Total Harmonic Distortion (THD) Calculator
Quantify how much a waveform deviates from a pure sine wave. Enter the fundamental amplitude and up to four harmonic amplitudes (2nd through 5th) to get the THD percentage — used in audio, power electronics, and electrical power quality analysis.
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THD = √(V₂²+V₃²+V₄²+V₅²) / V₁ × 100
- 1
Sum of squared harmonics
5² + 3² + 2² + 1² = 39Square each harmonic amplitude and add them together. - 2
RMS of harmonics
√(39) = 6.245 - 3
Total Harmonic Distortion
6.245 ÷ 100 × 100 = 6.245
How does this calculator work?
THD (%) = √(V₂² + V₃² + V₄² + V₅²) ÷ V₁ × 100. Enter the fundamental amplitude and harmonic amplitudes (0 if absent). For example, V₁=100 V, V₂=5 V, V₃=3 V gives THD = √(25+9)/100 × 100 ≈ 5.83%. Acceptable levels: <5% for power grids, <0.1% for quality audio.
Formula
How this is calculated
Total Harmonic Distortion (THD) measures how much higher-frequency components (harmonics) distort a fundamental signal. A pure sine wave has zero harmonics and therefore zero THD. Real-world signals — from amplifiers, power supplies, variable-speed motor drives, and the grid itself — contain harmonics at integer multiples of the fundamental frequency (50 Hz or 60 Hz for power, or whatever the base frequency in audio and RF applications).
The standard definition is THD = √(sum of squared harmonic amplitudes) / fundamental amplitude × 100. This calculator covers the 2nd through 5th harmonic; many standards (IEC 61000, IEEE 519) define THD up to the 40th or 50th harmonic for power quality, but the 2nd–5th typically dominate. The units of V₁ through V₅ can be peak voltage, RMS voltage, or peak current — as long as all entries use the same unit, the percentage result is identical. A THD below 5% is generally acceptable for power grids; audio amplifiers aim for below 0.1%; USB chargers and LED drivers often fall between 10–30%.
The calculator also shows the total RMS (√(V₁² + harmonics²)) and the distortion factor V₁/total RMS — the ratio of the fundamental to the full waveform, which equals cos(φ) only for displacement power factor but gives the pure distortion reduction here.
Frequently asked questions
It depends on the application. IEEE 519 requires grid THD below 5% at the point of common coupling. Audio amplifiers are often rated at 0.001–0.1% THD+N. Switch-mode power supplies in consumer electronics might run 10–30%. Higher THD means more wasted energy as heat and potential interference with equipment.
Non-linear loads — devices whose current draw is not proportional to voltage — generate harmonics. Common culprits include rectifiers, variable-frequency drives, switching power supplies, LED drivers, and fluorescent ballasts. Even saturated transformers and arcing equipment contribute.
Yes. THD (%) is a ratio, so you can enter peak or RMS voltage or current values — as long as all five entries use the same unit, the percentage result is the same. Current THD (THDᵢ) is often the more important figure for grid power quality analysis.
Also known as
TG we-Calculate Editorial Team. (2026). Total Harmonic Distortion (THD) Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/total-harmonic-distortion-calculator
TG we-Calculate Editorial Team. "Total Harmonic Distortion (THD) Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/total-harmonic-distortion-calculator.
TG we-Calculate Editorial Team, "Total Harmonic Distortion (THD) Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/total-harmonic-distortion-calculator
@misc{wecalculate_total_harmonic_distortion_calculator, title = {Total Harmonic Distortion (THD) Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/total-harmonic-distortion-calculator}}, year = {2026}, note = {TG we-Calculate} }
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