FFT Size & Bin Resolution Calculator
Calculate FFT bin width, window duration, and required size for a target frequency resolution at a given sample rate.
How to Use
- Enter sample rate and FFT size (or desired bin width).
- FFT size must be a power of 2 for typical radix-2 implementations.
- Bin width = fs / N. Smaller bins = finer resolution but longer window.
- Window duration = N / fs.
Show Work
Formulas
History of the FFT
The discrete Fourier transform (DFT) had been understood since Joseph Fourier\'s 1807 work, but naive computation is O(N²) — impractical for large N. James Cooley and John Tukey rediscovered and popularized a fast algorithm in their landmark 1965 paper "An Algorithm for the Machine Calculation of Complex Fourier Series", reducing complexity to O(N log N) — a factor of ~100× speedup at N = 1024, enough to make real-time digital signal processing practical.
The Cooley-Tukey algorithm\'s power-of-2 efficiency preference shaped decades of DSP hardware. Texas Instruments\' TMS32010 (1982, first commercial DSP chip) and every subsequent DSP family include hardware support for FFT — typically with bit-reversed addressing and butterfly-operation accelerators specifically tailored for radix-2. Modern FFTW library (1997, Frigo and Johnson) achieves near-optimal performance across any FFT size via machine-tuned code paths.
Most modern signal processing — spectrum analyzers, real-time audio plugins, SDR waterfalls, vibration monitoring, MRI reconstruction — runs on FFT. The bin-width / window-duration / sample-rate trade-off in this calculator is identical to the one every DSP engineer has analyzed since 1965.
About This Calculator
Enter a sample rate and FFT size N, or specify a desired bin width and let the tool solve for the required N. Returned values: bin width (frequency spacing), window duration (time span), number of usable bins (N/2 + 1 for real inputs), and the nearest power-of-2 FFT size for radix-2 efficiency.
Remember that bin width is not the same as true frequency resolution. Spectral leakage from real-world windowing (Hann, Hamming, Blackman) smears each tone across 1.5–3 bins. Zero-padding adds interpolated bins but doesn\'t improve real resolution. Everything runs client-side; no values leave your browser.
Frequently Asked Questions
What is FFT bin width?
The frequency spacing of output bins. Bin width = fs / N. For 48 kHz sample rate with 1024-point FFT, bin width = 46.875 Hz. Signals within the same bin can\'t be distinguished.
Why power of 2?
Radix-2 FFT algorithms (Cooley-Tukey) are O(N log N) and run fastest when N is a power of 2. Modern libraries (FFTW, CMSIS-DSP) handle other sizes efficiently but power-of-2 remains most common.
Bin width vs actual resolution?
Spectral leakage (from windowing) spreads a single tone across multiple bins. Actual frequency resolution depends on window choice. Hann window: ~1.5× bin width. Blackman: ~2× bin width. Rectangular: 1× but with severe side-lobes.
How do I pick FFT size?
Trade off: larger N = better frequency resolution but longer collection window and more CPU. Real-time audio: 512-4096 typical. Precision scientific: 16k-1M. Limited by buffer RAM and latency tolerance.
What about zero-padding?
Zero-padding interpolates between bins (smoother plot) but doesn\'t improve actual resolution. The resolving power of an FFT is still set by the signal window length, not the total padded size.
Common Use Cases
Audio Spectrum Analyzer
1024-pt FFT at 48 kHz: 46.9 Hz bins, 21.3 ms window — typical real-time audio DSP.
Precision Frequency Measurement
65536-pt FFT at 100 kHz: 1.53 Hz bins. 655 ms window needed to resolve ±1 Hz tones.
Vibration Analysis
Machinery monitoring: 2048-pt FFT at 25.6 kHz gives 12.5 Hz bins up to ~12.8 kHz.
RF Spectrum
SDR with 10 MHz bandwidth and 4096-pt FFT: 2.4 kHz bins — fine enough for wideband surveys.
Musical Note Detection
To resolve adjacent piano notes near A440 (~26 Hz apart), need bins < 13 Hz. At 44.1 kHz, that's N ≥ 4096.
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