Db Per Octave Calculator

The dB Per Octave Calculator helps users determine the rate of gain or attenuation over frequency changes in audio engineering, electronics, and signal processing.

An octave represents a doubling (or halving) of frequency, so this calculator is useful for:

• Audio equalization – Adjusting speaker and filter responses
• Loudspeaker design – Understanding high-frequency roll-off
• Filter slopes – Measuring attenuation in low-pass and high-pass filters
• Room acoustics and sound analysis – Evaluating how frequencies change across different environments

By using this tool, audio engineers, sound designers, and RF technicians can optimize frequency response and improve system performance.

Formula for Db Per Octave Calculator

The formula to calculate dB per octave is:

General Formula

dB per Octave = (dB Change) / (log2(Freq2 / Freq1))

Where:

• dB Change = Gain or loss in decibels between two frequencies
• Freq1, Freq2 = The two frequencies where measurements were taken
• log2 = Base-2 logarithm (since an octave represents a doubling of frequency)

Simplified Formula (for 1-Octave Differences)

Since an octave means the frequency doubles (Freq2 = 2 × Freq1), the equation simplifies to:

dB per Octave = dB Change / Number of Octaves

This means if a system experiences -6 dB attenuation over one octave, its slope is -6 dB per octave.

Reference Table – Common dB Per Octave Slopes

To make frequency response estimation easier, here is a reference table of common filter slopes and signal attenuation rates:

Filter Type	dB per Octave	Application
First-Order Filter	-6 dB/octave	Simple tone control, basic crossover design
Second-Order Filter	-12 dB/octave	Active crossovers, equalization circuits
Third-Order Filter	-18 dB/octave	Steeper filtering for precise frequency control
Fourth-Order Filter	-24 dB/octave	High-precision filtering in audio and RF circuits
Acoustic Attenuation	-3 dB/octave	Air absorption of high-frequency sounds

This table helps audio professionals and engineers understand how signals change per octave and how steep a filter or system response will be.

Example of Db Per Octave Calculator

1. Calculate dB Per Octave for a Sound System

A speaker system has a -12 dB loss between 500 Hz and 2000 Hz.

1. Find the number of octaves:
   Octaves = log2(2000 / 500)
   Octaves = log2(4) = 2 octaves
2. Apply the formula:
   dB per Octave = (-12 dB) / (2 octaves)
   dB per Octave = -6 dB per octave

This means the system attenuates by 6 dB for every frequency doubling.

2. Calculate dB Per Octave for a High-Pass Filter

A low-frequency signal drops by -18 dB between 250 Hz and 1000 Hz.

1. Find the number of octaves:
   Octaves = log2(1000 / 250)
   Octaves = log2(4) = 2 octaves
2. Apply the formula:
   dB per Octave = (-18 dB) / (2 octaves)
   dB per Octave = -9 dB per octave

This suggests the filter roll-off is steeper than a second-order filter (-12 dB/octave), making it closer to a third-order filter (-18 dB/octave).

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