Total Harmonic Distortion (THD)

Enter a fundamental amplitude and harmonic amplitudes to compute THD (%) and THD (dB). Optional THD+N supported.

How to Use

  1. Enter the Fundamental amplitude (V1).
  2. Enter harmonic amplitudes (V2..Vn). Leave unused harmonics blank or 0.
  3. Enable THD+N to include a noise RMS term.
  4. Open Show Work for the exact formula and steps.
Inputs & Settings
All math is performed client-side. THD uses RMS magnitudes: THD = √(Σ Vn²) / V1.
Tip: Use RMS amplitudes (common for audio/analyzers).
This limits how many harmonic rows are active.
Harmonic
Amplitude
Notes
2nd (V2)
2× fundamental frequency
3rd (V3)
3× fundamental frequency
4th (V4)
4× fundamental frequency
5th (V5)
5× fundamental frequency
6th (V6)
6× fundamental frequency
7th (V7)
7× fundamental frequency
8th (V8)
8× fundamental frequency
9th (V9)
9× fundamental frequency
10th (V10)
10× fundamental frequency
11th (V11)
11× fundamental frequency
12th (V12)
12× fundamental frequency
13th (V13)
13× fundamental frequency
14th (V14)
14× fundamental frequency
15th (V15)
15× fundamental frequency
16th (V16)
16× fundamental frequency
17th (V17)
17× fundamental frequency
18th (V18)
18× fundamental frequency
19th (V19)
19× fundamental frequency
20th (V20)
20× fundamental frequency
Used only when THD+N is enabled. Leave 0 if unknown.
THD dB is reported as 20·log10(THD ratio).
Show Work (step-by-step)
—
Work is shown using base RMS units and ratios for clarity.

Reference

THD ratio: THD = √(V2² + V3² + … + Vn²) / V1

  • THD (%): THD% = THD × 100
  • THD (dB): THD_dB = 20·log10(THD)
  • THD+N ratio (optional): THD+N = √(V2²+…+Vn²+N²)/V1
Inputs should be RMS magnitudes at each harmonic (typical analyzer output).

FAQ

Do I need harmonics in RMS?

Yes. THD is typically defined using RMS magnitudes. If your tool reports peak values, convert to RMS first.

Why can THD (dB) be negative?

THD is a ratio less than 1 for most systems, so 20·log10(THD) is negative (lower is better).

What’s the difference between THD and THD+N?

THD uses harmonics only. THD+N includes broadband noise as an additional RMS term.

Tool Info

Last updated:

Updates may include more harmonic orders, additional unit modes, and edge-case handling.