# Total Harmonic Distortion Calculator

Created by Filip Derma
Reviewed by Bogna Szyk and Steven Wooding
Last updated: Nov 15, 2022

Total harmonic distortion calculator helps you switch between distortion attenuation in decibels to distortion factor (THD) as a percent value. The total harmonic distortion parameter is important because it directly influences sound accuracy.

In the article below, you will read about what is total harmonic distortion and the total harmonic distortion calculation.

## What is total harmonic distortion?

Total harmonic distortion (THD) is a parameter measuring the harmonic distortion present in a signal. It is defined as the ratio of the sum of the powers of all harmonic components to the power of fundamental frequency.

In audio systems, lower distortion means that the components (speakers, microphones, headphones, amplifiers) produce a more accurate reproduction of an audio recording. For example, if you check the signal to noise ratio calculator, you'll see how the background noise in a signal can affect the sound.

The THD factor compares input and output audio signals, with the difference in levels measured as a percentage. All you need to understand is that the percentage represents the harmonic distortion or deviation of the output signal – lower percentages are better. An output signal is a reproduction, not a perfect copy of the input, especially when multiple audio components are involved in the audio system.

## Why is total harmonic distortion important?

The accuracy of the sound is disturbed if the total harmonic distortion has increased over a certain point. The root of these disturbances are unwanted frequencies that occur in the output signal but are not present in the input. Simplifying – harmonic distortion is added to the original signal. For example, a THD of 0.1% means that 0.1 percent of an output signal is false and contains unwanted distortion.

In reality, it is hard for the human ear to perceive THD, especially when it is only a small part of a percent. If you can't consistently hear half a percent difference, there's a low probability that you will notice a THD rating of 0.01 percent.

Every signal processing component adds some level of distortion. Small differences in THD from one brand of a component to another can be significant and may define audio signal quality.

## Total harmonic distortion calculation

Nonlinear distortions are given as total harmonic distortion (distortion factor $k$) in percent or as distortion attenuation ($a_k$) in decibels (dB) – the dB calculator can tell you more about this unit and why we use it.

THD itself is defined as the ratio of the sum of the power of all harmonic components to the power of the fundamental frequency.

The distortion factor is always smaller than 1 or less than 100%; consequently, distortion attenuation has to be a negative dB value.

Distortion attenuation is given by:

$a_k = 20 \log{(k/100)},$

with the result in dB (input $k$ in percent).

The distortion factor THD is calculated by the equation:

$k = 10^{(a_k/20)} \cdot 100,$

with the result in percent (input $a_k$ is given in dB with a minus sign).

Also, if you would like to know how sound propagates in the air, check our distance attenuation calculator.

Filip Derma
Distortion attenuation
dB
Distortion factor (THD)
%
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