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
| Symbol | Meaning | Unit |
|---|---|---|
sr | Sample rate | Hz |
nf | FFT size in points | — |
ov | Allowance for overlaps | % |
BW | Width of one frequency bin | Hz |
WT | How long the window is | ms |
NY | Highest frequency it can hold | Hz |
NB | Usable bins | — |
HP | Hop between windows | — |
HT | Time between windows | ms |
FS | Frames per second | 1/s |
LB | Lowest frequency it can place | Hz |
PO | Is it a power of two? | — |
SM | Semitones 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.