Hz to Bark Scale Converter (Critical Band)

One input, one number. Type a frequency in hertz and the page returns its position on the Bark scale using the analytic fit published by Zwicker and Terhardt in 1980: Bark = 13·arctan(0.00076·f) + 3.5·arctan((f/7500)²), both arctangents in radians. The default 1000 Hz comes out as 8.5105 Bark; 500 Hz gives 4.7365; 3 kHz gives 15.6024; 15.5 kHz gives 24.0123, which is exactly where the classic 24-band scale stops. There is no level input, no bandwidth output and no Bark-to-hertz direction. The figure recomputes on every keystroke, and that is the whole page.

The scale exists because hearing does not resolve the spectrum evenly. Zwicker's 1961 partition splits the audible range into 24 critical bands, each mapping to roughly 1.3 mm of basilar membrane, and one Bark equals the width of one band. Below about 500 Hz the bands stay near 100 Hz wide; above that the width scales with centre frequency. Zwicker's bandwidth expression, 25 + 75·(1 + 1.4·(f/1000)²)^0.69 hertz, puts the band at 1 kHz around 162 Hz and the band at 4 kHz at about 685 Hz. That is why masking models, perceptual codecs and speech front-ends bin energy on a Bark-spaced grid rather than a linear one: a step of one Bark carries roughly the same perceptual weight at 300 Hz as it does at 8 kHz.

Know where the fit drifts. Set against Traunmüller's 1990 expression, z = 26.81·f/(1960 + f) − 0.53, the two agree well through the middle of the range (8.511 versus 8.527 at 1 kHz) but split by more than 0.7 Bark at 13.5 kHz, and it is the Traunmüller expression that needs a correction below 200 Hz (0.77 against 1.00 Bark at 100 Hz), while the fit used here stays within 0.04 Bark down there and drifts more in the upper mid, around 0.2 Bark near 4.4 kHz and 12 kHz. Past 15.5 kHz this curve keeps climbing toward an asymptote of 25.92 Bark, a value that matches no critical band at all. Validation is absent too: feed it −1000 and it returns −8.3861 Bark without complaint, and an empty box reads as zero and prints 0 instead of a dash. Anything outside 20 Hz to 15.5 kHz should be treated as extrapolation, not measurement.