Total Harmonic Distortion (THD) Calculator

This calculator computes the Total Harmonic Distortion (THD) of a signal in audio and electric power systems and outputs a graph of the actual distorted waveform. THD quantifies the deviation of a signal's harmonic content from a pure signal by comparing the voltages of the signal's harmonic components to the voltage of the signal's fundamental frequency.
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CalculationInputs﻿﻿V1
:1.00V​
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﻿﻿V2
:0.50V​
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﻿﻿V3
:0.20V​
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﻿﻿f1
:50.00Hz​
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Output﻿﻿THD
:0.539​
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THD=V22+V32V1THD = \frac {\sqrt{V_{2} ^ 2 + V_{3} ^ 2}}{V_1} THD=V1​V22​+V32​​​
💡Note, the fundamental frequency is not an input to the THD equation, it is an input to the sinusoidal function for the signal waveforms. 
Output graphsThe waveform generated can either be from an audio signal or an electric power system, depending on the application. 
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ExplanationTotal Harmonic Distortion (THD) measures the deviation of a signal from its intended pure form due to harmonics, which are multiples of the fundamental frequency. Harmonics can originate from the signal's interaction with equipment or external noise, affecting signal quality. While a signal may possess an infinite number of harmonics, the first three are primarily analyzed because they significantly impact audio fidelity and power efficiency. The focus on these harmonics is practical, as higher-order harmonics have diminishing effects on overall signal quality.
THD is critical in assessing the purity of audio and electrical power signals, where a lower THD suggests a signal that closely resembles the original sound or intended electrical frequency, leading to improved audio reproduction and power system performance.
Typically, the THD value can be interpreted as:
THD < 1%, indicates minimal distortion, ideal for high-fidelity audio and critical power systems.
THD 1% to 5%, acceptable in many consumer audio and some industrial power applications, with possible noticeable distortion in high-quality settings.
THD > 5%, considered poor, with likely perceptible distortion affecting audio quality and causing inefficiencies in sensitive power systems.
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See the equations used in this calculator in the toggles below.
📝 Equation for THD
📝 Equation for the signal waveforms
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Discover more about the different parameters in the toggles below.
💡What is RMS voltage?
💡What is a harmonic?
💡What is a fundamental frequency?
💡What is a combined waveform?
Applications of THDWaveform analysis of THD is applied in the real-world, for example, to create an Active Harmonic Filter (AHF). An active filter setup demonstrating corrective action on a non-linear load is shown in the below image. The AHF produces a compensating current ﻿IF​
, which, when combined with the distorted load current ﻿IR​
, results in a 'clean' source current ﻿IX​
 with minimal Total Harmonic Distortion.
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An active filter setup demonstrating corrective action on a non-linear load. The harmonic spectrum of each current is illustrated.
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Additionally, the significance of THD includes:
Audio quality improvement, lower THD values mean that audio equipment such as loudspeakers, amplifiers, and microphones produce a sound that is more true to the original recording, with fewer unwanted harmonics.
Power system efficiency, in electric power systems a lower THD reduces peak currents, heating, emissions, and losses in motors, leading to improved operational efficiency and longevity of equipment.
Signal purity, THD provides a quantitative measure of signal purity, essential for applications requiring high fidelity and precision.
ReferencesDugan, R. C., McGranaghan, M. F., Santoso, S., & Beaty, H. W. (2012). Electrical Power Systems Quality (3rd ed.). McGraw-Hill Education.
Mehta, V. K., & Mehta, R. (2013). Principles of Power System (4th ed.). S. Chand.
Prandoni, P., & Vetterli, M. (2008). Signal Processing for Communications. CRC Press.
Zobaa, A. F., & Bansal, R. C. (Eds.). (2012). Power System Harmonics. John Wiley & Sons.
Related ResourcesOhm's Law To Calculate Voltage In a Circuit
Simple Harmonic Motion Calculator
Wire Voltage Drop Calculator to AS/NZS 3008
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