Total harmonic distortion is not one number. The same measurement on the same amplifier is quoted at least four different ways, and two of them differ by a factor that grows as the distortion rises. Before comparing any two THD figures, you have to know which definition produced each one, whether noise was included, and over what bandwidth. This calculator computes both published amplitude definitions side by side, converts to decibels, and adds THD+N and SINAD from a noise floor you supply, so the convention is never ambiguous.
The headline figure on this page is THD referred to the fundamental, sometimes written THD-F: the RMS sum of the harmonic amplitudes divided by the amplitude of the fundamental alone. The grid also shows THD referred to the total RMS, THD-R, which divides by the RMS of the whole signal including its harmonics. Arb Digital built the page to show both because most textbooks and most amplifier datasheets use THD-F, while many bench distortion meters that work by notching out the fundamental naturally report THD-R. At 1 per cent the two agree to four decimal places; at 50 per cent they are 50 and 44.7, and at high distortion the divergence is glaring.
What This Total Harmonic Distortion Calculator Does
You enter the fundamental amplitude and up to six harmonic amplitudes, either as linear levels or as dBc below the fundamental, plus the integrated noise floor and the bandwidth over which it was measured. The tool returns THD-F as a percentage, THD-R as a percentage, THD expressed in decibels relative to the carrier, THD+N as a percentage, and SINAD in decibels. It also breaks down which individual harmonic is contributing most of the total, which is usually more diagnostic than the aggregate.
What it does not do is measure anything. A meaningful THD figure comes from a distortion analyser or an FFT analyser driven by a source whose own residual distortion is well below the device under test, at a stated output level, into a stated load, at a stated frequency, over a stated bandwidth. This page is the arithmetic that turns a set of measured amplitudes into a comparable figure. If the amplitudes are wrong, or the analyser's own residual is not below the device, no arithmetic will rescue the number.
How to Use It
- Choose your amplitude entry mode. Linear if your analyser gave you volts or a raw FFT magnitude, dBc if it gave you each harmonic as a negative decibel value relative to the fundamental.
- Enter the fundamental. Use the RMS amplitude at the test frequency. In dBc mode this stays a linear reference and only the harmonic boxes are read as decibels.
- Enter the harmonics you actually resolved. Leave a box at zero if that harmonic is buried in the noise. Typing in the noise floor as though it were a harmonic is the most common way to inflate a THD figure.
- Enter the noise floor and bandwidth. The noise is the integrated RMS across the band with fundamental and harmonics excluded. The bandwidth is recorded because THD+N and SINAD are meaningless without it.
- Compare the two THD columns before quoting anything. If someone else's figure was produced on the other basis, the hero number and the first grid item tell you exactly how much of the difference is convention rather than performance.
The Formulas, and Which Convention Each One Is
Let V1 be the RMS amplitude of the fundamental and V2 to Vn the RMS amplitudes of the harmonics. Define the harmonic sum H = √(V22 + V32 + …). Then:
THD-F = H/V1, usually expressed as a percentage. This is the definition used in almost all analogue audio literature and on amplifier datasheets, and it is unbounded — a badly clipped signal can exceed 100 per cent.
THD-R = H/√(V12 + H2), the harmonic content as a fraction of the total signal RMS. This is what a classic notch-filter distortion analyser reads directly, because it measures everything left after the fundamental is removed and compares it with the unfiltered total. It can never exceed 100 per cent.
THD in decibels = 20 log10(H/V1). Here is a trap worth naming: because power is proportional to amplitude squared, the ratio of harmonic power to fundamental power is the square of the amplitude ratio, and 10 log10 of a power ratio equals 20 log10 of the corresponding amplitude ratio. The decibel figure is therefore the same either way — but a THD quoted as a power percentage is the square of the amplitude percentage, and 1 per cent amplitude distortion is 0.01 per cent in power terms. Datasheets essentially always mean the amplitude definition. Our decibel calculator covers the 10-log versus 20-log distinction in general, and it is the same error that appears in the signal to noise ratio calculator.
THD+N = √(H2 + N2)/√(V12 + H2 + N2), and SINAD = 20 log10 of the reciprocal of that ratio. THD+N is what the great majority of published audio specifications actually quote, because it is what a notch analyser measures without any FFT at all. The relationships are set out in the LibreTexts treatment of compliance and distortion, and the power-systems form of the same quantity is developed in MIT OpenCourseWare's Power Electronics course notes. In power engineering the current-distortion limits are set by IEEE Std 519, Standard for Harmonic Control in Electric Power Systems, which defines its own total demand distortion measure alongside THD.
Worked example, matching the defaults. With V1 = 1 and harmonics 0.02, 0.01, 0.005 and 0.002, the sum of squares is 0.000529, so H = 0.023 exactly. THD-F = 2.3 per cent. In decibels that is 20 log10(0.023) = −32.77 dBc. THD-R = 0.023/√1.000529 = 2.2994 per cent. With a noise floor of 0.001, THD+N = √0.00053/√1.000530 = 2.3016 per cent and SINAD = 32.76 dB. Every one of those was computed by hand before the code was written and the page reproduces them.
Which Harmonic Is Big Tells You More Than the Total
A single aggregate percentage throws away the most useful information in the measurement. The spectrum's shape points at the mechanism. Dominant second harmonic, with the even orders falling away quickly, is the signature of an asymmetric transfer curve — a single-ended stage, an unbalanced circuit, a device operating on one side of its characteristic. Dominant third harmonic with strong odd orders and little even content is symmetric compression: a differential or push-pull stage running into its limits, or soft clipping at both rails.
Higher-order harmonics that do not decay smoothly are the ones to worry about. A spectrum where the seventh and ninth sit close to the third indicates hard clipping or crossover distortion rather than gentle compression, and those upper orders are far more audible than their amplitude suggests because they fall outside the masking region of the fundamental. The bar chart on this page ranks each harmonic's contribution to the total for exactly this reason. A 0.5 per cent THD made almost entirely of second harmonic and a 0.5 per cent THD spread across the seventh to fifteenth are not the same result.
Why Level, Load and Frequency Belong in Every Quoted Figure
THD is not a property of a device. It is a property of a device at an operating point. Distortion in most amplifiers falls as level rises out of the noise, sits flat across a middle region, then climbs steeply approaching clipping, so a single number quoted without a level is unanchored. The load matters just as much: an output stage measured into a benign resistive load and the same stage into a reactive loudspeaker impedance can differ by an order of magnitude. Frequency matters because feedback loop gain falls with frequency, so distortion typically rises towards the top of the band.
Bandwidth is the one that gets quietly abused. A THD+N figure measured through a 22 kHz brick-wall filter and the same device measured to 80 kHz will differ, sometimes substantially, because the wider measurement integrates more noise and catches harmonics the narrower one discards. A published figure without a stated bandwidth cannot be compared with anything. If you are working on the noise side of the same problem, the noise figure calculator handles cascaded noise contributions and the RMS voltage calculator covers the RMS conversions underneath all of this.
Harmonic Distortion in Power Systems Is a Different Problem
The same arithmetic is used in electrical power engineering, but what it means there is not audibility — it is heating, losses and equipment stress. Non-linear loads such as rectifier front ends, variable-speed drives and switch-mode supplies draw current in pulses rather than sinusoids, and the resulting harmonic currents flow back into the supply. Triplen harmonics, the third and its multiples, add rather than cancel in the neutral of a three-phase four-wire system, which is why a neutral conductor can carry more current than any phase in an installation full of single-phase electronics.
Voltage and current distortion also behave differently. A high current THD on a small load may cause little voltage distortion because the source impedance is low, while the same current into a weak supply distorts the voltage for everything else on that bus. The power factor calculator is the neighbouring tool: distortion reduces true power factor even when voltage and current are perfectly in phase, which a simple cos φ reading cannot see.
Where This Page Stops
This is a calculator, not an analyser. It assumes your amplitudes are RMS values of genuine harmonics of a single-tone test, correctly identified and correctly measured. It cannot detect intermodulation distortion, which needs a two-tone test and reports difference and sum products rather than integer harmonics, and which often correlates better with perceived quality than THD does. It cannot see jitter-induced sidebands, aliasing products in a sampled system, or anything that is not an integer multiple of the fundamental.
It also cannot tell you whether a number is good. Audibility depends on harmonic order, programme material and masking, and no threshold percentage separates audible from inaudible in general. For loudspeaker crossovers the speaker crossover calculator is the neighbouring tool, and the harmonic series calculator shows where the harmonic frequencies fall musically.
Arb Digital builds technical calculators and reference pages for audio, electronics and manufacturing sites — the kind that earn links because the maths is correct and the assumptions are stated.
Browse the free tools Talk to Arb DigitalCommon Mistakes to Avoid
- Comparing THD-F with THD-R. They are different definitions. Below about 5 per cent the gap is negligible, but above that the total-RMS basis reads systematically lower, and at 50 per cent the two figures are 50 and 44.7.
- Quoting THD without level, load, frequency and bandwidth. Distortion is a property of an operating point, not of a device. A bare percentage is not comparable with anything.
- Including the noise floor in the harmonic boxes. If a harmonic is not resolved above the noise, enter zero. Typing the floor value in as a harmonic inflates the figure and hides what is really happening.
- Confusing THD with THD+N. Most published audio specifications are THD+N. A pure THD figure from an FFT will usually be lower on the same device, and the difference is your noise floor rather than better linearity.
- Treating a lower number as automatically better. Harmonic order and spectral shape affect audibility more than the aggregate. Half a per cent of second harmonic and half a per cent spread over the upper odd orders are very different results.
Related Free Tools From Arb Digital
For the decibel conversions that sit underneath every distortion figure, use the decibel calculator; for the general power-versus-voltage ratio definitions, the signal to noise ratio calculator; and for cascaded noise in a receiver chain, the noise figure calculator. On the electrical side the RMS voltage calculator converts between RMS, peak and average for common waveforms, the RMS to watts calculator handles amplifier power, the op amp gain calculator covers the feedback network that sets loop gain and therefore distortion, and the power factor calculator deals with the distortion component of true power factor. Browse the full free online tools hub for the rest.
Frequently Asked Questions
It is the ratio of the combined RMS amplitude of a signal's harmonics to a reference amplitude, expressed as a percentage or in decibels. The harmonics are integer multiples of the fundamental test frequency, and they exist because the device under test is not perfectly linear.
THD-F divides the harmonic RMS by the fundamental alone; THD-R divides it by the RMS of the whole signal including the harmonics. Below a few per cent they agree closely, but at 50 per cent THD-F they read 50 and 44.7 respectively, so the basis must always be stated.
THD counts only the harmonics. THD+N counts the harmonics plus all the noise in the measurement bandwidth, which is what a notch-filter analyser reads directly. Most published audio specifications are THD+N figures, and they are always equal to or higher than the pure THD on the same device.
Take twenty times the base-ten logarithm of the ratio. One per cent, a ratio of 0.01, is minus 40 dB; 0.1 per cent is minus 60 dB. Because power goes as amplitude squared, ten log of the power ratio gives the same decibel figure, but a THD quoted as a power percentage is the square of the amplitude percentage.
Because a wider bandwidth integrates more noise into a THD+N figure and captures higher harmonics that a narrower measurement discards. The same device measured to 22 kHz and to 80 kHz can give noticeably different numbers, so a figure without a bandwidth cannot be compared with another.
Strong odd-order harmonics with little even content usually indicate symmetric compression, such as a push-pull or differential stage approaching its limits. A dominant second harmonic with rapidly falling even orders points instead at an asymmetric transfer characteristic in a single-ended stage.
They are related but inverted. SINAD is the ratio of the total signal to everything that is not the fundamental, expressed in decibels, so a high SINAD corresponds to a low THD+N. On this page SINAD is computed as twenty log of the reciprocal of the THD+N ratio.
No. It converts amplitudes you already have into comparable figures. A real THD result requires a distortion or FFT analyser whose own residual distortion is well below the device under test, driven at a stated level and frequency into a stated load over a stated bandwidth.
This tool is provided for education and engineering estimation only. It performs published distortion arithmetic on amplitudes you enter and does not measure, verify or certify the performance of any equipment. Figures quoted for comparison or compliance should come from a calibrated distortion or FFT analyser under documented conditions, and harmonic limits in electrical installations are governed by the applicable power quality standards.
