What Is Total Harmonic Distortion plus Noise (THD+N)?

In professional audio, many measurements are used to judge the quality of audio gear, but Total Harmonic Distortion plus Noise (THD+N) is arguably one of the most important and widely referenced. Whether it’s studio monitors, home Hi-Fi systems, or portable players, THD+N has a direct bearing on the purity of audio quality we perceive. This article offers a clear introduction to this crucial metric: starting from its definition and measurement, through to its real-world meaning and impact—showing how THD+N plays a decisive role in audio fidelity.

What Is THD+N?

THD+N (Total Harmonic Distortion plus Noise) quantifies the combined level of all harmonics and noise in the output signal—everything except the original (fundamental) tone—expressed as a ratio to the level of that fundamental. Lower THD+N values mean cleaner, purer sound¹². When discussing how “clean” an audio device sounds, we’re essentially referring to its THD+N.

Understanding Harmonic Distortion and Noise

THD measures only harmonic distortion. By contrast, THD+N covers both harmonics and all kinds of noise—thermal noise, quantization noise, power supply interference, and more. This matches more closely to what we actually hear²³. In theory, a perfect audio system would output an exact copy of its input, adding nothing and losing nothing. In reality, physical components always introduce some distortion (due to non-linearities) as well as various types of noise.

THD+N provides an objective measure of these unwanted additions, so we can directly compare how accurately different devices reproduce sound. The lower the THD+N, the less deviation from the source and the higher the audio fidelity.

THD+N vs. THD

While THD (Total Harmonic Distortion) focuses strictly on harmonic byproducts, THD+N is more comprehensive. Its measurement includes:

1. Harmonic distortion: Harmonics at multiples of the fundamental, caused by nonlinear behavior
2. Noise: Such as thermal, quantization, and power noise
3. Other distortion not strictly harmonic: Like intermodulation and crosstalk

As a result, THD+N figures are typically higher than pure THD. Most importantly, THD+N aligns better with real-world listening, since our ears perceive the combined impact of distortion and noise together.

Why Emphasize THD+N?

Historical perspective: Before fast digital analysis (like FFT) was available, measuring every individual harmonic was difficult. Instead, it was simpler to filter out the fundamental and measure everything left—making THD+N practical and reliable as a standard⁴. That’s why it became—and remains—the industry default.

From a listener’s perspective, we don’t consciously separate distortion from noise: we judge the total impression. As a single-number metric, THD+N captures this combined effect, making it invaluable from product design through quality control, especially as digital audio continues to evolve.

How Is THD+N Calculated and Expressed?

To correctly read datasheets or compare products, it’s vital to understand how THD+N is defined and measured. The same number may be expressed in ways that look different but mean the same thing—so knowing the conversions is key.

The Formula for THD+N

The mathematical definition of THD+N is⁵:

$$\text{THD+N} \% = 100 \times \frac{\sqrt{\sum V_i^2 + V_\text{noise}^2}}{V_\text{fundamental}}$$

Where:

• $V_i$ is the RMS voltage of each harmonic

• $V_\text{noise}$ is the RMS voltage of noise

• $V_\text{fundamental}$ is the RMS voltage of the original signal (the denominator uses just the fundamental, not the signal’s total power)

In systems where distortion is very low, this distinction makes almost no difference—but for accurate comparison, the denominator should always be the fundamental.

In practical measurement, engineers often filter out the fundamental and compare what’s left against the original, which is an efficient way to capture the combined impact of noise and all types of distortion.

Percentage and dB: How THD+N Is Shown

THD+N can be written as either a percentage or in decibels (dB)⁶⁷:

• Percentage: Shows directly what fraction of the output is unwanted content (e.g., 0.1%, 0.01%)
• dB: Puts this ratio on a log scale, typically a negative value (e.g., -60 dB, -80 dB)

Conversion:

$$\text{THD+N}(\text{dB}) = 20 \log_{10}\left(\frac{\text{THD+N}\%}{100}\right)$$

Some common examples:

• 1% THD+N = -40 dB
• 0.1% THD+N = -60 dB
• 0.01% THD+N = -80 dB

The dB scale is popular in the audio industry because it highlights tiny improvements when the numbers get very small.

Reference Conditions Matter

THD+N must be measured under consistent conditions⁸:

1. Signal: 1 kHz sine wave is standard
2. Signal level: 0 dBFS or +4 dBu
3. Bandwidth: 20 Hz to 20 kHz, unless otherwise stated
4. Filters: Some tests use A-weighting or low-pass filters (often 22 kHz)

Always check the bandwidth: most use the audible range (20 Hz–20 kHz), but sometimes higher bandwidth is specified to show the impact of ultrasonic frequencies.

What Causes Harmonic Distortion?

Harmonic distortion is a key part of THD+N, and understanding it sheds light on audio device design.

Linear vs. Nonlinear Distortion

Audio distortion falls into two main categories:

• Linear distortion: Alters the balance of frequencies or phases, but does not generate new frequencies. Examples: uneven frequency response, phase shift, group delay. Linear distortion may color the sound but doesn’t create harmonics.

• Nonlinear distortion: Produces harmonics—new frequency components at multiples of the original. Nonlinearities in amplifiers, DACs, transformer cores, etc., all create this kind of distortion. Feeding a pure 1 kHz tone through a nonlinear system causes 2 kHz, 3 kHz, and higher multiples to appear.

Harmonic Patterns and Listening Experience

The type of harmonics matters for how distortion sounds⁹:

• Even-order harmonics (2nd, 4th, etc.) tend to sound “warm” and “rich,” and in small amounts, may be pleasing to listeners.
• Odd-order harmonics (3rd, 5th, etc.) are often perceived as “harsh” or “gritty,” and high levels can sound very unpleasant—even if the overall THD+N seems low.

This explains why tube amplifiers, which often have higher THD+N but mostly even harmonics, can sound more musical¹⁰. Amplifiers where harmonic levels drop rapidly with each step (e.g., 2nd harmonic at -60 dB, 3rd at -70 dB, etc.) tend to sound more natural than those with strong higher-order harmonics.

Main Sources of Harmonic Distortion

Different types of audio equipment generate distortion in different ways:

• Power amplifiers: Nonlinear behavior in output transistors/tubes, especially at high power
• Preamplifiers: Lack of open-loop gain or feedback in op-amps
• DACs: Quantization errors, poor filtering, or nonlinearity in current/voltage (I/V) stages
• ADCs: Jitter, nonlinear input stages, and quantization noise
• Transformers/Inductors: Magnetic core saturation at high signal levels
• Loudspeakers: Mechanical irregularities, coil/magnet misalignment, cabinet coloration

Other forms like crossover and switching distortion, or compression artifacts, can contribute as well. Recognizing the sources helps designers target improvements in their products.

How Noise Contributes to THD+N

Along with distortion, noise is the other main ingredient in THD+N. Once harmonic distortion is reduced below roughly -100 dB, the measurement is often limited by the device's noise floor (including thermal, quantization, 1/f noise, etc.)⁵.

Types of Noise in Audio

Different noises affect the overall sound in different ways:

• White noise: Equal power at every frequency (“flat” spectrum), sourced from random electron motion (thermal noise) in resistors and semiconductors. It increases with temperature.
• Pink noise: Power decreases as frequency increases (“1/f” spectrum), meaning more energy at low frequencies. Common in electronics, and subjectively more audible.
• Quantization noise: Comes from the finite bit depth in digital systems; very low-level digital signals are especially affected.

How Noise Impacts THD+N

Because noise can be dominant, datasheets will often quote test conditions (such as “1 kHz, A-weighted, -60 dBFS”) to clarify whether the value is mostly from distortion or noise⁸. In high-end audio, once distortion is minimized, noise becomes the primary performance bottleneck.

Why Is THD+N Still Used?

Even though THD+N isn’t a perfect predictor of sound quality, it’s still standard in engineering practice⁴:

• It’s easy to use: A single number quickly characterizes linearity and cleanliness.
• It compares apples to apples: Analog and digital equipment, DACs, ADCs, and DSPs can all be evaluated the same way.
• It roughly tracks subjective listening: Lower THD+N almost always means cleaner, less fatiguing sound.

Frequently Asked Questions

Why is THD+N so important?

THD+N is the go-to measurement for assessing sound cleanliness in professional audio. It tells you, in one figure, how much a device alters the original signal through distortion or noise—a key for everything from studio work to home listening.

What’s the difference between THD+N and THD?

THD only covers harmonic distortion; THD+N adds all types of noise and other distortions. THD+N is broader and gives a more realistic picture of what you’ll actually hear.

How do you calculate THD+N?

Use this formula:
$$\text{THD+N} \% = 100 \times \frac{\sqrt{\sum V_i^2 + V_\text{noise}^2}}{V_\text{fundamental}}$$
where the reference is just the original (fundamental) component. Usually, the fundamental is filtered out and the ratio of what remains to the original is measured.

How is THD+N shown?

You’ll see it as a percentage or in decibels (dB). Percentage is straightforward; dB emphasizes small differences. Conversion:
$$\text{THD+N}(\text{dB}) = 20 \log_{10}\left(\frac{\text{THD+N}\%}{100}\right)$$

Where does harmonic distortion come from?

It comes from nonlinearities in audio circuits. These create extra tones at multiples of the original signal—especially in power amps, DACs, transformer cores—whenever circuit behavior is not perfectly linear.

What role does noise play in THD+N?

Noise becomes key once distortion is suppressed. Types of noise (white, pink, quantization, etc.) can dominate the total “unwanted signal” and set the practical lower limit for THD+N in high-performance audio.

Conclusion

Total Harmonic Distortion plus Noise (THD+N) is a core metric for judging audio performance, offering a practical snapshot of how faithfully equipment reproduces sound. Because it blends distortion and noise—just as listeners do—it’s one of the most reliable and meaningful ways to compare products.

From R&D to manufacturing and quality checks, THD+N is indispensable. As audio technology advances, truly understanding THD+N empowers smarter choices about what to buy or recommend. When comparing audio products in the future, let THD+N help you find the sound quality you deserve.

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