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

    Frequently Asked Questions

    Why do CDs use 44.1 kHz?

    Humans hear up to about 20 kHz. The 44.1 kHz rate provides a Nyquist frequency of 22.05 kHz, covering the full hearing range with a small guard band for the anti-aliasing filter.

    What happens if I sample too slowly?

    Frequencies above the Nyquist limit alias to lower frequencies, causing distortion that cannot be removed after sampling.

    Does oversampling help?

    Yes. Oversampling (sampling faster than 2x) relaxes anti-aliasing filter requirements and can improve effective resolution.

    Ready to run the numbers?

    Open Nyquist Frequency Calculator