FFT Bin Resolution

Δf = Fs / N

Quick answer

This calculator solves Δf = Fs / N for Frequency Resolution. With Sampling Frequency 100 kHz, FFT Size (points) 0.5, the result is 0.2 MHz. It solves in 3 directions, so you can enter the values you have and get the one you need.

Calculator

Frequency Resolution (Hz)
—

Formula

Δf = Fs / N

Description

The frequency resolution of an FFT is determined by the sampling rate divided by the number of points in the transform. Each FFT bin spans Δf hertz, and the total number of usable bins is N/2 (due to the Nyquist limit). To resolve two closely spaced frequencies, Δf must be smaller than their separation. Increasing N improves resolution but requires a longer time-domain record (T = N/Fs) and more computation. Zero-padding increases the number of bins but does not improve true spectral resolution.

Variables

  • Δf — Frequency resolution per FFT bin (Hz)
  • Fs — Sampling frequency (Hz)
  • N — Number of FFT points

Practical Notes

For audio analysis at Fs = 48 kHz with N = 4096: Δf = 11.7 Hz. For finer resolution, increase N to 16384 giving Δf = 2.9 Hz but requiring 341 ms of data. Windowing functions (Hann, Hamming, Blackman) reduce spectral leakage but slightly widen the effective bin width. Real-time spectrum analyzers use overlapping FFT blocks for continuous coverage.

Symbols and units

Symbol Meaning Default unit Accepted units
df Frequency Resolution Hz Hz, kHz, MHz, GHz
Fs Sampling Frequency kHz Hz, kHz, MHz, GHz
N FFT Size (points) — —

Step by step

  1. 1. What you know: Sampling Frequency 100 kHz, FFT Size (points) 0.5
  2. 2. The relation: Δf = Fs / N
  3. 3. Substitute: Fs = 100 kHz, N = 0.5
  4. 4. Result: Frequency Resolution = 0.2 MHz

Worked examples

Minimum range

Given: Sampling Frequency 100 Hz, FFT Size (points) 0.025

Result: Frequency Resolution = 4 kHz

Low range

Given: Sampling Frequency 1 kHz, FFT Size (points) 0.25

Result: Frequency Resolution = 4 kHz

Typical

Given: Sampling Frequency 100 kHz, FFT Size (points) 0.5

Result: Frequency Resolution = 0.2 MHz

High range

Given: Sampling Frequency 0.5 MHz, FFT Size (points) 0.8

Result: Frequency Resolution = 0.625 MHz

Maximum range

Given: Sampling Frequency 5 MHz, FFT Size (points) 8

Result: Frequency Resolution = 0.625 MHz

Solving for each variable

Solve for Frequency Resolution

Sampling Frequency 100 Hz, FFT Size (points) 0.025 → 4 kHz

Solve for Sampling Frequency

Frequency Resolution 5 Hz, FFT Size (points) 0.025 → 0.125 Hz

Solve for FFT Size (points)

Frequency Resolution 5 Hz, Sampling Frequency 100 Hz → 20

How Frequency Resolution changes with Sampling Frequency

Sampling Frequency (input) Frequency Resolution (result)
10 kHz 20 kHz
25 kHz 50 kHz
50 kHz 100 kHz
75 kHz 150 kHz
100 kHz 0.2 MHz
150 kHz 0.3 MHz
0.2 MHz 0.4 MHz
0.4 MHz 0.8 MHz
0.7 MHz 1.4 MHz
1 MHz 2 MHz

The same result in other units

Unit Value
Hz 200000
kHz 200
MHz 0.2
GHz 0.0002

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Frequently asked questions

How do you calculate FFT Bin Resolution?

Use Δf = Fs / N. With Sampling Frequency 100 kHz, FFT Size (points) 0.5, Frequency Resolution works out to 0.2 MHz.

What is the formula for FFT Bin Resolution?

The formula is Δf = Fs / N. The frequency resolution of an FFT is determined by the sampling rate divided by the number of points in the transform.

How do you find Sampling Frequency when you know the other values?

Rearrange for Sampling Frequency: with Frequency Resolution 5 Hz, FFT Size (points) 0.025, Sampling Frequency is 0.125 Hz.

How do you find FFT Size (points) when you know the other values?

Rearrange for FFT Size (points): with Frequency Resolution 5 Hz, Sampling Frequency 100 Hz, FFT Size (points) is 20.

What units does FFT Bin Resolution use?

Frequency Resolution is shown in Hz, kHz, MHz, GHz. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

Related Concepts

All Signal Processing formulas →
FFT Bin Resolution Averaging SNR Improvement Decimation ENOB Gain FFT Frequency Bin Decimation Resolution Gain FFT Processing Gain FFT Noise Floor

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