Total Harmonic Distortion (THD) Calculator for Voltage and Current
THD from the fundamental and up to six harmonics, the same distortion against the total RMS value (THD-R), the total RMS and the largest single harmonic.
Results
What this tool does
THD is the RMS of all the harmonics divided by the fundamental, so a clean sine is 0 % and a heavily distorted current can pass 100 %. Standards use the fundamental as the reference (IEEE 519, IEC 61000), while some analysers also show THD-R against the total RMS, which cannot exceed 100 %. Enter the harmonics in the same unit as the fundamental, as RMS values or percentages — the result is the same. Public-supply standards such as EN 50160 limit the voltage THD to 8 %; current distortion limits depend on the size of the installation.
Formula
THD = √(H₂² + H₃² + … + Hₙ²) ÷ H₁ × 100 · THD-R = √(H₂² + …) ÷ √(H₁² + H₂² + …) × 100 · total RMS = √(H₁² + H₂² + …)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
v1 | Fundamental (1st harmonic) | — |
h2 | 2nd harmonic | — |
h3 | 3rd harmonic | — |
h5 | 5th harmonic | — |
h7 | 7th harmonic | — |
h9 | 9th harmonic | — |
h11 | 11th harmonic | — |
TH | THD (relative to the fundamental) | % |
TR | THD-R (relative to the total RMS) | % |
TT | Total RMS value | — |
MX | Largest harmonic as a share of the fundamental | % |
Worked example
- Fundamental (1st harmonic)230
- 2nd harmonic2
- 3rd harmonic6
- 5th harmonic9
- 7th harmonic5
- 9th harmonic2
- 11th harmonic2
- THD (relative to the fundamental)5.40 %
- THD-R (relative to the total RMS)5.39 %
- Total RMS value230.335
- Largest harmonic as a share of the fundamental3.91 %
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.