FFT Resolution Calculator Formula

Understand the math behind the fft resolution calculator. Each variable explained with a worked example.

Use the FFT Resolution Calculator

Formulas Used

Frequency Resolution

freq_resolution = sample_rate_hz / fft_size

Useful Frequency Bins

num_bins = fft_size / 2 + 1

Maximum Frequency

max_freq = sample_rate_hz / 2

Time Window Duration

time_window = fft_size / sample_rate_hz * 1000

Variables

VariableDescriptionDefault
sample_rate_hzSampling Rate(Hz)48000
fft_sizeFFT Size (points)1024

How It Works

FFT Frequency Resolution

The FFT converts time-domain data into frequency-domain bins. The resolution depends on how long you observe the signal.

Formulas

Frequency Resolution = Sample Rate / FFT Size

Time Window = FFT Size / Sample Rate

Useful Bins = FFT Size / 2 + 1 (for real signals)

Trade-off

Better frequency resolution requires longer observation windows. This is the time-frequency uncertainty principle.

  • Larger FFT = finer frequency resolution but slower updates
  • Smaller FFT = coarser resolution but faster updates

    • Worked Example

    1024-point FFT at 48 kHz sampling rate.

    sample_rate_hz = 48000fft_size = 1024
    1. 01Resolution: 48,000 / 1,024 = 46.875 Hz
    2. 02Useful bins: 1024/2 + 1 = 513
    3. 03Max frequency: 48,000 / 2 = 24,000 Hz
    4. 04Time window: 1024/48,000 x 1000 = 21.33 ms

    Ready to run the numbers?

    Open FFT Resolution Calculator