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
| THD | dB |
|---|---|
| 10% | −20 dB |
| 1% | −40 dB |
| 0.1% | −60 dB |
| 0.01% | −80 dB |
| 0.001% | −100 dB |
Inputs explained
| Field | What to enter |
|---|---|
| Calculate | Choose one: Attenuation in dB from THD in %, THD in % from attenuation in dB, THD from harmonic amplitudes |
| Total harmonic distortion (THD) | In % |
| Distortion attenuation | In 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
Formula
THD_F = √(V₂² + V₃² + … + Vₙ²) ÷ V₁ · THD_R = √(ΣVₙ²) ÷ √(V₁² + ΣVₙ²) · a (dB) = 20 log₁₀(THD) · THD (%) = 10^(a/20) × 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.
Frequently asked questions
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.