FFT Frequency Bin
Δf = Fs / N
Quick answer
This calculator solves Δf = Fs / N for Bin Width. With Sample Rate 100 kHz, FFT 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
Formula
Description
Each FFT output bin represents a frequency range of width Fs/N hertz. The k-th bin corresponds to the frequency k × Δf. The total number of unique frequency bins is N/2 + 1 (from DC to Nyquist). Choosing the FFT size involves a tradeoff between frequency resolution (finer with larger N), time resolution (faster update with smaller N), and computational cost. Power-of-two FFT sizes (256, 512, 1024, 2048, 4096) are most efficient for radix-2 FFT algorithms.
Variables
- Δf — Frequency width per bin (Hz)
- Fs — Sampling frequency (Hz)
- N — Number of FFT points
Practical Notes
For real-time spectrum analysis: N = 256 gives fast updates but coarse resolution, N = 4096 gives fine resolution but slower updates. Overlap processing (50-75% overlap between consecutive FFT frames) improves time resolution without sacrificing frequency resolution. The spectrogram (waterfall display) shows how the spectrum evolves over time using successive FFT frames.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| df | Bin Width | Hz | Hz, kHz, MHz, GHz |
| Fs | Sample Rate | kHz | Hz, kHz, MHz, GHz |
| N | FFT Points | — | — |
Step by step
- 1. What you know: Sample Rate 100 kHz, FFT Points 0.5
- 2. The relation: Δf = Fs / N
- 3. Substitute: Fs = 100 kHz, N = 0.5
- 4. Result: Bin Width = 0.2 MHz
Worked examples
Minimum range
Given: Sample Rate 100 Hz, FFT Points 0.025
Result: Bin Width = 4 kHz
Low range
Given: Sample Rate 1 kHz, FFT Points 0.25
Result: Bin Width = 4 kHz
Typical
Given: Sample Rate 100 kHz, FFT Points 0.5
Result: Bin Width = 0.2 MHz
High range
Given: Sample Rate 0.5 MHz, FFT Points 0.8
Result: Bin Width = 0.625 MHz
Maximum range
Given: Sample Rate 5 MHz, FFT Points 8
Result: Bin Width = 0.625 MHz
Solving for each variable
Solve for Bin Width
Sample Rate 100 Hz, FFT Points 0.025 → 4 kHz
Solve for Sample Rate
Bin Width 5 Hz, FFT Points 0.025 → 0.125 Hz
Solve for FFT Points
Bin Width 5 Hz, Sample Rate 100 Hz → 20
How Bin Width changes with Sample Rate
| Sample Rate (input) | Bin Width (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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<p><a href="https://vbatpower.com/formulas/fft-bin/">FFT Frequency Bin</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate FFT Frequency Bin?
Use Δf = Fs / N. With Sample Rate 100 kHz, FFT Points 0.5, Bin Width works out to 0.2 MHz.
What is the bin width of an fft size 52428800 and sample frequency 23.4375mhz?
Rearrange for Bin Width: with Sample Rate 1 kHz, FFT Points 0.25, Bin Width is 4 kHz.
What is the formula for FFT Frequency Bin?
The formula is Δf = Fs / N. Each FFT output bin represents a frequency range of width Fs/N hertz.
How do you find Sample Rate when you know the other values?
Rearrange for Sample Rate: with Bin Width 5 Hz, FFT Points 0.025, Sample Rate is 0.125 Hz.
How do you find FFT Points when you know the other values?
Rearrange for FFT Points: with Bin Width 5 Hz, Sample Rate 100 Hz, FFT Points is 20.
What units does FFT Frequency Bin use?
Bin Width is shown in Hz, kHz, MHz, GHz. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
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