Harmonic Distortion (THD) Calculator

Enter the fundamental and harmonic RMS values to calculate THD%, total signal RMS, fundamental purity, and dominant harmonic contribution.

Created by Luis GonzalezLast updated: May 9, 2026

How to Use This Calculator

1
Enter the Fundamental RMS (V)
Input the RMS voltage or current of the base frequency component of your signal.
2
Specify 2nd Harmonic RMS (V)
Enter the RMS amplitude of the second harmonic (twice the fundamental frequency).
3
Input 3rd Harmonic RMS (V)
Provide the RMS amplitude of the third harmonic, which is often dominant in power systems.
4
Enter 5th Harmonic RMS (V)
Input the RMS amplitude of the fifth harmonic, commonly found in variable frequency drives.
5
Specify 7th Harmonic RMS (V)
Enter the RMS amplitude of the seventh harmonic, significant in six-pulse rectifier loads.
6
Review your results
The calculator will display the Total Harmonic Distortion (THD%), harmonic RMS sum, total signal RMS, and fundamental purity, along with an assessment of signal quality.

Example Calculation

An electrical engineer is analyzing a power signal with a 120 V RMS fundamental, and measured harmonics: 2nd at 2 V, 3rd at 5 V, 5th at 3 V, and 7th at 2 V.

Fundamental RMS (V)

120

2nd Harmonic RMS (V)

3rd Harmonic RMS (V)

5th Harmonic RMS (V)

7th Harmonic RMS (V)

Results

5.401%

Tips

Measure Harmonics Accurately

Use a true RMS meter or a spectrum analyzer to accurately measure the RMS voltage or current of each harmonic component. Inaccurate measurements of individual harmonics will lead to an incorrect THD calculation.

Identify Dominant Harmonics

Pay close attention to the dominant harmonics, typically the 3rd, 5th, and 7th in power systems. These often indicate specific types of non-linear loads, such as rectifiers or variable frequency drives, which require targeted mitigation strategies.

Consider Load Type

The type of electrical load heavily influences the harmonic content. Linear loads (e.g., resistive heaters) produce almost no harmonics, while non-linear loads (e.g., computers, LED lighting, motor drives) are major sources of harmonic distortion. Understanding the load helps predict and mitigate THD.

Analyzing Power Quality with the Total Harmonic Distortion (THD) Calculator

The Harmonic Distortion (THD) Calculator is a critical tool for electrical engineers, technicians, and facility managers to assess power quality. It quantifies the level of distortion in an AC waveform by calculating the Total Harmonic Distortion (THD%) from the fundamental and individual harmonic RMS components. Understanding THD is vital, as excessive distortion (above the IEEE 519-2022 recommended 5% limit for voltage THD) can lead to equipment overheating, reduced efficiency, and system reliability issues in modern electrical grids, which are increasingly burdened by non-linear loads in 2025.

Power Quality Analysis: Why THD Matters

Power quality analysis, particularly focusing on Total Harmonic Distortion (THD), is paramount in modern electrical systems. Non-linear loads, such as variable frequency drives, LED lighting, and switch-mode power supplies, draw current in non-sinusoidal patterns, creating harmonic frequencies that distort the pure sinusoidal waveform of the power supply. These distortions can lead to a cascade of problems: increased energy losses in transformers and motors, nuisance tripping of circuit breakers, communication interference, and premature aging of equipment. Monitoring and mitigating THD ensures efficient operation, extends equipment lifespan, and prevents costly downtime, making it a cornerstone of reliable electrical infrastructure management.

The THD Calculation for Power System Analysis

The Harmonic Distortion (THD) Calculator uses the root mean square (RMS) values of the fundamental frequency and its harmonics to determine the overall distortion. The formula for THD is defined as the ratio of the RMS sum of all harmonic components to the RMS value of the fundamental component, expressed as a percentage.

Calculate Sum of Squares of Harmonics: Square each harmonic RMS value (2nd, 3rd, 5th, 7th) and sum them.
Calculate Harmonic Sum (RMS): Take the square root of the Sum of Squares of Harmonics.
Calculate THD: Divide Harmonic Sum by Fundamental RMS, then multiply by 100.
Calculate Total Signal RMS: Take the square root of (Fundamental RMS squared + Sum of Squares of Harmonics).

sum sq = h2^2 + h3^2 + h5^2 + h7^2
harmonic sum = sqrt(sum sq)
thd = (harmonic sum / fundamental rms) × 100
total rms = sqrt(fundamental rms^2 + sum sq)

The sum sq variable is an intermediate step that represents the total harmonic power relative to a 1-ohm resistance.

💡 To calculate the effective voltage of a pure sinusoidal waveform, our RMS Voltage Calculator provides fundamental insights into AC power measurements.

Analyzing a Power Signal's Harmonic Distortion

Let's analyze a power signal with a 120 V RMS fundamental frequency. The measured harmonics are: 2nd at 2 V RMS, 3rd at 5 V RMS, 5th at 3 V RMS, and 7th at 2 V RMS.

Fundamental RMS: 120 V
2nd Harmonic RMS: 2 V
3rd Harmonic RMS: 5 V
5th Harmonic RMS: 3 V
7th Harmonic RMS: 2 V

The calculation proceeds:

Sum of Squares of Harmonics: 2^2 + 5^2 + 3^2 + 2^2 = 4 + 25 + 9 + 4 = 42
Harmonic Sum (RMS): sqrt(42) = 6.4807 V
THD: (6.4807 V / 120 V) × 100 = 5.40058%
Total Signal RMS: sqrt(120^2 + 42) = sqrt(14400 + 42) = sqrt(14442) = 120.175 V

The primary result, "Total Harmonic Distortion," is 5.401%.

💡 For a deeper understanding of how components interact in AC circuits, our RLC Series Circuit Calculator can help analyze impedance and resonance.

Industry Benchmarks for Total Harmonic Distortion

Total Harmonic Distortion (THD) is a critical metric with well-defined industry benchmarks, primarily set by the IEEE Standard 519-2022. For voltage THD at the point of common coupling (PCC) in low-voltage systems (below 1 kV), the recommended limit is typically 5%. This means the combined RMS value of all harmonics should not exceed 5% of the fundamental voltage. For current THD, limits are more complex, depending on the short-circuit current ratio and voltage level, but often range from 5% to 20% for different load types. In sensitive applications like medical facilities or data centers, even lower voltage THD limits (e.g., 3%) may be specified to ensure the reliable operation of critical equipment. Conversely, some non-linear loads, such as certain types of motor drives, might inherently produce higher current THD (e.g., up to 30%) but require careful filtering to keep voltage THD at the PCC within acceptable limits.

Frequently Asked Questions

What is Total Harmonic Distortion (THD) in electrical systems?

Total Harmonic Distortion (THD) is a measure of the harmonic content in an AC voltage or current waveform, expressed as a percentage of the fundamental component. It quantifies how much the waveform deviates from a pure sinusoid due to the presence of harmonics. High THD indicates poor power quality, which can lead to equipment overheating, increased energy losses, and system instability in electrical networks.

Why are odd harmonics (3rd, 5th, 7th) more common in power systems?

Odd harmonics (3rd, 5th, 7th) are more common in power systems because they are primarily generated by non-linear loads that draw current in short, sharp pulses rather than smoothly. Examples include rectifiers, variable frequency drives, and switching power supplies. Even harmonics are less common in balanced three-phase systems but can appear in single-phase systems or due to specific equipment malfunctions, such as transformer saturation.

What are the typical acceptable THD limits for power systems?

Typical acceptable THD limits for power systems vary by standard and application, but the IEEE Standard 519-2022, 'Recommended Practice and Requirements for Harmonic Control in Electric Power Systems,' is widely referenced. It generally recommends a maximum THD of 5% for voltage distortion at the point of common coupling in industrial systems, with lower limits (e.g., 3%) for sensitive applications or higher voltage levels, to ensure reliable operation and prevent equipment damage.