FFT Bin Resolution Calculator

The FFT\'s bin structure — N output values corresponding to frequencies 0, f_s/N, 2f_s/N, ... — falls directly out of the Cooley-Tukey algorithm published in 1965. Each bin is the magnitude of the complex coefficient at that specific integer multiple of 1/T where T = N/f_s is the window duration. Signals whose frequency doesn\'t land exactly on a bin center "leak" energy into neighboring bins — the famous spectral leakage problem.

Windowing functions (Hann 1946, Hamming 1970, Blackman-Harris 1978, Kaiser 1966) trade main-lobe width for side-lobe suppression to manage leakage. Rectangular (no window) has the narrowest main lobe but worst side lobes (−13 dB first side lobe). Hann gives a good balance (−32 dB side lobes, 1.5× wider main lobe). Blackman-Harris achieves −92 dB side lobes at the cost of 2× main lobe width.

Modern practice: for waveforms known to have content at exactly one bin frequency, no window is needed. For arbitrary signals or spectrum surveys, Hann is the default; Blackman-Harris or Kaiser when side-lobe rejection matters more than main-lobe width. Every DSP library and spectrum-analyzer firmware implements a selection of these, chosen from a menu.

Enter sample rate and FFT size. The tool returns bin width Δf, capture window duration T, the maximum meaningful frequency (Nyquist = f_s/2), and the number of useful bins (N/2 + 1).

Use these numbers for: sizing FFT buffers in firmware, designing oscilloscope FFT display parameters, sizing SDR waterfall displays, and matching FFT resolution to signal requirements (audio ~10 Hz bins, precision measurement ~1 Hz, RF wideband ~1 kHz). All math runs client-side.