ConverterHub

Mel to Hertz Converter

Enter a value in mel to convert to hertz.

How it is calculated

The tool converts a pitch on the mel scale back to frequency with f = 700 × (10m/2595 − 1), where m is the pitch in mel and f is the frequency in hertz. This is the common O'Shaughnessy version of the mel scale. It is roughly linear below about 1000 Hz and logarithmic above, so equal steps in mel are small steps in hertz at low pitch and large steps at high pitch. A value of 0 mel gives 0 Hz, and negative mel values are rejected. Other published mel formulas exist (for example Slaney's), so numbers will not match software that uses a different variant exactly. The result is rounded to two decimals.

Worked example

Convert 2000 mel. Divide by 2595: 2000 ÷ 2595 = 0.7707. Raise 10 to that power: 100.7707 ≈ 5.8981. Subtract 1: 4.8981. Multiply by 700: 3,428.68 Hz. For comparison, 1000 mel gives 1,000.02 Hz, so doubling the mel value more than triples the frequency.

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Common mistakes

  • Using this tool for the opposite direction. It converts mel to hertz only; typing a frequency such as 1000 into the mel box returns a very large frequency, not 1000 mel.
  • Assuming mel and hertz are proportional. At 2000 mel the frequency is well over twice the 1000 mel frequency.
  • Mixing mel formula variants. A library that uses the Slaney formula or a different constant will give different values from this 2595 and 700 version.
  • Entering a negative mel value. The tool returns no result for it.
  • Confusing the mel scale with the musical note scale or cents; mel is a perceptual scale used in audio analysis, not a tuning system.

About this calculator

The mel scale is a perceptual pitch scale built so that equal distances in mel correspond to equal distances in perceived pitch, unlike hertz which is linear in physical frequency but not in how the ear hears it. The most common formula, from Douglas O'Shaughnessy, is f = 700·(10^(m/2595) − 1), which maps 1000 Hz to 1000 mel and compresses higher frequencies the way the human cochlea does.

Speech and audio engineers rely on mel-to-Hz conversion to build Mel-Frequency Cepstral Coefficients (MFCCs), the standard front-end features for speech recognition, speaker identification and music information retrieval, as well as to design mel-spectrogram inputs for machine learning models.

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