Total Harmonic Distortion Calculator
Convert total harmonic distortion between a percent of the fundamental signal and the equivalent amplitude-ratio level in decibels.
Signal distortion inputs
Enter a negative decimal number from – 6000 up to, but not including, 0.
Enter a percentage greater than 0 and less than 100; type the number without the percent sign.
Edit either field. A valid change becomes the source value and the other field is converted immediately.
Live conversion
Distortion factor (THD)
1.0000%
Distortion attenuation
– 40.00 dB
1.0000% THD is equivalent to – 40.00 dB.
Enter either a valid attenuation or THD value to calculate the conversion.
How to use the Total Harmonic Distortion calculator
What this calculator does
This calculator converts one total harmonic distortion quantity between two equivalent representations: Distortion factor (THD) as a percentage and Distortion attenuation in decibels. The percentage expresses the RMS harmonic content relative to the fundamental component, while the decibel value expresses that same amplitude ratio on a logarithmic scale. The conversion does not measure a signal, identify which harmonics are present, include broadband noise, or determine whether a device meets a particular product or power-quality standard. For the underlying definition of THD as harmonic RMS content relative to the fundamental, see the IEEE overview of total harmonic distortion.
When to use it
Use this conversion when a data sheet reports distortion in dB but another specification uses percent THD; when comparing audio, converter, amplifier, or instrumentation specifications that express the same ratio differently; when translating a measurement result for a report; or when checking whether two published numbers are mathematically consistent. It is especially helpful because a small change in a negative dB figure can represent a large multiplicative change in distortion percentage.
How to calculate
- The calculator opens with a ready-to-use demonstration: – 40 dB and 1% THD. The matching XLSX workbook is validated during initialization, so Download Excel is available immediately.
- To start from a logarithmic specification, replace Distortion attenuation. To start from a percentage specification, replace Distortion factor (THD). The field edited most recently becomes the source and the other value updates live.
- Read the same conversion in Live conversion. The large THD result and dB result are exact transformations of one underlying amplitude ratio, rounded only for display.
- Select Download Excel to export the current validated model to a real Office Open XML workbook containing Summary, Inputs, and Notes sheets. Select Reset to clear the demonstration values, results, validation state, and workbook cache. After Reset, export is disabled until you enter one complete valid source value again.
Input guide
Distortion attenuation is a required source when calculating from dB. Enter a plain decimal number in dB, without typing the “dB” suffix. The accepted range is from – 6000 dB through values just below 0 dB. A realistic example is – 80 dB, which converts to 0.01% THD. Making attenuation more negative lowers the distortion ratio; moving it toward 0 raises the ratio toward 100%. Commas, scientific notation, unit text, 0 dB, and positive values are rejected rather than silently reinterpreted.
Distortion factor (THD) is a required source when calculating from percent. Enter a plain decimal number greater than 0 and less than 100; the percent symbol is already shown beside the field and should not be typed. A realistic example is 0.1, meaning 0.1% THD, which converts to – 60 dB. A larger percentage produces a less-negative dB value; a smaller percentage produces a more-negative dB value. Do not confuse 0.1% with the decimal fraction 0.1: in this field, typing 0.1 means one tenth of one percent, not ten percent.
Output guide
Distortion factor (THD) measures harmonic RMS amplitude relative to the fundamental and is shown as a percentage. Lower values represent less harmonic content relative to the fundamental; values approaching 100% represent harmonic RMS amplitude approaching the fundamental amplitude. Distortion attenuation is the logarithmic representation of that same ratio. It is negative throughout this calculator's valid range; a more-negative figure corresponds to lower THD. The header pills repeat these same two canonical outputs for quick scanning, not as separate calculations. Both outputs are exact mathematical conversions under the stated definition rather than recommendations about audibility or acceptable equipment performance.
Worked example
The startup example begins at – 40 dB. The calculator first converts that dB value to an amplitude ratio: 10( – 40/20) = 0.01. It then converts the ratio to percent by multiplying by 100, producing 1.0000% THD. Reversing the calculation gives 20 × log10(1/100) = – 40.00 dB. These are the values shown on first open and written to the startup workbook. Analog Devices explains how harmonic levels and combined THD are reported in percent, ppm, dB, and dBc in its guide to amplifier distortion specifications.
Learn more
THD is distinct from THD+N: the latter includes noise over a specified bandwidth as well as harmonic products. That distinction matters when comparing instruments or converter data sheets. The Analog Devices MT-053 tutorial on HD, THD, THD+N, IMD and related metrics discusses that measurement distinction and the root-sum-square treatment of harmonics.
Formula and interpretation
Let k be THD in percent and a be distortion attenuation in dB. The conversion used here is:
a = 20 × log10(k / 100) and k = 100 × 10^(a / 20)
The factor of 20 is used because the relationship is based on an amplitude ratio. The two displayed quantities are therefore not independent measurements; they are two ways of writing one ratio. A chart is omitted because plotting the same scalar twice in different units would imply a comparison that does not exist.