Harmonic Distortion Calculator

A harmonic distortion calculator determines the combined harmonic RMS and total harmonic distortion (THD) of a voltage or current waveform from its fundamental RMS value and selected harmonic RMS components.

The primary result, THD, expresses the RMS magnitude of the included harmonic content as a percentage of the fundamental. It is commonly used when reviewing nonlinear load effects on a branch circuit, feeder, transformer, generator, UPS, VFD system, or power-quality measurement. A high THD result does not by itself establish conductor ampacity, raceway fill, voltage drop, or equipment suitability; it identifies waveform distortion that may require a separate load, neutral-current, heating, and manufacturer-data review.

RMS Harmonic Components

The calculator uses these input fields:

Input field	Electrical meaning
Fundamental RMS	RMS magnitude of the waveform’s fundamental-frequency component
2nd harmonic RMS	RMS magnitude at twice the fundamental frequency
3rd harmonic RMS	RMS magnitude at three times the fundamental frequency
5th harmonic RMS	RMS magnitude at five times the fundamental frequency
7th harmonic RMS	RMS magnitude at seven times the fundamental frequency

Enter all values in the same RMS unit. For a current analysis, the entries may be amperes RMS. For a voltage analysis, they may be volts RMS. The calculator preserves the entered unit in the Combined harmonic RMS result, while the harmonic percentages and total harmonic distortion are dimensionless percentages.

A harmonic not included in the measurement or calculation should be entered as 0. The calculation only includes the four listed harmonic orders: 2nd, 3rd, 5th, and 7th.

Total Harmonic Distortion Formula

The calculator first combines the selected harmonic RMS values by root-sum-square:

\(\displaystyle I_{h,\text{combined}} = \sqrt{ I_2^2 + I_3^2 + I_5^2 + I_7^2 }\)

Where:

• \(I_2\) = 2nd harmonic RMS
• \(I_3\) = 3rd harmonic RMS
• \(I_5\) = 5th harmonic RMS
• \(I_7\) = 7th harmonic RMS

It then calculates total harmonic distortion:

\(\displaystyle \text{THD} = \left( \frac{I_{h,\text{combined}}}{I_1} \right) \times 100\)

Where \(I_1\) is the Fundamental RMS value.

Each listed harmonic percentage is calculated independently:

\(\displaystyle \text{Harmonic percentage} = \left( \frac{I_h}{I_1} \right) \times 100\)

The individual harmonic percentages do not add directly to THD. Harmonic RMS components combine by root-sum-square, not ordinary arithmetic addition.

Calculation Example

For the following current-waveform inputs:

Field	Entered value
Fundamental RMS	100 RMS
2nd harmonic RMS	10 RMS
3rd harmonic RMS	20 RMS
5th harmonic RMS	0 RMS
7th harmonic RMS	0 RMS

The combined harmonic RMS is:

\(\displaystyle \sqrt{10^2 + 20^2 + 0^2 + 0^2} = \sqrt{500} = 22.3607\ \text{RMS}\)

The resulting THD is:

\(\displaystyle \mathrm{THD} = \frac{22.3607}{100} \times 100\% = 22.3607\%\)

Result	Value
Combined harmonic RMS	22.3607 RMS
Total harmonic distortion	22.3607%
2nd harmonic	10%
3rd harmonic	20%
5th harmonic	0%
7th harmonic	0%

The 3rd harmonic is 20% of the fundamental, while the calculated total harmonic distortion is 22.3607%. The THD is greater than either individual component but less than the 30% that would result from directly adding 10% and 20%.

Harmonic Current in Electrical Distribution

Current THD is often evaluated where nonlinear loads reshape the normal sinusoidal current waveform. Common sources include electronic power supplies, LED drivers, data-processing equipment, rectifiers, variable frequency drives, UPS equipment, and other power-electronic loads.

The result can support a load review by identifying whether harmonic current is material enough to investigate:

• Neutral conductor loading, particularly from triplen harmonic content such as the 3rd harmonic in a 4-wire wye system
• Transformer, generator, UPS, and switchgear harmonic-current capability
• Additional conductor, termination, bus, and equipment heating
• Nuisance operation or reduced performance of protective devices and power-electronic equipment
• Voltage distortion caused by harmonic current flowing through the impedance of conductors, transformers, and the source

For a three-phase, four-wire system, 3rd-harmonic and other triplen currents can be in phase on each phase conductor and can add in the neutral rather than cancel. A low phase-load imbalance does not prove that the neutral current will be low when substantial nonlinear load is present.

Field Limits and Design Review

The calculation reports THD from the harmonic orders entered. It does not calculate total RMS current, neutral current, K-factor, transformer derating, conductor ampacity, voltage drop, fault current, or thermal loading.

A conductor-sizing or feeder-design decision requires the actual circuit configuration and applicable installation data, including conductor material, AWG or kcmil size, insulation temperature rating, terminal rating, ambient temperature, adjustment factor, correction factor, number of current-carrying conductors, load profile, and equipment listing instructions. Harmonic current can affect those decisions, but THD alone is not an ampacity value.

Use RMS values taken from a suitable power-quality meter, analyzer, or documented equipment data. Verify whether the measurement is current THD or voltage THD, confirm the measurement location, and confirm which harmonic orders the instrument includes. If harmonics above the 7th order are present, this worksheet’s result will represent only the entered 2nd, 3rd, 5th, and 7th components rather than complete waveform distortion. Final installation and equipment decisions remain subject to the applicable code requirements, manufacturer instructions, and AHJ acceptance.

Related calculations: Power Factor Calculator, Three-Phase Load Balance Calculator.