FFT Calculator

Discrete Fourier transform and frequency spectrum

X[k] = Σ x[n]·e^(−2πi·kn/N)

Samples (N)4Sample rate4 HzFrequency resolution Δf1 HzNyquist frequency2 HzDC component (mean)2.5Dominant frequency1 Hz

N is a power of two — a radix-2 FFT applies exactly.

Single-sided spectrum

k	Freq (Hz)	Real	Imag	\|X[k]\|	Phase	Amplitude
0	0	10	0	10	0°	2.5
1	1	-2	2	2.8284	135°	1.4142
2	2	-2	0	2	180°	0.5

Bins above the Nyquist frequency mirror those below as complex conjugates, so only the single-sided spectrum is listed.

About this calculator

The FFT Calculator computes the discrete Fourier transform of up to 64 real samples and presents the full frequency spectrum: every bin's real and imaginary parts, magnitude, phase, and single-sided amplitude. It reports the frequency resolution fs/N, the Nyquist frequency, the DC component (signal mean), and the dominant frequency. The transform is evaluated at 30-digit precision with precomputed twiddle factors, matching NumPy's FFT convention exactly; a sample rate can be supplied to map bins to real hertz.

How to use the FFT Calculator calculator

Enter the values for your problem into the input fields.
Read the result — it updates instantly as you type.
Check the formula and the visual explanation to follow how the answer was found.
Copy the page URL to share the exact calculation.

Common examples

8 samples of one sine cycle → dominant bin k = 1 with amplitude ≈ 1, DC ≈ 0
1 + 2cos(2πt·2/8) sampled 8 times → DC component ≈ 1 and bin k = 2 with amplitude 2
16 samples of a 50 Hz sine at fs = 800 Hz → resolution 50 Hz, Nyquist 400 Hz, dominant frequency 50 Hz
Constant signal 2, 2, 2, 2 → DC = 2 and no dominant frequency (flat spectrum)

Frequently asked questions

How does the FFT Calculator calculator work?

Enter your values and the calculator applies the exact mathematical method for this problem, showing the result together with the formula it used. Everything is computed with high-precision arithmetic, so the answer you see is not limited by ordinary floating-point rounding.

When would I use the FFT Calculator calculator?

It is useful for homework and exam preparation, for checking work done by hand, and whenever a step in a larger problem needs this calculation done quickly and reliably.

How accurate are the results?

Calculations run at 30 significant digits of precision internally. Displayed values are rounded for readability, but the underlying result is far more precise than a typical hand or pocket-calculator computation.

Can I share a specific calculation with someone else?

Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same calculation for whoever clicks it.