Nyquist Frequency Calculator Formula

Understand the math behind the nyquist frequency calculator. Each variable explained with a worked example.

Use the Nyquist Frequency Calculator

Formulas Used

Nyquist Frequency

nyquist_hz = sampling_rate_hz / 2

Nyquist Frequency

nyquist_khz = sampling_rate_hz / 2000

Sampling Period

period_us = 1000000 / sampling_rate_hz

Variables

VariableDescriptionDefault
sampling_rate_hzSampling Rate(Hz)44100

How It Works

The Nyquist-Shannon Sampling Theorem

To perfectly reconstruct a signal, you must sample at least twice the highest frequency present.

Formula

f_Nyquist = f_sample / 2

Any signal component above the Nyquist frequency will alias (fold back) into the baseband, creating distortion. This is why anti-aliasing filters are placed before ADCs.

Common Examples

  • CD audio: 44.1 kHz sampling, 22.05 kHz Nyquist
  • Phone: 8 kHz sampling, 4 kHz Nyquist
  • Professional audio: 96 kHz sampling, 48 kHz Nyquist

    • Worked Example

    CD-quality audio at 44,100 Hz sampling rate.

    sampling_rate_hz = 44100
    1. 01Nyquist frequency: 44,100 / 2 = 22,050 Hz
    2. 02In kHz: 22.050 kHz
    3. 03Sampling period: 1,000,000 / 44,100 = 22.676 microseconds

    Ready to run the numbers?

    Open Nyquist Frequency Calculator