Octave Band Frequency Calculator Formula

Understand the math behind the octave band frequency calculator. Each variable explained with a worked example.

Use the Octave Band Frequency Calculator

Formulas Used

Lower Band Edge

f_lower = centre_freq / pow(2, 1 / (2 * band_fraction))

Upper Band Edge

f_upper = centre_freq * pow(2, 1 / (2 * band_fraction))

Bandwidth

bandwidth = centre_freq * pow(2, 1 / (2 * band_fraction)) - centre_freq / pow(2, 1 / (2 * band_fraction))

Variables

VariableDescriptionDefault
centre_freqCentre Frequency(Hz)1000
band_fractionFraction (1=octave, 3=third-octave)1

How It Works

Octave and Fractional-Octave Bands

Sound analysis often divides the spectrum into bands of constant percentage bandwidth.

Formulas

f_upper = f_c * 2^(1/(2N)) f_lower = f_c / 2^(1/(2N))

where N is the fraction denominator (1 for full octave, 3 for third-octave).

For a full octave band (N=1): f_upper/f_lower = 2 (one octave). For third-octave (N=3): the ratio is 2^(1/3) = 1.26.

Worked Example

1000 Hz full octave band.

centre_freq = 1000band_fraction = 1
  1. 01f_upper = 1000 * 2^(1/2) = 1000 * 1.4142 = 1414.2 Hz
  2. 02f_lower = 1000 / 2^(1/2) = 1000 / 1.4142 = 707.1 Hz
  3. 03Bandwidth = 1414.2 - 707.1 = 707.1 Hz

Ready to run the numbers?

Open Octave Band Frequency Calculator