Octave Bandwidth Calculator

Overview

Given a low and high corner frequency, computes the bandwidth, number of octaves and decades, center frequencies, and quality factor of the band.

Formulas

Center Frequencies

f_c (arithmetic) = (f_high - f_low) / 2
f_c (geometric)  = √(f_low × f_high)

Bandwidth

BW = f_high - f_low

Octaves and Decades

Octaves = log₂(f_high / f_low)
Decades = log₁₀(f_high / f_low)

Quality Factor

Q = f_c (arithmetic) / BW

Input Parameters

Parameter	Range	Default	Description
f_low	1 – 10¹²	1000	Lower corner frequency
f_high	1 – 10¹²	2000	Upper corner frequency

Both frequencies must share the same unit (Hz, kHz, MHz, etc.). The calculator does not perform unit conversion — the outputs inherit whatever unit the inputs use.

Output

Parameter	Description
Central freq (Arithmetic mean)	Midpoint of the band
Central freq (Geometric mean)	Log-scale midpoint; preferred for RF
BW	Linear bandwidth
# Octaves	Number of frequency doublings in the band
# Decades	Number of frequency ×10 steps in the band
Q	Quality factor of the band

An error is displayed if f_high ≤ f_low. Q is shown as ∞ when BW is effectively zero.

Example

Input:

• f_low: 1000 MHz

• f_high: 4000 MHz

Calculation:

f_c (arithmetic) = (4000 - 1000) / 2        = 1500 MHz
f_c (geometric)  = √(1000 × 4000)           = 2000 MHz
BW               = 4000 - 1000              = 3000 MHz
Octaves          = log₂(4000 / 1000)        = log₂(4) = 2.0
Decades          = log₁₀(4000 / 1000)       = log₁₀(4) ≈ 0.6
Q                = 1500 / 3000              = 0.5

Output:

Parameter	Value
Central freq (Arithmetic mean)	1500.0
Central freq (Geometric mean)	2000.0
BW	3000.0
# Octaves	2.0
# Decades	0.6
Q	0.5

Notes

• Exactly 1 octave corresponds to a 2:1 frequency ratio; 1 decade to a 10:1 ratio