What does THD+N mean in the THD + N formula?

THD+N is Total distortion + noise ratio (fraction).

THD + N

Q: How do you calculate THD + N?

Use the formula THD+N = √(Σharmonics² + Σnoise²) / V1. Total harmonic distortion plus noise combines all the harmonic distortion products and the broadband noise into a single fidelity figure, referenced to the fundamental. Enter the values you know in the calculator above and it solves for the remaining variable.

Q: What is the formula for THD + N?

The THD + N formula is THD+N = √(Σharmonics² + Σnoise²) / V1, where THD+N—Total distortion + noise ratio (fraction); Vharm—RMS sum of harmonic components (V); Vnoise—RMS noise (V); V1—Fundamental RMS amplitude (V).

THD+N = √(Vharm² + Vnoise²) / V1

Quick answer

This calculator solves THD+N = √(Σharmonics² + Σnoise²) / V1 for THD + N. With Harmonic RMS 0.6 V, Noise RMS 1.32 V, Fundamental RMS 12 V, the result is 12.08 %. It solves in 4 directions, so you can enter the values you have and get the one you need.

Calculator

Harmonic RMS

Noise RMS

Fundamental RMS

THD + N (%)

—

Formula

THD+N = √(Σharmonics² + Σnoise²) / V1

Description

Total harmonic distortion plus noise combines all the harmonic distortion products and the broadband noise into a single fidelity figure, referenced to the fundamental. It is the most common audio and signal-chain quality metric because it captures everything that is not the wanted signal. Over the full bandwidth, THD+N is equivalent to SINAD expressed as a ratio rather than in decibels.

Variables

THD+N — Total distortion + noise ratio (fraction)
Vharm — RMS sum of harmonic components (V)
Vnoise — RMS noise (V)
V1 — Fundamental RMS amplitude (V)

Practical Notes

In dB, THD+N = 20·log10(ratio) and SINAD = −THD+N(dB). A 0.001% THD+N (−100 dB) is excellent audio performance; measurement bandwidth strongly affects the noise term.

Symbols and units

Symbol	Meaning	Default unit	Accepted units
THDN	THD + N	%	—, %
Vharm	Harmonic RMS	mV	pV, nV, µV, mV, V, kV
Vnoise	Noise RMS	mV	pV, nV, µV, mV, V, kV
V1	Fundamental RMS	V	pV, nV, µV, mV, V, kV

Step by step

1. What you know: Harmonic RMS 0.6 V, Noise RMS 1.32 V, Fundamental RMS 12 V
2. The relation: THD+N = √(Σharmonics² + Σnoise²) / V1
3. Substitute: Vharm = 0.6 V, Vnoise = 1.32 V, V1 = 12 V
4. Result: THD + N = 12.08 %

Worked examples

Minimum range

Given: Harmonic RMS 10 mV, Noise RMS 22 mV, Fundamental RMS 0.33 V

Result: THD + N = 7.323 %

Low range

Given: Harmonic RMS 100 mV, Noise RMS 0.22 V, Fundamental RMS 3.3 V

Result: THD + N = 7.323 %

Typical

Given: Harmonic RMS 0.6 V, Noise RMS 1.32 V, Fundamental RMS 12 V

Result: THD + N = 12.08 %

High range

Given: Harmonic RMS 0.9 V, Noise RMS 1.98 V, Fundamental RMS 0.23 kV

Result: THD + N = 0.9456 %

Maximum range

Given: Harmonic RMS 9 V, Noise RMS 19.8 V, Fundamental RMS 2.3 kV

Result: THD + N = 0.9456 %

Solving for each variable

Solve for THD + N

Harmonic RMS 10 mV, Noise RMS 22 mV, Fundamental RMS 0.33 V → 7.323 %

Solve for Fundamental RMS

THD + N 0.5 %, Harmonic RMS 10 mV, Noise RMS 22 mV → 4.833 V

Solve for Harmonic RMS

THD + N 500 %, Noise RMS 22 V, Fundamental RMS 0.33 kV → 1.65 kV

Solve for Noise RMS

THD + N 500 %, Harmonic RMS 10 V, Fundamental RMS 0.33 kV → 1.65 kV

How THD + N changes with Harmonic RMS

Harmonic RMS (input)	THD + N (result)
60 mV	11.01 %
150 mV	11.07 %
0.3 V	11.28 %
0.45 V	11.62 %
0.6 V	12.08 %
0.9 V	13.31 %
1.2 V	14.87 %
2.4 V	22.83 %
4.2 V	36.69 %
6 V	51.2 %

The same result in other units

Unit	Value
%	0.1208
%	12.08

Embed this calculator

Paste this into any page. It keeps working when this page updates, and credits the source.

<iframe src="https://vbatpower.com/embed/thd-plus-noise/" width="100%" height="460" style="border:1px solid #1f2a37;border-radius:12px" loading="lazy" title="THD + N"></iframe>
<p><a href="https://vbatpower.com/formulas/thd-plus-noise/">THD + N</a> Calculator by vbatpower.com</p>

Frequently asked questions

How do you calculate THD + N?

Use THD+N = √(Σharmonics² + Σnoise²) / V1. With Harmonic RMS 0.6 V, Noise RMS 1.32 V, Fundamental RMS 12 V, THD + N works out to 12.08 %.

What is the formula for THD + N?

The formula is THD+N = √(Σharmonics² + Σnoise²) / V1. Total harmonic distortion plus noise combines all the harmonic distortion products and the broadband noise into a single fidelity figure, referenced to the fundamental.

How do you find Fundamental RMS when you know the other values?

Rearrange for Fundamental RMS: with THD + N 0.5 %, Harmonic RMS 10 mV, Noise RMS 22 mV, Fundamental RMS is 4.833 V.

How do you find Harmonic RMS when you know the other values?

Rearrange for Harmonic RMS: with THD + N 500 %, Noise RMS 22 V, Fundamental RMS 0.33 kV, Harmonic RMS is 1.65 kV.

What units does THD + N use?

THD + N is shown in %, %. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

Related Concepts

All Signal & dB formulas →

dB (Power) dB (Voltage) dBm to Watts dBV (Voltage Level) dBu (Voltage Level) dBm to dBW Conversion Receiver Noise Floor THD + N

Need more features?

Save calculations, import telemetry data, simulate battery discharge, and collaborate with your team.

Try the App