FFT Bin Frequency

An N-point FFT breaks a sampled signal into evenly spaced frequency bins, and this formula gives the center frequency of the k-th bin. The spacing between adjacent bins is the sampling rate divided by the FFT length, f_s/N, because the FFT is effectively measuring sinusoids whose periods fit an integer number of cycles across the N samples. So multiplying the bin index k by f_s/N maps a discrete frequency index back into physical units of hertz.

Use this when interpreting FFT or spectrum-analyzer output and you need to know what real-world frequency a peak or bin corresponds to. It is especially useful in vibration analysis, audio processing, RF/signal diagnostics, and any task where you convert FFT indices into hertz.

• Using the bin number as the frequency without multiplying by f_s/N
• Forgetting that an FFT bin represents a frequency spacing, not a narrow exact tone frequency
• Confusing FFT size N with the number of unique positive-frequency bins in a real-valued signal