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Nyquist Sampling Rate Calculator

The minimum sample rate that avoids aliasing for a signal's highest frequency.

How it is calculated

You enter the highest frequency present in the signal, fmax, in hertz. The tool returns the minimum sample rate fs = 2 × fmax, also in hertz, and repeats fmax as the Nyquist frequency, which is the highest frequency that a system sampling at the minimum rate can represent (half of the sample rate). The value must be greater than zero. This is the theoretical lower bound for an ideal signal that is strictly limited to fmax. Real converters use a higher rate, because a filter in front of the converter cannot cut off at exactly fmax, and any noise or component above fmax will fold into the band as aliasing. The tool does not add any margin for this.

Worked example

Suppose the highest frequency you want to capture is 20,000 Hz. Doubling it gives a minimum sample rate of 2 × 20,000 = 40,000.00 Hz. The Nyquist frequency is 20,000.00 Hz, half of that sampling rate. Sampling at exactly 40,000 Hz would leave no room for a real filter, which is why practical systems choose a higher figure, such as the common 44,100 Hz or 48,000 Hz. A 25,000 Hz component sampled at 44,100 Hz would alias to 19,100 Hz.

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Common mistakes

  • Entering the sample rate you already use instead of the highest signal frequency. The field is the signal's maximum frequency; the sample rate is the output.
  • Entering kilohertz (20) when the field is in hertz. That gives 40 Hz, a result a thousand times too small.
  • Sampling at exactly the minimum rate in practice. A real anti-aliasing filter needs room between the highest wanted frequency and half the sample rate.
  • Ignoring noise or interference above the signal band. Frequencies above the Nyquist frequency are not removed by sampling; they fold back and appear as false lower frequencies unless filtered out first.
  • Confusing the two names. The Nyquist rate is twice the signal frequency (the first result); the Nyquist frequency is half the sample rate (the second result).

About this calculator

The Nyquist–Shannon sampling theorem states that to fully reconstruct a signal without distortion, it must be sampled at a rate of at least twice its highest frequency component — this minimum rate is the Nyquist rate (f_s ≥ 2 × f_max). Sampling below this threshold causes aliasing, where high frequencies fold back and masquerade as lower, incorrect ones in the recorded data.

Audio engineers rely on this principle to justify the 44.1 kHz or 48 kHz sample rates used in digital audio (a little above twice the 20 kHz limit of human hearing, which leaves room for the anti-aliasing filter), while DSP and telecommunications engineers use it to set analog-to-digital converter speeds for sensors, radio receivers and any system that digitizes a continuous signal.

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