Mathematics · Complex and Fourier
Total Harmonic Distortion Percentage Calculator
Calculate harmonic distortion percentage from root-sum-square harmonic amplitude and fundamental amplitude.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use c=100a/b with root-sum-square harmonic amplitude=0.08 and fundamental amplitude=1.6.
- harmonic distortion percentage=5.
Understand Total Harmonic Distortion Percentage
One idea, three depths
Choose how deeply to explain Total Harmonic Distortion Percentage
Total Harmonic Distortion Percentage: Calculate harmonic distortion percentage from root-sum-square harmonic amplitude and fundamental amplitude.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Total Harmonic Distortion Percentage to answer this question: calculate harmonic distortion percentage from root-sum-square harmonic amplitude and fundamental amplitude? Enter root-sum-square harmonic amplitude and fundamental amplitude; the calculator shows harmonic distortion percentage. For example: root-sum-square harmonic amplitude=0.08 and fundamental amplitude=1.6 produce harmonic distortion percentage=5. The answer tells you harmonic distortion percentage.
Age 15Explain it to a 15-year-oldConnect it to the formula
Amplitude total harmonic distortion compares the root-sum-square of selected harmonic amplitudes with the fundamental amplitude. This page evaluates the relationship directly. The rule is c=100a/b. Its input values are root-sum-square harmonic amplitude, fundamental amplitude, and the main result is harmonic distortion percentage. For example: root-sum-square harmonic amplitude=0.08 and fundamental amplitude=1.6 produce harmonic distortion percentage=5.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated total harmonic distortion percentage relation over the valid real-number domain stated below. The implemented relation is c=100a/b, evaluated from root-sum-square harmonic amplitude, fundamental amplitude to produce harmonic distortion percentage. Amplitude total harmonic distortion compares the root-sum-square of selected harmonic amplitudes with the fundamental amplitude. This page evaluates the relationship directly. State which harmonics and bandwidth are included, and do not include broadband noise unless using THD plus noise.
Inputs and valid domain
- root-sum-square harmonic amplitude must be a finite real number.
- fundamental amplitude must be a finite real number.
Important boundary: State which harmonics and bandwidth are included, and do not include broadband noise unless using THD plus noise.
The formula
c=100a/b
How the calculator works through it
It substitutes root-sum-square harmonic amplitude, fundamental amplitude into the formula and exposes every numerical step above. The main output is harmonic distortion percentage.
Read the result correctly
The harmonic distortion percentage is the direct answer to “calculate harmonic distortion percentage from root-sum-square harmonic amplitude and fundamental amplitude.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
root-sum-square harmonic amplitude=0.08 and fundamental amplitude=1.6 produce harmonic distortion percentage=5.
Where this model stops being reliable
State which harmonics and bandwidth are included, and do not include broadband noise unless using THD plus noise.
Learn it by changing one value
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Dictionary terms behind this calculator
Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.
These foundations help you understand why Total Harmonic Distortion Percentage works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Total Harmonic Distortion Percentage uses c=100a/b. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.
Review this foundation about 4 min
Strong support
- Complex numbers and components
Real and imaginary components provide the notation needed to interpret Total Harmonic Distortion Percentage correctly.
Review this foundation about 7 min
Optional enrichment
- Functions and periodic behaviour
A function viewpoint connects Total Harmonic Distortion Percentage to signals, periodicity and transformations.
Review this foundation about 6 min
Mathematics → algorithm → program
Implement this calculation in code
These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.
Algorithm
- Read root-sum-square harmonic amplitude, fundamental amplitude.
- Evaluate the principal relationship: c=100a/b.
- Return harmonic distortion percentage and check the domain conditions described above.
Python
from math import *
def harmonic_distortion_percentage_calculator(a, b) -> float:
return ((100.0 * a) / b)
assert abs(harmonic_distortion_percentage_calculator(0.08, 1.6) - 5) < 1e-6 * max(1.0, abs(5))
C
#include <assert.h>
#include <math.h>
double harmonic_distortion_percentage_calculator(double a, double b) {
return ((100.0 * a) / b);
}
int main(void) {
const double expected = 5;
const double actual = harmonic_distortion_percentage_calculator(0.08, 1.6);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double harmonic_distortion_percentage_calculator(double a, double b) {
return ((100.0 * a) / b);
}
int main() {
constexpr double expected = 5;
const double actual = harmonic_distortion_percentage_calculator(0.08, 1.6);
assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
Linux x86-64 assembly
x86-64 NASM · System V ABI · Linux · SSE2 with libm where required
; double harmonic_distortion_percentage_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global harmonic_distortion_percentage_calculator
section .text
harmonic_distortion_percentage_calculator:
push rbp
mov rbp, rsp
sub rsp, 48
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
mov rax, 0x4059000000000000
movq xmm0, rax
movsd [rbp-40], xmm0
movsd xmm0, [rbp-40]
mulsd xmm0, [rbp-8]
movsd [rbp-32], xmm0
movsd xmm0, [rbp-32]
divsd xmm0, [rbp-16]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = harmonic_distortion_percentage_calculator(a, b)
result = ((100.0 * a) / b);
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_] := ((100.0 * a) / b);
Continue in mathematical software
The downloaded file includes your current inputs and first calculated result. It is created locally.
Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.
Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS
These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.
APA 7
MW SysArc. (2026, July 21). Total Harmonic Distortion Percentage Calculator. MW SysArc Tools. https://math.mwsysarc.com/complex-fourier/harmonic-distortion-percentage-calculator
MLA 9
MW SysArc. “Total Harmonic Distortion Percentage Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/complex-fourier/harmonic-distortion-percentage-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Total Harmonic Distortion Percentage Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/complex-fourier/harmonic-distortion-percentage-calculator.
Harvard
MW SysArc (2026) ‘Total Harmonic Distortion Percentage Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/complex-fourier/harmonic-distortion-percentage-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_harmonic_distortion_percentage_calculator_2026,
author = {{MW SysArc}},
title = {Total Harmonic Distortion Percentage Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/complex-fourier/harmonic-distortion-percentage-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Total Harmonic Distortion Percentage Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/complex-fourier/harmonic-distortion-percentage-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Total Harmonic Distortion Percentage do?
Calculate harmonic distortion percentage from root-sum-square harmonic amplitude and fundamental amplitude.
How does the Total Harmonic Distortion Percentage work?
The calculator applies c=100a/b. Amplitude total harmonic distortion compares the root-sum-square of selected harmonic amplitudes with the fundamental amplitude. This page evaluates the relationship directly.
What can I learn from the Total Harmonic Distortion Percentage?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed . Calculations tested .