FFT Bin Width

Compute FFT frequency resolution: Δf = fs / N. Includes time window, Nyquist, bin mapping, and Show Work.

How to Use

  1. Enter sample rate (fs) and FFT size (N).
  2. (Optional) Enter a target frequency to map it to the nearest bin index.
  3. Results update instantly; open “Show Work” to see the steps.
  4. Use “Share Link” only when you want a URL that restores this state.
Resolution Overview
Δf, time window length, Nyquist, and bin mapping.
Δf
—
Window (T)
—
Nyquist
—
Bins (1-sided)
—
Quality: —
Formula
Δf = fs / N
Window length
T = N / fs
Frequency at bin k
f(k) = k · Δf (one-sided)
Nearest bin for f
k ≈ round(f / Δf)

Notes: If you apply windowing, it affects leakage—not the fundamental bin spacing (Δf).

Inputs & Settings
Enter sample rate and FFT size. Optional target frequency for bin mapping.
Common: 8000, 44100, 48000, 96000, 192000
Typical: 256, 512, 1024, 2048, 4096…
Maps to nearest bin k and the exact bin center frequency.
One-sided bins: 0..N/2 (inclusive) when N is even.
Show Work (step-by-step)
—
Work is shown in base units (Hz, seconds) for clarity.

Reference

  • Bin width / resolution: Δf = fs / N
  • Time window length: T = N / fs seconds
  • Nyquist frequency: fN = fs/2
  • One-sided bins (real signal, even N): k = 0..N/2 (count = N/2 + 1)
  • Two-sided bins: k = 0..N−1 (negative freqs map above N/2)

Tip: Increasing N improves frequency resolution (smaller Δf) but increases time window length (T).

FAQ

Is “FFT resolution” the same as bin width?

Bin spacing is Δf = fs/N. Practical ability to separate tones also depends on windowing, noise, and leakage.

Does windowing change Δf?

No—Δf is set by fs and N. Windowing changes spectral leakage and main-lobe width.

Why does a larger N help frequency resolution?

Because Δf becomes smaller. But you also need a longer time record: T = N/fs.

How do I find the bin index for a frequency?

Use k ≈ round(f/Δf). This tool also shows the exact bin center f(k) and the error f − f(k).

Tool Info

Last updated:

Updates may include unit support, mapping edge-case handling, and UI polish.