Harmonic Distortion (THD) Calculator
Calculate Total Harmonic Distortion from a fundamental amplitude and any number of harmonic amplitudes. Reports both THD-F (relative to the fundamental) and THD-R (relative to total RMS), plus each harmonic's individual contribution.
Input
RMS (or peak — just be consistent with the harmonics below) amplitude of the fundamental.
Amplitudes of the 2nd, 3rd, 4th… harmonics in order, same unit as the fundamental.
Output
| Harmonic | Amplitude | % of Fundamental |
|---|---|---|
| No data yet | ||
| Quantity | Value |
|---|---|
| No data yet | |
Guides
Every non-sinusoidal waveform — a switching power supply, a VFD output, a clipped amplifier — can be broken into a fundamental sine wave plus a stack of harmonics riding on top. Total Harmonic Distortion (THD) is the standard way to express how much of that stack there is relative to the fundamental. This calculator takes a fundamental amplitude and any number of harmonic amplitudes and works out THD both ways engineers actually need it.
How to use it
- Enter the fundamental amplitude (V₁) — RMS or peak, just be consistent with the harmonics.
- Enter the harmonic amplitudes (h₂, h₃, h₄, …) in order, separated by commas, spaces, or newlines. List as many as you have measurements for — there's no fixed limit to 2nd through 9th.
You get a per-harmonic breakdown (each one's amplitude and its percentage of the fundamental) plus a summary with both THD figures.
THD-F vs THD-R
- THD-F —
√(Σhₙ²) ÷ V₁ × 100%— the harmonic RMS relative to the fundamental alone. This is the IEEE 519 definition and the one most instruments display by default. - THD-R —
√(Σhₙ²) ÷ √(V₁² + Σhₙ²) × 100%— relative to the total RMS of the whole waveform (fundamental + harmonics). This is the IEC definition.
The two track closely at low distortion and diverge as distortion rises — at 50% THD-F, THD-R is already several points lower, since the denominator itself is inflated by the harmonics being measured. Report the one your standard or instrument specifies; if in doubt, THD-F is the more common convention.
What counts as a "harmonic"?
An integer multiple of the fundamental frequency. If your fundamental is a 60 Hz line frequency, the 3rd harmonic is 180 Hz, the 5th is 300 Hz, and so on — the classic signature of nonlinear loads like rectifiers and switch-mode supplies is odd harmonics (3rd, 5th, 7th…) dominating.
Why does THD matter?
High THD on a power system means extra heating in transformers and motors, nuisance neutral currents on 3-phase systems (triplen harmonics add rather than cancel), and possible interference with sensitive equipment. Utilities and standards like IEEE 519 set THD limits at the point of connection.
Privacy
Everything is calculated in your browser. No values are sent to a server.
Related tools
For the PWM/switching-frequency side of a waveform, see the PWM Duty & Frequency Calculator. To convert amplitude ratios into decibels instead of percentages, use the Decibel Converter.
Use it from code
From 3 credits per callREST API
curl -X POST https://api.iotools.cloud/v1/tool/harmonic-distortion-thd-calculator \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"fundamental": "120",
"harmonics": "12, 8, 5, 3, 2"
}'Swap in your own key from your account. The tool's fields are the body — no wrapper.
Ask an AI agent
Use the IOTools `harmonic-distortion-thd-calculator` tool (Harmonic Distortion (THD) Calculator) on this input:
YOUR_INPUT_HEREPaste this at any agent connected to the IOTools MCP server, then add your input.