Calculate logarithmic sweep rate, duration, or ending frequency in octaves per minute, with octave span, frequency ratio, local Hz/s rate, and fractional-octave dwell time.

Choose a solve target, then complete the visible required fields marked with *.

Octaves per Minute Formula

The calculator uses the octave sweep relationship between starting frequency, final frequency, time, and octave rate.

f₂ = f₁ × 2⁽r × t)
  • f_1 = starting frequency
  • f_2 = final frequency
  • r = octave rate
  • t = time

If r is in octaves per minute, then t must be in minutes. The calculator converts Hz, kHz, MHz, seconds, minutes, hours, and rate units before solving.

Rearranged formulas:

f₁ = f₂ / 2⁽r × t)
t = log₂(f₂ / f₁) / r
r = log₂(f₂ / f₁) / t

Frequencies must be greater than zero. Time must be zero or greater. A positive octave rate increases frequency over time. A negative octave rate decreases it.

Useful Tables

Use these conversions when checking inputs or interpreting the result.

Frequency unit Equivalent in Hz
1 Hz 1 Hz
1 kHz 1,000 Hz
1 MHz 1,000,000 Hz
Octave change Frequency ratio Meaning
-2 octaves 1/4 Final frequency is one quarter of the start
-1 octave 1/2 Final frequency is half the start
0 octaves 1 No frequency change
1 octave 2 Final frequency is double the start
2 octaves 4 Final frequency is four times the start

Quick Example

If a sweep starts at 100 Hz and ends at 800 Hz, the change is 3 octaves because 800 / 100 = 8 and log2(8) = 3.

If that sweep takes 2 minutes, the rate is:

r = 3 / 2 = 1.5 octaves per minute

Use a negative rate only when the final frequency is lower than the starting frequency.