About Total Harmonic Distortion
Total Harmonic Distortion (THD) measures how much a periodic signal — a voltage, current, or audio waveform — deviates from a pure sine wave at its fundamental frequency. A perfectly clean 60 Hz sine wave has 0% THD. Real-world signals from switching power supplies, variable-frequency drives, LED dimmers, and nonlinear loads contain energy at multiples of the fundamental frequency (the 2nd, 3rd, 4th harmonics, and so on), and THD quantifies how much of that unwanted harmonic energy is present relative to the fundamental.
The formula
For a fundamental amplitude V1 and harmonic amplitudes V2, V3, V4, ... Vn (at 2, 3, 4, ... n times the fundamental frequency), the standard definition is:
THD = √(V2² + V3² + V4² + ... + Vn²) / V1 × 100%
The numerator is the RMS (root-mean-square) magnitude of every harmonic combined; the denominator is just the fundamental. This calculator sums the 2nd through 5th harmonics as a practical illustration — a full instrument-grade measurement would include every harmonic the analyzer captures, added under the same square root.
Two common reference bases
There are two conventions for the denominator. Relative to fundamental (sometimes written THD-F) divides by V1 alone, as shown above — this is the most common convention in power engineering. Relative to total RMS (sometimes written THD-R) instead divides by the RMS of the entire waveform, √(V1² + harmonic RMS²), which is used in some audio and IEC contexts. The two values are nearly identical at low distortion and diverge as distortion grows, because the total-RMS denominator is always the larger of the two.
Reading the dominant harmonic
Beyond the single THD percentage, it is often useful to know which harmonic is doing the most damage. This calculator reports the largest of the entered harmonic amplitudes and the share of the total harmonic power (the sum of squares) that it represents. In power systems, a large 3rd harmonic often points to single-phase nonlinear loads; a large 5th or 7th harmonic is a common signature of variable-frequency drives and other six-pulse rectifier equipment.
Typical benchmarks
There is no single pass/fail THD number that applies everywhere. IEEE 519 is a widely cited power-quality standard that treats roughly 5% total voltage THD as a general guideline for many distribution systems, with tighter limits at higher voltage levels. Audio equipment typically targets much lower THD — often well under 1% — because the ear can detect distortion at levels that would be inconsequential on a power line. Always check the standard or specification that applies to your specific equipment or system.