Calculate sampling frequency or Nyquist frequency from the other, with results in Hz, kHz, MHz, or GHz for signal sampling and unit conversion.

For uniform real-valued sampling. Nyquist frequency is fs/2; practical baseband sampling needs filter margin below it. Zone analysis describes a single nonnegative input frequency.

Nyquist Zone Frequency Formula

This calculator finds the Nyquist frequency from a known sampling frequency, or the sampling frequency from a known Nyquist frequency. In signal processing, the Nyquist frequency is one-half of the sampling rate, and it also represents the width of each Nyquist zone.

fN = (fₛ) / (2)

Where:

  • fN = Nyquist frequency
  • fs = sampling frequency

If you already know the Nyquist frequency and need to solve for the sampling frequency, rearrange the equation as follows:

fₛ = 2fN

How to Use the Calculator

  1. Choose the calculation and enter the required frequency values.
  2. Select the correct unit: Hz, kHz, MHz, or GHz.
  3. Click calculate to solve for the missing value.
  4. Interpret the result as the highest baseband frequency limit for standard real-valued sampling.

Choose the result unit independently; the calculator converts Hz, kHz, MHz and GHz consistently.

What a Nyquist Zone Means

Nyquist zones divide the frequency axis into equal bands, each with a width equal to the Nyquist frequency. This is useful in ADC, DSP, RF sampling, and aliasing analysis.

Zone 1: 0 to (fₛ) / (2)
Zone 2: (fₛ) / (2) to fₛ
Zone 3: fₛ to (3fₛ) / (2)
Zone n: ((n - 1)fₛ) / (2) to (nfₛ) / (2)

The Nyquist-frequency mode returns the width of every zone. The signal-zone mode also identifies the zone and folded alias. It uses lower-inclusive, upper-exclusive intervals; a frequency exactly on a boundary is flagged.

Finding the Nyquist Zone Number

For a positive input frequency, the zone number can be estimated with:

z = lfloor (2f) / (fₛ) rfloor + 1

Where:

  • z = Nyquist zone number
  • f = input signal frequency
  • fs = sampling frequency

Examples

If the sampling frequency is 150 Hz, the Nyquist frequency is:

fN = (150) / (2) = 75 Hz

If the desired Nyquist frequency is 12 MHz, the required sampling frequency is:

fₛ = 2(12 MHz) = 24 MHz

If the sampling frequency is 100 MHz, the zone boundaries are:

(fₛ) / (2) = (100 MHz) / (2) = 50 MHz

So the first three zones are 0 to 50 MHz, 50 to 100 MHz, and 100 to 150 MHz.

Nyquist Frequency vs. Nyquist Rate

These terms are related, but they are not the same:

  • Nyquist frequency is half of an actual sampling rate.
  • Nyquist rate is the minimum sampling rate needed to capture a signal with a highest frequency component.
fₛ > 2fₘₐₓ

For arbitrary baseband signals, avoid equality at the Nyquist edge and leave practical anti-alias filter margin. Use the calculator on this page when you need to convert directly between sampling frequency and Nyquist frequency.

Why This Calculation Matters

  • It defines the frequency limit before standard aliasing begins in baseband sampling.
  • It helps size anti-aliasing filters ahead of an ADC.
  • It is essential when choosing sample rates for data acquisition, oscilloscopes, RF receivers, and digital audio systems.
  • It provides the bandwidth of each Nyquist zone when analyzing undersampling or bandpass sampling systems.

Practical Notes

  • Always keep your units consistent when entering values.
  • A higher sampling frequency increases the Nyquist frequency and expands the first usable zone.
  • Signals above the first zone can still be intentionally sampled in some applications, but their aliased position must be controlled carefully.
  • Even-numbered zones often appear spectrally inverted after sampling, which matters in RF and communication system design.

Common Mistakes

  • Confusing the sampling frequency with the Nyquist frequency.
  • Using mixed units across Hz, kHz, MHz, and GHz.
  • Assuming the Nyquist frequency is the same as the Nyquist rate.
  • Ignoring aliasing when the input signal contains frequency content above the first zone.