Total Harmonic Distortion Calculator - THD Percent, THD+R, and dB Attenuation

A total harmonic distortion calculator reads a list of harmonic RMS amplitudes V1, V2, V3, ... and returns the standard distortion factors THD_F (fundamental-referenced) and THD_R (RMS-referenced) in percent, plus the distortion attenuation a_k in decibels.

• • Quantify amplifier distortion from a harmonic list: Type V1..V6 from a bench analyzer FFT and read THD percent alongside the dB attenuation.
• • Confirm the textbook values for square, sawtooth, and triangle waves: Check that a square wave reads THD_F = 48.3 %, a sawtooth reads 80.3 %, and a triangle reads 12.1 %.
• • Convert between distortion factor k and attenuation a_k: Move between percent and dB columns to convert k = 1 % to a_k = -40 dB, or a_k = -20 dB to k = 10 %.
• • Check a power-quality reading against IEEE 519 limits: Compare a measured THD percent against the IEEE Std 519-2022 limits the calculator surfaces.

This total harmonic distortion calculator is the standard single-number summary of how much a non-linear device (an amplifier, an inverter, a power supply) has reshaped a clean sine wave. In audio it appears as the THD percent on a datasheet; in power systems it is the same ratio on a 50 or 60 Hz mains waveform, where lower THD means less heating and less electromagnetic emission.

The 1/n coefficient on each harmonic amplitude V_n is the same 1/n pattern the Harmonic Series Calculator sums across the first n reciprocals of the harmonic series.

The calculator squares each entered harmonic amplitude, sums those squares, takes the square root to get the harmonic RMS, and divides by the fundamental V1. The percent result is the fundamental-referenced distortion factor THD_F; the dB result is twenty times the log10 of THD_F. A second branch on the same form converts between percent and dB.

• V1: RMS amplitude of the fundamental. Must be greater than zero; the form rejects V1 <= 0.
• V2 .. V6: RMS amplitudes of the second through sixth harmonics in the same unit as V1.
• harmonicRms: Square root of the sum of squared harmonic amplitudes; the THD_F numerator.
• THD_F: Fundamental-referenced distortion factor (as a fraction, multiplied by 100 in the result panel).
• THD_R: RMS-referenced factor, equal to THD_F / sqrt(1 + THD_F^2). Never exceeds 100 %.
• a_k: Distortion attenuation in dB, equal to 20 log10(THD_F). Clamped to -120 dB when THD_F = 0.
• k: Distortion factor as a percentage. Forward: a_k = 20 log10(k / 100); inverse: k = 10^(a_k/20) * 100.

The forward and inverse branches use the same 20 log10(k / 100) identity that audio analyzer front panels implement in firmware, so this total harmonic distortion calculator reads back exactly the numbers a bench instrument would.

Closed-form references: square wave THD_F = sqrt(pi^2/8 - 1), sawtooth THD_F = sqrt(pi^2/6 - 1), triangle THD_F = sqrt(pi^4/96 - 1).

According to Wikipedia (Total harmonic distortion), total harmonic distortion is defined as THD_F = sqrt(V2^2 + V3^2 + V4^2 + ...) / V1 and THD_R = THD_F / sqrt(1 + THD_F^2), and a pure square wave reads THD_F = 48.3 % and THD_R = 43.5 %

For broader power and voltage dB arithmetic, Decibel Calculator handles 10 log10 and 20 log10 conversions across any input and reference pair.

Four ideas are enough to interpret every number on the result panel.

The harmonic RMS sum is the raw ingredient; THD_F and THD_R are two normalizations of it; the dB attenuation is the logarithmic version of THD_F. The same squared-and-summed structure is what THD+N (total harmonic distortion plus noise) builds on.

For matching and reflection analysis that pairs with a low-distortion transmission line, Cable Impedance Calculator returns characteristic impedance Z0 alongside capacitance and delay for any coax or twisted-pair cross-section.

Five short steps cover both the harmonics-to-THD analysis and the percent / dB converter workflow.

1. 1 Enter the fundamental RMS amplitude V1: Type V1 in volts (or the same RMS unit). The form rejects V1 = 0 or negative inputs.
2. 2 Enter up to five harmonic amplitudes V2..V6: Use the second through sixth harmonic rows. Leave unused rows at 0; only non-zero rows contribute to the harmonic RMS sum.
3. 3 Read THD_F, THD_R, and the dB attenuation: The top three result rows print THD percent, THD+R percent, and the dB attenuation. Compare THD_F to your amplifier datasheet spec or the IEEE Std 519-2022 limit.
4. 4 Use the percent <-> dB converter for spec translation: Type a percent value and read the dB row, or a dB value and read the percent row.
5. 5 Cross-check the closed-form values for square, sawtooth, and triangle: Set V1 = 1 and enter the textbook odd-harmonic series (1/3, 1/5, 1/7, 1/9, ...) for a square wave. THD_F converges toward 48.3 % as more odd harmonics are added.

To check an amplifier datasheet's 0.01 % THD spec at the bench, type V1 = 1, V2 = 0.0001, V3..V6 = 0 and read THD_F = 0.01 %, a_k = -80 dB.

The nth term of the harmonic series that drives the V_n coefficients of a square or sawtooth wave is the 1/n value Harmonic Number Calculator returns as the partial-sum H_n term index.

The calculator replaces the manual square-root-and-divide step that a harmonic list would otherwise require.

• • Two THD definitions in one panel: Both THD_F and THD_R print side by side, so the same reading covers an audio datasheet and an IEC power-quality spec.
• • Direct percent <-> dB conversion: The bottom two rows convert k = 1 % to a_k = -40 dB and back.
• • Five harmonic slots cover the audio band: Up to five harmonic rows model the dominant harmonics in a typical audio amplifier, where the second and third harmonic usually carry 90 % of the distortion energy.
• • Domain error for zero or negative V1: If the fundamental amplitude is missing, the calculator returns a domain error instead of dividing by zero.
• • Pairs with the Decibel Calculator: For power, voltage, or current dB arithmetic, the Decibel Calculator in Math & Conversion handles 10 log10 and 20 log10 conversions with the same convention.

For the dB-to-percent conversion, the inverse branch uses the standard k = 10^(a_k/20) * 100 identity, matching the readings from audio analyzer front panels in firmware.

Once THD is in hand, the dBm, dBu, and dBV readings on the same datasheet are the unit conversions RF Unit Converter handles.

Three things decide the result, plus two caveats about how THD behaves at boundaries.

• • The calculator accepts up to five harmonic amplitudes (V2..V6). Real-world signals often contain significant energy above the sixth harmonic, so the partial-sum reading underestimates the true THD.
• • THD+N (total harmonic distortion plus noise) is not the same as THD. THD+N adds a noise term before dividing by the fundamental; this calculator reads the pure harmonic THD only.

When you scale the harmonics by a constant, the harmonic RMS sum scales by the same constant, THD_F scales by it, and the dB attenuation shifts by 20 log10 of the constant. This linearity lets you scale an existing harmonic list without re-running the FFT.

According to Wikipedia (Signal-to-noise ratio), SNR_dB = 10 log10(P_signal / P_noise) for power ratios and 20 log10(A_signal / A_noise) for amplitude ratios, and SINAD is the reciprocal of THD+N over the same bandwidth.

According to Omni Calculator (Total Harmonic Distortion), distortion attenuation a_k in decibels is given by a_k = 20 log10(k/100) with k as a percentage, and the inverse is k = 10^(a_k/20) * 100.

The propagation delay and rise-time numbers that drive the THD+N of a long cable sit alongside the bit-rate and frame analysis the Baud Rate Calculator returns.