FFT Bin Frequency Resolution Calculator | Work out Δf = sr/N and window length at a glance
Pick a sample rate and FFT size N to see bin resolution Δf = sr/N, the Nyquist frequency, the analysis window T = N/sr, and the usable one-sided bin count (N/2+1). It also shows how many cents one bin spans at 100 Hz, 1 kHz, and 10 kHz, so you can size your FFT for pitch work without guessing.
💡 About this tool
The first wall everyone hits when building a spectrogram or pitch tracker is "what FFT size should I use?" Bump N up and your frequency resolution Δf gets finer, but the analysis window T = N/sr grows too, which means more latency, more CPU, and worse time resolution. That time-versus-frequency trade-off is the whole game, and most people end up punching sr/N into a calculator over and over to feel it out.
This tool does it in one shot: choose sr and N, get Δf, Nyquist, window length, and bin count together. The cents readout is the part you won't find in a plain resolution calculator. At 100 Hz, a single bin can be hundreds of cents wide; at 10 kHz, it shrinks below one cent. That exposes the core weakness of the FFT - resolution feels coarse in the low end - and makes it obvious why you need a bigger N to separate a bass note or a kick fundamental.
🧐 Frequently Asked Questions
Q. How is bin resolution Δf determined? A. Δf = sample rate / FFT size (sr/N). At 44 100 Hz with N=1024 that's 43.07 Hz. Double N and Δf halves.
Q. Why does resolution look worse at low frequencies? A. Δf is constant across the band in Hz, but musical pitch distance (cents) is logarithmic. The same Δf maps to far more cents when the fundamental is low, so separating two close low notes near 100 Hz needs a larger N than it would up high.
Q. Why is the usable bin count N/2+1 instead of N? A. The FFT of a real signal is symmetric, so only the one-sided spectrum from DC to Nyquist - that's N/2+1 bins - carries independent information. The rest is a mirror image.
Q. Does a window function change the resolution? A. Applying a Hanning or Hamming window trades leakage suppression for a wider main lobe, so effective resolution drops to roughly 1.4-2 bins. The Δf shown here is the rectangular-window (no window) theoretical value.
Q. What's the point of a high sample rate like 192 kHz? A. It raises Nyquist (sr/2) so you can analyze ultrasonic content, but at the same N your Δf gets coarser. If you only care about pitch accuracy in the audible band, lowering sr and raising N is often the better move.
📚 Why bigger FFTs aren't free
A common reflex on audio-dev forums is "just crank the FFT size for more resolution," but every doubling of N also doubles the window length, and that delay is exactly what makes a real-time analyzer feel laggy. A frame at 44.1 kHz with N=4096 already spans about 93 ms - long enough that a fast vibrato or a transient drum hit smears across the window. Plug 44 100 Hz and 4096 into this calculator and you'll see Δf land near 10.8 Hz with that ~93 ms window, which is the tell-tale sign you've traded time resolution for frequency resolution. The practical sweet spot for most music analysis sits around N=2048-4096 at 44.1/48 kHz; push higher only when you genuinely need to resolve closely spaced low-frequency partials and can tolerate the lag.