Harmonics Distortion (THD)

Enter a fundamental plus harmonic amplitudes to compute THD instantly. Includes spectrum view and Show Work.

How to Use

  1. Enter the fundamental amplitude and select units (V, mV, etc.).
  2. Fill in harmonic amplitudes (2nd, 3rd, 4th…); leave unused harmonics blank.
  3. Optional: add a noise value if you want a THD+N style result.
  4. Open Show Work to see the formula and intermediate sums.
  5. Use Share Link only when you’re ready (URL never auto-updates).
Spectrum View
Bars represent relative amplitude vs. fundamental. (Visualization only.)
THD
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THD+N
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Fund
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Σ Harm
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Quality: —
Amplitude (relative) Harmonic # 1 2 3 4 5 6 7 8 9 10 Tip: THD is based on RMS sum of harmonics divided by fundamental.
Inputs & Settings
Enter amplitudes in the same unit family. Blank harmonics are treated as 0.
Use RMS amplitude for best consistency.
Optional; used for labeling and spectrum context.
If provided, THD+N uses √(Σharm² + noise²) / fundamental.
Higher max includes more rows (added/hidden by JS).
Harmonics
Enter amplitude for each harmonic (same unit family as fundamental).
2 × f
3 × f
4 × f
5 × f
6 × f
7 × f
8 × f
9 × f
10 × f
Show Work (step-by-step)
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Work is shown in base units for clarity. THD definition used: THD = √(V2² + V3² + …) / V1.

Formulas

Total Harmonic Distortion (THD) is the ratio of the RMS sum of harmonic components to the RMS fundamental.

  • THD (ratio): THD = √(V₂² + V₃² + … + Vₙ²) / V₁
  • THD (%): THD% = THD × 100
  • Optional THD+N (ratio): THD+N = √(Σharm² + Vnoise²) / V₁
  • Optional dB: THD(dB) = 20·log10(THD)
Where V₁ is the fundamental amplitude, and V₂..Vₙ are harmonic amplitudes (same units).

FAQ

Do I enter peak or RMS amplitude?

Use RMS whenever possible. If you use peak, use peak for all entries consistently.

What harmonics should I include?

Include harmonics you have measured or care about. Audio often reports up to 10th (or higher). Power systems may focus on specific orders.

Why does THD sometimes look “good” but still sounds bad?

THD is a single number; it does not describe the distribution of distortion products. A small amount of higher-order harmonics can be more objectionable than larger low-order harmonics.

Is THD+N the same as THD?

No. THD+N adds broadband noise into the numerator. This tool can compute a THD+N style number if you provide a noise amplitude.

Tool Info

Last updated:

Updates may include UI improvements, harmonic row scaling, and edge-case handling.