Harmonic Distortion Calculator

General THD-F formula: THD % = (√(H2² + H3² + H4² + ...) ÷ H1) × 100, where H1 is the fundamental RMS magnitude and H2, H3... are individual harmonic RMS magnitudes. A perfectly clean AC voltage or current waveform is a pure sine wave at the fundamental frequency (50 Hz or 60 Hz depending on region). Real-world non-linear loads distort this waveform, and that distortion can be mathematically decomposed into the fundamental frequency plus a series of harmonic components at whole-number multiples of it. Total Harmonic Distortion (THD) combines all these harmonic components into a single percentage describing overall waveform distortion.

Formula used by this calculator: because each harmonic you enter below is already expressed as a percentage of the fundamental (rather than a raw RMS magnitude), the general formula above simplifies to THD (%) = √(H3² + H5² + H7² + H9² + H11² + H13²), using only the 3rd through 13th harmonics. This is a root-sum-square combination, not a simple sum — harmonic components are effectively orthogonal sinusoids at different frequencies, so their contributions combine by root-sum-square rather than by direct arithmetic addition.

Worked example: a measurement shows 3rd harmonic at 25% of fundamental, 5th at 18%, 7th at 10%, 9th at 5%, 11th at 6%, and 13th at 4%. THD = √(25² + 18² + 10² + 5² + 6² + 4²) = √(625 + 324 + 100 + 25 + 36 + 16) = √1126 ≈ 33.56%. This is an illustrative high-distortion example mixing characteristic 6-pulse harmonics (5th, 7th, 11th, 13th) with non-characteristic components (3rd, 9th) — actual harmonic spectra vary by equipment type and system conditions.

Why the root-sum-square (not simple sum) combination: harmonics exist at different frequencies and generally don't align in phase with each other or with the fundamental in a way that would make direct addition meaningful — the root-sum-square method is the mathematically correct way to combine independent sinusoidal components based on their RMS (root-mean-square) contribution to total waveform distortion, analogous to how independent random errors combine in statistics, or how orthogonal vector components combine via the Pythagorean theorem.

Individual harmonic limits versus overall THD limits: standards like IEEE 519 typically specify limits both for overall THD and for individual harmonic magnitudes separately — a waveform can pass an overall THD limit while still exceeding an individual harmonic's specific limit, or vice versa, since THD is a combined figure that doesn't reveal which specific harmonics contribute most to the total. This is why a complete power quality assessment checks both the overall THD figure and each individual significant harmonic against its own specific limit, not just the single combined THD number this calculator produces.

THD-F versus THD-R: there are two closely related but technically distinct THD definitions in common use — THD-F (the formula used here) expresses harmonic content as a percentage of the fundamental component alone, while THD-R expresses it as a percentage of the total RMS value of the waveform (fundamental plus all harmonics combined). For waveforms with modest distortion, these two definitions give very similar numerical results, but they diverge more noticeably at very high distortion levels — always confirm which definition a specific meter, standard, or specification is actually using, since mixing the two without realizing it can introduce confusion when comparing figures from different sources.

Relationship between current THD and system loading: a facility's current THD, measured at its main incoming supply, isn't purely a function of its non-linear load's characteristics in isolation — it also depends on how much linear (non-distorting) load is present alongside the non-linear load, since linear load current adds to the fundamental without adding harmonic content, effectively diluting the overall current THD percentage. This is why a facility's measured current THD can change meaningfully throughout the day as its overall load mix shifts, even if its harmonic-producing equipment's own behavior remains constant — a useful thing to understand when interpreting THD measurements taken at different times or under different loading conditions.

Summary: use THD = √(H3²+H5²+H7²+...) combining harmonics by root-sum-square, distinguish voltage THD from current THD when checking against limits, remember dominant harmonics depend on the source's pulse number (5th/7th for 6-pulse, higher orders for 12-pulse and beyond), and check both overall THD and individual harmonic limits, not just the single combined figure, for a complete power quality assessment.

Harmonic mitigation options, briefly: passive tuned filters (an inductor-capacitor combination tuned to absorb a specific problem harmonic frequency) are a common, relatively economical mitigation for a known dominant harmonic. Active harmonic filters (power-electronic devices that actively inject a canceling current waveform in real time) offer more flexible, broader-spectrum mitigation but at higher cost, useful where harmonic content varies or spans multiple significant frequencies. Higher-pulse-number rectifier configurations (discussed above) address the problem at its source for large VFD or DC drive installations, avoiding certain harmonics entirely rather than filtering them out after the fact. The right mitigation approach depends on the specific harmonic profile, the criticality of achieving compliance, and budget — often determined through a dedicated harmonic study for facilities with significant non-linear load and a genuine compliance or equipment-protection concern.

Measuring harmonics in practice: a power quality meter or harmonic analyzer capable of capturing individual harmonic magnitudes (not just an overall THD summary reading) gives the most useful diagnostic data, since it reveals which specific harmonics dominate and therefore which mitigation approach (if any is needed) would be most effective. Many modern power quality meters display both individual harmonic spectra and calculated THD simultaneously, and some can log this data over time, which is valuable for capturing how harmonic content varies with load conditions throughout a typical operating day or production cycle, rather than relying on a single spot measurement that might not represent worst-case or typical conditions.

Whether you're troubleshooting equipment sensitive to power quality, evaluating whether a new large VFD installation might need mitigation, or verifying compliance with a utility or code requirement, starting from actual measured harmonic data (not assumed or generic figures) and applying the correct root-sum-square formula gives a defensible, accurate THD figure to work from — the foundation for any further mitigation or compliance decision.

1. Adding individual harmonic percentages directly instead of using root-sum-square. Harmonics don't combine by simple addition — using THD = H3+H5+H7+... instead of the correct √(H3²+H5²+H7²+...) formula significantly overstates actual THD.

2. Confusing voltage THD with current THD when checking against a limit. These measure different things and often have different applicable limits — comparing a measured current THD figure against a voltage THD limit (or vice versa) is comparing incompatible quantities.

3. Assuming a single universal THD limit applies everywhere. Applicable THD limits vary by standard, system voltage level, and specific measurement point (often relative to system short-circuit capacity for current THD specifically) — always check the specific limit applicable to your actual system and measurement point, not a generic remembered number.

4. Ignoring even harmonics or non-integer inter-harmonics from unusual load types. Most calculations (including the formula presented here) focus on the commonly dominant odd harmonics from typical rectifier-type loads — some loads (arc furnaces, certain unusual equipment) produce significant even harmonics or inter-harmonics that a standard odd-harmonic-only calculation would miss.

5. Adding power factor correction capacitors without checking for harmonic resonance risk. Capacitor banks can resonate with system inductance at specific frequencies, potentially amplifying an existing harmonic dramatically — a harmonic study before adding significant capacitance is prudent practice in facilities with meaningful non-linear load.

6. Not measuring enough individual harmonics to capture the true THD. Stopping the measurement/summation at a lower-order harmonic (say, only through the 7th) when significant higher-order harmonics (11th, 13th, and beyond) are actually present understates true THD — use a harmonic analyzer capturing a sufficiently wide range of harmonic orders for an accurate result.

7. Overlooking triplen harmonic buildup in the neutral conductor for facilities with substantial single-phase non-linear load. Unlike most other harmonics, 3rd/9th/15th harmonics from single-phase loads can add in the neutral rather than cancel, sometimes producing higher neutral current than phase current — standard THD calculation alone doesn't flag this specific, important neutral sizing consideration.

8. Confusing THD-F and THD-R without realizing they're different definitions. These give similar but not identical results, diverging more at high distortion levels — confirm which definition your specific meter or standard is using before directly comparing figures from different sources.