3²+h5²+h7²+h9²+h11²) and multiplies by 100 for a percentage. For h3=20%, h5=12%, h7=7%, h9=3%, h11=2%, the result is THD ≈ 24.62%.
Harmonics come from non-linear loads that do not draw current smoothly in proportion to the voltage waveform. Diode rectifiers, switch-mode power supplies, variable-frequency drives and LED drivers pull current in sharp pulses near the voltage peaks. By Fourier's theorem this non-sinusoidal current can be written as the fundamental plus integer-multiple harmonics. In power systems the odd harmonics (3rd, 5th, 7th…) dominate, and the multiples of three (3rd, 9th…) are called triplen harmonics.
Harmonic currents add extra heating in transformers and motors, lowering efficiency and shortening their life. In a three-phase four-wire system the triplen harmonics (3rd, 9th) do not cancel in the neutral but add up, so the neutral conductor can be overloaded and overheat even when the phase currents are modest. Harmonics also cause nuisance breaker tripping, capacitor overload and resonance, and electromagnetic interference with electronics. Because these effects cost real money, standards such as IEEE 519 cap the voltage THD at about 5%.
There are three main families of cures. (1) Install passive or active harmonic filters that absorb or cancel specific harmonic currents. (2) Use a multi-pulse rectifier — 12-pulse or 18-pulse instead of 6-pulse — so the low-order harmonics cancel. (3) Adopt an active power-factor-correction (PFC) front-end that forces the input current close to a sine wave. At the design stage, selecting low-THD equipment and arranging transformer connections (delta-wye) and load placement so that triplen harmonics do not concentrate also helps.
Real-World Applications
Power-quality management in factories and buildings: A site with many inverter-driven motors, variable-frequency drives (VFDs) and rectifiers can easily push the bus voltage THD to 5-15%. Facility engineers monitor THD continuously with a power-quality analyser, and if it exceeds the IEEE 519 or IEC 61000 limits they identify the offending loads and consider adding filters. Breaking down the contribution of each order, as this tool does, is the first step toward a fix.
Data centres and server power supplies: Large numbers of switch-mode power supplies once produced input-current THD well over 100%. Today, active power-factor correction (PFC) is near-mandatory and holds the input-current THD down to around 5%. In the three-phase distribution of a server room, triplen harmonics concentrate in the neutral, so it is common practice to size the neutral conductor larger than the phase conductors.
Solar PV and grid-tied inverters: When a power conditioner converts the DC from solar panels into AC for the grid, the output-current THD is tightly limited by grid-interconnection codes (often 5% or less). The inverter's PWM control and the design of its LCL filter are the keys to achieving low THD.
Quality metric for audio and measurement equipment: THD is used not only in power systems but also as a fidelity figure for amplifiers and D/A converters. A spec like "THD+N 0.001%" states the fraction of harmonic distortion plus noise in the output signal — the smaller, the more faithful to the original. The concept of THD itself is identical in power and in audio.
Common Misconceptions and Pitfalls
The most common confusion is the difference between THD-F and THD-R. This tool computes THD-F (the IEEE 519 definition), which uses the fundamental as the denominator: THD = √(ΣVn²)/V1. THD-R (part of the IEC convention) instead uses the total RMS as the denominator, √(ΣVn²)/Vrms, and is therefore always below 100%. When the distortion is large the two diverge enough to matter — for THD-F of 50%, THD-R is about 44.7%. Always check which definition a standard or instrument is using before quoting a number.
Next, "large current THD" does not mean "large voltage THD". A load may draw a heavily distorted current (large current THD), yet if the source impedance of the supply is low enough, the voltage waveform barely distorts and the voltage THD stays small. Conversely, on a weak system (high impedance) the same current distortion produces a heavily distorted voltage. This is exactly why IEEE 519 specifies voltage THD and current distortion (TDD) separately. This tool deals with the distortion of the waveform itself, but in the field "where the THD was measured" is what matters.
Finally, do not ignore the phase of the harmonics. The THD formula depends only on the amplitudes (RMS values) of the harmonics; phase plays no part. But the "shape" of the composite waveform and its peak value (the crest factor) depend strongly on harmonic phase. For the same THD, different phase combinations make the waveform peaky or flat. This tool combines every harmonic as a sine (in phase), but a real waveform assessment must include phase information. The crest factor matters in particular for sizing the peak rating of capacitors and rectifier diodes.
How to Use
Enter the 3rd harmonic amplitude as percentage of fundamental (e.g., 15% for a rectifier output)
Input 5th, 7th, and 9th harmonic magnitudes in the corresponding fields
Click Calculate to compute THD%, RMS multiplier, distortion factor, crest factor, and IEEE 519-2022 compliance status
Review the dominant harmonic component and cross-check against facility power quality limits
Worked Example
6-pulse industrial rectifier supplying a 50 kW VFD: fundamental 230 V, 3rd harmonic 18%, 5th harmonic 24%, 7th harmonic 17%, 9th harmonic 8%. THD = sqrt(18² + 24² + 17² + 8²) / 100 = 32.1%. RMS voltage becomes 230 × 1.162 = 267 V. Distortion factor drops to 0.92. Crest factor reaches 3.4. Dominant harmonic is 5th at 55 A peak. IEEE 519 limit for general distribution (120 V–69 kV) is 5% THD; this rectifier violates compliance and requires 12-pulse conversion or active filtering.
Practical Notes
Non-linear loads (switch-mode power supplies, arc furnaces, soft starters) generate odd harmonics; measure actual waveforms with a power quality analyzer to populate inputs accurately
Motor inrush currents and capacitor bank switching create transient harmonics not captured by steady-state THD; use oscilloscope data for load step events
IEEE 519-2022 permits 5% THD for most utility customers; industrial facilities with rectifiers or VFDs must implement K-rated transformers, series reactors, or LC filters to stay compliant
Crest factor >3.5 indicates peak voltage stress; verify cable insulation and transformer saturation margins when THD exceeds 20%