Harmonic Distortion Calculator Formula
Understand the math behind the harmonic distortion calculator. Each variable explained with a worked example.
Formulas Used
Total Harmonic Distortion
thd = rss_harmonics / fundamental * 100True RMS Value
rms_total = sqrt(pow(fundamental, 2) + pow(harmonic_3, 2) + pow(harmonic_5, 2) + pow(harmonic_7, 2))Variables
| Variable | Description | Default |
|---|---|---|
fundamental | Fundamental Component (V1 or I1)(V or A) | 230 |
harmonic_3 | 3rd Harmonic(V or A) | 15 |
harmonic_5 | 5th Harmonic(V or A) | 12 |
harmonic_7 | 7th Harmonic(V or A) | 8 |
rss_harmonics | Derived value= sqrt(pow(harmonic_3, 2) + pow(harmonic_5, 2) + pow(harmonic_7, 2)) | calculated |
How It Works
Total Harmonic Distortion (THD)
THD quantifies how much the waveform deviates from a pure sinusoid.
Formula
THD = sqrt(V3^2 + V5^2 + V7^2 + ...) / V1 x 100%
where V1 is the fundamental component and V3, V5, V7 are harmonic magnitudes. IEEE 519 recommends voltage THD below 5% at the point of common coupling for general systems.
Worked Example
A 230V supply with 15V 3rd harmonic, 12V 5th, and 8V 7th.
fundamental = 230harmonic_3 = 15harmonic_5 = 12harmonic_7 = 8
- 01RSS harmonics = sqrt(225 + 144 + 64) = sqrt(433) = 20.81
- 02THD = 20.81 / 230 x 100 = 9.05%
- 03This exceeds the 5% IEEE 519 limit; mitigation is needed.
Ready to run the numbers?
Open Harmonic Distortion Calculator