Nyquist Frequency Calculator
The Nyquist frequency is half the sampling rate and sets the highest frequency a digital system can represent without aliasing. The Nyquist-Shannon sampling theorem requires sampling at more than twice the highest frequency present in a signal. This calculator returns the Nyquist frequency for a chosen sample rate, the minimum sample rate needed to capture a target signal frequency, and whether your current sample rate captures that signal. Use it to choose audio sample rates, set anti-aliasing filters, and check that a digitiser is fast enough for the bandwidth you need.
Nyquist formula
Nyquist frequency = sample rate / 2
Minimum sample rate = 2 * highest signal frequency
Captured if: sample rate > 2 * signal frequency
A signal is captured without aliasing only when its highest frequency is strictly below the Nyquist frequency. Frequencies at or above Nyquist alias into the band and must be filtered out before sampling.
Worked example
At a 44,100 hertz sample rate the Nyquist frequency is 22,050 hertz. A 20,000 hertz signal needs a minimum sample rate of 40,000 hertz, so 44,100 hertz captures it with room to spare for the anti-aliasing filter.
Nyquist frequency: frequently asked questions
What is the Nyquist frequency?
The Nyquist frequency is half the sampling rate. It is the highest frequency a sampled signal can represent without aliasing. The Nyquist-Shannon sampling theorem states that to capture a signal faithfully you must sample at more than twice its highest frequency component. At a 44,100 hertz sample rate the Nyquist frequency is 22,050 hertz.
What is aliasing?
Aliasing is the distortion that occurs when a signal contains frequencies above the Nyquist frequency. Those components fold back into the audible range as false lower-frequency tones. To prevent it, an anti-aliasing low-pass filter removes content above the Nyquist frequency before sampling.
What is the formula?
Nyquist frequency = sample rate divided by 2. To capture a signal of frequency f without aliasing you need a sample rate greater than 2 times f, so the minimum theoretical sample rate is just over 2f. In practice a margin is added above 2f to allow for a realisable anti-aliasing filter.
Why is CD audio sampled at 44,100 hertz?
Human hearing extends to about 20,000 hertz. A 44,100 hertz sample rate places the Nyquist frequency at 22,050 hertz, comfortably above the audible limit, leaving a transition band for the anti-aliasing filter between 20,000 and 22,050 hertz. That is why 44,100 hertz became the compact disc standard.
Official sources
- U.S. National Institute of Standards and Technology: nist.gov (digital signal sampling references).
- NIST Reference on Constants, Units, and Uncertainty: SI units.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.