# Total Harmonic Distortion Calculator (THD)

URL: https://speedycalculator.com/calculators/other/total-harmonic-distortion/
Last updated: 2026-10-30

> The total harmonic distortion calculator converts THD between percent and decibels in both directions and computes THD from the RMS amplitudes of the fundamental and its harmonics, giving THD_F, THD_R, the distortion attenuation in dB and the harmonic power share.

## Inputs

- Calculate
- Total harmonic distortion (THD) (%)
- Distortion attenuation (dB) — A negative value, e.g. −60 dB.
- Fundamental amplitude (RMS) — Any unit (V, mV, A) – use the same unit for the harmonics.
- Harmonic amplitudes (2nd, 3rd, 4th, …)

## Results

- Total harmonic distortion (THD_F)
- Distortion attenuation
- THD_R (relative to the total RMS)
- Harmonic power as a share of the fundamental
- Total RMS of the signal (fundamental + harmonics)
- Largest single harmonic

## Formula

```
THD_F = √(V₂² + V₃² + … + Vₙ²) ÷ V₁ · THD_R = √(ΣVₙ²) ÷ √(V₁² + ΣVₙ²) · a (dB) = 20 log₁₀(THD) · THD (%) = 10^(a/20) × 100
```

## Explanation

When an amplifier, power supply or converter is fed a pure sine wave, its output is never perfectly sinusoidal. Small nonlinearities add harmonics – components at two, three or more times the original frequency. Total harmonic distortion (THD) sums them up into one figure: the RMS of all harmonics relative to the fundamental. The lower the THD, the more faithful the reproduction.

THD is quoted either as a percentage or in decibels. A THD of 1% means the harmonics together have 1% of the fundamental's amplitude, which is −40 dB; 0.1% is −60 dB and 0.01% is −80 dB. Good hi-fi amplifiers reach 0.01% or better, while small loudspeakers often distort several percent at high volume. In power systems THD describes how much harmonic current non-linear loads inject into the grid, and standards such as IEEE 519 set limits around 5–8% for voltage.

Two definitions are in use: THD_F divides by the fundamental (the usual one in audio and power), while THD_R divides by the total RMS of the signal and can never exceed 100%. For small distortion they are almost identical. If you measured the individual harmonic levels with a spectrum analyser, enter them to compute THD directly.

### How to use the Total Harmonic Distortion Calculator

- **Calculate**
- **Total harmonic distortion (THD)**
- **Distortion attenuation** — A negative value, e.g. −60 dB.
- **Fundamental amplitude (RMS)** — Any unit (V, mV, A) – use the same unit for the harmonics.
- **Harmonic amplitudes (2nd, 3rd, 4th, …)**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose the conversion, enter THD in percent or the attenuation in dB, or the fundamental and harmonic amplitudes. The calculator converts with a = 20 log₁₀(THD) and, for measured harmonics, takes the square root of the sum of their squares divided by the fundamental.

### Worked example

A 1 V fundamental has harmonics of 0.05 V, 0.02 V and 0.01 V. THD_F = √(0.0025 + 0.0004 + 0.0001) ÷ 1 = √0.003 = **5.477%**, which is −25.23 dB. THD_R is 5.469%, and the harmonics carry 0.3% of the fundamental's power. An amplifier specified at 1% THD has a distortion attenuation of −40 dB.

### THD in percent and dB

THDdB10%−20 dB1%−40 dB0.1%−60 dB0.01%−80 dB0.001%−100 dB

### Inputs explained

FieldWhat to enterCalculateChoose one: Attenuation in dB from THD in %, THD in % from attenuation in dB, THD from harmonic amplitudesTotal harmonic distortion (THD)In %Distortion attenuationIn dB. A negative value, e.g. −60 dB.Fundamental amplitude (RMS)A number. Any unit (V, mV, A) – use the same unit for the harmonics.Harmonic amplitudes (2nd, 3rd, 4th, …)A list of numbers separated by commas, spaces or new lines

### What each result means

- **Total harmonic distortion (THD_F)** = [THD as a ratio]×100
- **Distortion attenuation** = 20×log10([THD as a ratio])
- **THD_R (relative to the total RMS)** = [THD as a ratio]÷sqrt(1 + [THD as a ratio]^2)×100
- **Harmonic power as a share of the fundamental** = [THD as a ratio]^2×100
- **Total RMS of the signal (fundamental + harmonics)** = sqrt([Fundamental amplitude (RMS)]^2 + ss([Harmonic amplitudes (2nd, 3rd, 4th, …)]))
- **Largest single harmonic** = max([Harmonic amplitudes (2nd, 3rd, 4th, …)])÷[Fundamental amplitude (RMS)]×100

## Worked example

Inputs — Calculate: Attenuation in dB from THD in %; Total harmonic distortion (THD): 1 %.

Results — **Total harmonic distortion (THD_F) = 1 %**; Distortion attenuation = -40 dB; THD_R (relative to the total RMS) = 0.99995 %; Harmonic power as a share of the fundamental = 0.01 %.

## Key terms

- **Fundamental**: The original frequency of the signal.
- **Harmonic**: A component at an integer multiple of the fundamental frequency.
- **THD_F**: Harmonic RMS divided by the fundamental RMS.
- **THD+N**: Total harmonic distortion plus noise.

## FAQ

**What is a good THD for an amplifier?**
Below 0.1% is good for hi-fi; high-end amplifiers reach 0.001–0.01%.

**How do I convert THD percent to dB?**
a = 20 log₁₀(THD ÷ 100): 1% = −40 dB, 0.1% = −60 dB, 0.01% = −80 dB.

**How do I convert dB to THD percent?**
THD = 10^(a ÷ 20) × 100: −50 dB = 0.316%.

**Can people hear 0.1% THD?**
Usually not on music; audibility depends on which harmonics they are – high-order harmonics are more objectionable than 2nd and 3rd.

**What is the difference between THD_F and THD_R?**
THD_F divides by the fundamental, THD_R by the total RMS; they differ noticeably only above about 10%.

**What is THD+N?**
THD plus noise: everything except the fundamental, measured with a notch filter, so it also includes hum and noise.


## Sources

- [Analog Devices – MT-003: Understand SINAD, ENOB, SNR, THD, THD + N, and SFDR](https://www.analog.com/media/en/training-seminars/tutorials/MT-003.pdf)
- [Total harmonic distortion – Wikipedia](https://en.wikipedia.org/wiki/Total_harmonic_distortion)