Total Harmonic Distortion

THD = √(V₂²+V₃²+V₄²+V₅²) / V₁ × 100%

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Result
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Formula

THD = √(V₂² + V₃² + V₄² + V₅²) / V₁ × 100%

Description

Total harmonic distortion measures how much an amplifier, DAC, or other audio component adds unwanted harmonics to a pure sine wave input. It is calculated as the RSS (root sum of squares) of all harmonic amplitudes divided by the fundamental amplitude. Lower THD indicates a more linear, transparent device. THD below 0.1% is generally inaudible for music, while professional audio equipment targets THD below 0.01%. Even-order harmonics (2nd, 4th) sound more musical, while odd-order harmonics (3rd, 5th) sound harsher.

Variables

  • THD — Total harmonic distortion (ratio, displayed as %)
  • V₁ — Fundamental amplitude (V)
  • V₂ through V₅ — Harmonic amplitudes (V)

Practical Notes

THD+N (total harmonic distortion plus noise) is a more comprehensive metric used in audio specifications. Typical THD values: tube amplifiers 0.5-5% (dominated by 2nd harmonic), solid-state amplifiers 0.001-0.1%, high-end DACs < 0.001%. Class D amplifiers have improved dramatically and now achieve THD below 0.01% in many designs.

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