Total Harmonic Distortion
THD = √(V₂²+V₃²+V₄²+V₅²) / V₁ × 100%
Quick answer
This calculator solves THD = √(V₂² + V₃² + V₄² + V₅²) / V₁ × 100% for THD. With Fundamental (V₁) 12 V, 2nd Harmonic (V₂) 26.4 V, 3rd Harmonic (V₃) 56.4 V, 4th Harmonic (V₄) 5.64 V, 5th Harmonic (V₅) 120 V, the result is 1128 %.
Calculator
Formula
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 — Second harmonic amplitude (V)
- V₃ — Third harmonic amplitude (V)
- V₄ — Fourth harmonic amplitude (V)
- V₅ — Fifth harmonic amplitude (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.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| THD | THD | % | —, % |
| V1 | Fundamental (V₁) | V | pV, nV, µV, mV, V, kV |
| V2 | 2nd Harmonic (V₂) | V | pV, nV, µV, mV, V, kV |
| V3 | 3rd Harmonic (V₃) | V | pV, nV, µV, mV, V, kV |
| V4 | 4th Harmonic (V₄) | V | pV, nV, µV, mV, V, kV |
| V5 | 5th Harmonic (V₅) | V | pV, nV, µV, mV, V, kV |
Step by step
- 1. What you know: Fundamental (V₁) 12 V, 2nd Harmonic (V₂) 26.4 V, 3rd Harmonic (V₃) 56.4 V, 4th Harmonic (V₄) 5.64 V, 5th Harmonic (V₅) 120 V
- 2. The relation: THD = √(V₂² + V₃² + V₄² + V₅²) / V₁ × 100%
- 3. Substitute: V1 = 12 V, V2 = 26.4 V, V3 = 56.4 V, V4 = 5.64 V, V5 = 120 V
- 4. Result: THD = 1128 %
Worked examples
Minimum range
Given: Fundamental (V₁) 0.33 V, 2nd Harmonic (V₂) 0.726 V, 3rd Harmonic (V₃) 1.55 V, 4th Harmonic (V₄) 155 mV, 5th Harmonic (V₅) 3.3 V
Result: THD = 1127 %
Low range
Given: Fundamental (V₁) 3.3 V, 2nd Harmonic (V₂) 7.26 V, 3rd Harmonic (V₃) 15.5 V, 4th Harmonic (V₄) 1.55 V, 5th Harmonic (V₅) 33 V
Result: THD = 1127 %
Typical
Given: Fundamental (V₁) 12 V, 2nd Harmonic (V₂) 26.4 V, 3rd Harmonic (V₃) 56.4 V, 4th Harmonic (V₄) 5.64 V, 5th Harmonic (V₅) 120 V
Result: THD = 1128 %
High range
Given: Fundamental (V₁) 0.23 kV, 2nd Harmonic (V₂) 0.506 kV, 3rd Harmonic (V₃) 1.08 kV, 4th Harmonic (V₄) 108 V, 5th Harmonic (V₅) 2.3 kV
Result: THD = 1127 %
Maximum range
Given: Fundamental (V₁) 2.3 kV, 2nd Harmonic (V₂) 5.06 kV, 3rd Harmonic (V₃) 10.8 kV, 4th Harmonic (V₄) 1.08 kV, 5th Harmonic (V₅) 23 kV
Result: THD = 1127 %
How THD changes with Fundamental (V₁)
| Fundamental (V₁) (input) | THD (result) |
|---|---|
| 1.2 V | 11280 % |
| 3 V | 4510 % |
| 6 V | 2255 % |
| 9 V | 1503 % |
| 12 V | 1128 % |
| 18 V | 751.7 % |
| 24 V | 563.8 % |
| 48 V | 281.9 % |
| 84 V | 161.1 % |
| 120 V | 112.8 % |
The same result in other units
| Unit | Value |
|---|---|
| % | 11.28 |
| % | 1128 |
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<p><a href="https://vbatpower.com/formulas/thd/">Total Harmonic Distortion</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Total Harmonic Distortion?
Use THD = √(V₂² + V₃² + V₄² + V₅²) / V₁ × 100%. With Fundamental (V₁) 12 V, 2nd Harmonic (V₂) 26.4 V, 3rd Harmonic (V₃) 56.4 V, 4th Harmonic (V₄) 5.64 V, 5th Harmonic (V₅) 120 V, THD works out to 1128 %.
What is the formula for Total Harmonic Distortion?
The formula is THD = √(V₂² + V₃² + V₄² + V₅²) / V₁ × 100%. Total harmonic distortion measures how much an amplifier, DAC, or other audio component adds unwanted harmonics to a pure sine wave input.
What units does Total Harmonic Distortion use?
THD is shown in %, %. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
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