Paritian

Developers

FFT Resolution Calculator

Frequency bin width, window length, usable bins and hop size, from the sample rate and the FFT size.

Results

Width of one frequency bin 46.87500 Hz
How long the window is 21.3333 ms
Highest frequency it can hold 24,000.0 Hz
Usable bins 513
Hop between windows 512
Time between windows 10.6667 ms
Frames per second 93.750 1/s
Lowest frequency it can place 46.87500 Hz
Is it a power of two? Yes
Semitones one bin covers at 100 Hz 6.6551

What this tool does

An FFT trades time against frequency and there is no way around it: a longer window resolves finer frequencies and blurs when things happened. At 48 kHz, 1024 points give 47 Hz bins over a 21 ms window — fine above a few hundred hertz, useless for telling two low bass notes apart, which are less than a bin wide. The page shows both sides of the trade at once, including how many semitones a bin covers down at 100 Hz.

Formula

bin width = sample rate ÷ N · window = N ÷ rate · Nyquist = rate ÷ 2 · usable bins = N ÷ 2 + 1

Variables

SymbolMeaningUnit
srSample rateHz
nfFFT size in points
ovAllowance for overlaps%
BWWidth of one frequency binHz
WTHow long the window isms
NYHighest frequency it can holdHz
NBUsable bins
HPHop between windows
HTTime between windowsms
FSFrames per second1/s
LBLowest frequency it can placeHz
POIs it a power of two?
SMSemitones one bin covers at 100 Hz

Worked example

  • Sample rate48,000 Hz
  • FFT size in points1024
  • Allowance for overlaps50 %
  • Width of one frequency bin46.87500 Hz
  • How long the window is21.3333 ms
  • Highest frequency it can hold24,000.0 Hz
  • Usable bins513
  • Hop between windows512
  • Time between windows10.6667 ms
  • Frames per second93.750 1/s
  • Lowest frequency it can place46.87500 Hz
  • Is it a power of two?Yes
  • Semitones one bin covers at 100 Hz6.6551

Limitations

  • The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.
  • Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.