Total Harmonic Distortion (THD) Calculator
Enter the RMS amplitudes of the fundamental and each harmonic component to find the total harmonic distortion as a percentage and in decibels. Switch to the Total RMS method if you only have the overall RMS and fundamental RMS from a meter. Results update instantly and include a harmonic spectrum breakdown, quality rating, and IEEE 519 compliance context.
Formula
Worked example
A 100 V fundamental with harmonics H2 = 5 V, H3 = 3 V, H5 = 2 V, H7 = 1 V: harmonic RMS = sqrt(25 + 9 + 4 + 1) = sqrt(39) = 6.245 V. THD = 6.245 / 100 x 100 = 6.24%, or 20 x log10(0.0624) = -24.1 dB. This exceeds the IEEE 519 5% limit for medium-voltage systems.
What is total harmonic distortion?
Total harmonic distortion (THD) is a measure of how much a waveform deviates from a perfect sine wave due to the presence of harmonic frequencies. Every real-world AC signal contains not only the fundamental frequency (50 Hz or 60 Hz in power systems, 1 kHz in audio testing) but also integer multiples of it called harmonics: the 2nd harmonic is twice the fundamental, the 3rd is three times, and so on. THD expresses the combined energy of all these harmonic components as a percentage of the fundamental. A perfectly pure sine wave has THD = 0%; a badly distorted waveform may exceed 10% or more. Lower THD means better waveform fidelity, less heat in conductors and transformers, and reduced interference with sensitive equipment.
How to use this calculator
Select "Individual harmonics" if you have a spectrum analyzer, oscilloscope FFT, or power quality meter that reports each harmonic order separately. Enter the RMS amplitude of the fundamental (H1) and each harmonic component H2 through H9 in the same units (volts, amps, or any consistent scale). The calculator outputs THD in both percent and decibels, along with the individual harmonic levels relative to the fundamental. Select "Total RMS method" if you only have a total RMS reading and a fundamental RMS reading, for example from a true-RMS multimeter and a power analyzer. Enter both values and the calculator derives the combined harmonic RMS and THD using the relationship: harmonic RMS = sqrt(Vrms squared minus V1 squared). Both methods are mathematically equivalent when the same harmonics are present.
THD in power quality and IEEE 519
In electrical power systems, harmonic distortion is generated by non-linear loads such as variable frequency drives, switching power supplies, LED drivers, and rectifiers. These loads draw current in pulses rather than smoothly, injecting harmonics back into the supply. The IEEE 519-2022 standard sets limits on both current and voltage THD at the point of common coupling. For voltage THD, the limit is 8% for systems at or below 1 kV, 5% for systems from 1 kV to 69 kV, and 2.5% for systems from 69 kV to 161 kV. Exceeding these limits can cause transformer overheating, motor vibration, nuisance tripping of protective devices, and measurement errors in metering equipment. Common mitigation strategies include passive harmonic filters, active power factor correction, 12-pulse or 18-pulse rectifiers, and harmonic-blocking transformers.
THD in audio systems
In audio, THD (often written THD+N when noise is included) measures amplifier and converter quality. The dominant contributors are crossover distortion in Class B amplifiers, clipping at high power levels, and non-linearities in transducers. High-end amplifiers typically achieve THD below 0.01% (around -80 dB). Consumer amplifiers are usually under 1%. THD above 3-5% is clearly audible as harshness or grittiness, especially on sustained tones. Audio THD is measured with a pure sine wave (often 1 kHz at a specified output power) and analyzed by a notch filter that removes the fundamental while measuring the remaining signal. The decibel form of THD is useful in audio because it maps directly onto signal chain noise floors and dynamic ranges.
THD quality ratings and IEEE 519-2022 voltage limits
| THD range | Rating | IEEE 519 bus voltage context |
|---|---|---|
| < 1% | Excellent | Below all IEEE limits; high-end audio and precision supplies |
| 1% - 3% | Good | Below all IEEE limits; suitable for sensitive electronics |
| 3% - 5% | Acceptable | Meets the 5% limit for systems at 1.0 to 69 kV |
| 5% - 8% | Poor | Exceeds the 5% IEEE limit for most industrial systems |
| > 8% | Unacceptable | Exceeds all IEEE 519 limits including the 8% limit for low-voltage (<1 kV) systems |
IEEE 519-2022 defines maximum THD limits by system voltage. Audio quality ratings apply to consumer and professional audio equipment.
Frequently asked questions
What is a good THD value?
It depends on the application. For power systems, IEEE 519-2022 requires voltage THD below 5% at medium-voltage buses (1-69 kV) and below 8% at low-voltage buses (under 1 kV). For audio amplifiers, THD below 1% is considered good, below 0.1% is excellent, and below 0.01% is audiophile-grade. For precision instrumentation and power supplies, THD below 1% is generally the target.
What is the difference between THD percent and THD in dB?
Both express the same quantity on different scales. THD in dB is calculated as 20 times the logarithm base 10 of the THD ratio (THD% divided by 100). A THD of 1% equals -40 dB, 3.16% equals about -30 dB, and 10% equals -20 dB. The dB form is used in audio and RF work because it aligns with how noise floors and signal levels are expressed in those fields. For power quality work, the percentage form is standard.
Why is the 3rd harmonic particularly important in three-phase systems?
In a balanced three-phase system, odd-order harmonics that are multiples of three (the 3rd, 9th, 15th, etc.) are called triplen harmonics. They are in phase with each other across all three phases, so instead of canceling in the neutral conductor as the fundamental and most harmonics do, they add up. A high 3rd harmonic content can cause the neutral current to exceed the phase current, potentially overloading neutral conductors that were not sized for it. This is a common problem with office buildings full of computers and switch-mode power supplies.
What causes high harmonic distortion?
High THD is caused by non-linear loads - equipment that does not draw current proportionally to voltage. Common sources include variable frequency drives (VFDs), uninterruptible power supplies (UPS), computers and servers, LED lighting drivers, arc furnaces, and large rectifiers. In audio systems, the main causes are amplifier non-linearity, overdriving inputs or outputs, and crossover distortion in push-pull amplifier stages.
How do you reduce total harmonic distortion?
For power systems: passive harmonic filters (tuned LC circuits that trap specific harmonics), active harmonic filters that inject opposing harmonics, 12-pulse or 18-pulse transformer-rectifier configurations, and phase-shifting transformers. For audio systems: careful biasing of amplifier stages to minimize crossover distortion, negative feedback, higher idle current (Class A or AB bias), and better component matching. In both cases, moving to switching topologies with higher carrier frequencies (such as Class D audio amplifiers or modern power factor-corrected supplies) can push harmonics above audible or problematic ranges.
What is THD+N and how is it different from THD?
THD+N (total harmonic distortion plus noise) includes both harmonic distortion and broadband noise in a single figure. It is measured by applying a pure sine wave to the device under test, removing the fundamental with a notch filter, and measuring all remaining signal power - harmonics and noise together. THD alone only counts the discrete harmonic components. THD+N is the more common specification in audio equipment because it captures the combined effect of all imperfections. At low signal levels, noise dominates THD+N; at high signal levels, harmonic distortion dominates.