Enter the sampling frequency (Hz) into the Nyquist Frequency (Nyquist limit) Calculator. The calculator will evaluate the Nyquist frequency (Fs/2), which is the boundary between Nyquist zones.

Nyquist Frequency Calculator

Enter one value to calculate the other

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.

f_N = \frac{f_s}{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:

f_s = 2f_N

How to Use the Calculator

  1. Enter either the sampling frequency or the Nyquist frequency.
  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.

Because the calculation is simply “divide by 2” or “multiply by 2,” the unit stays consistent. If the sampling frequency is entered in MHz, the Nyquist frequency will also be in MHz.

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.

\text{Zone }1: 0 \text{ to } \frac{f_s}{2}
\text{Zone }2: \frac{f_s}{2} \text{ to } f_s
\text{Zone }3: f_s \text{ to } \frac{3f_s}{2}
\text{Zone }n: \frac{(n-1)f_s}{2} \text{ to } \frac{nf_s}{2}

This calculator returns the Nyquist frequency, which defines the width of every zone. If you want to determine which zone a signal falls into, compare the signal frequency to the zone boundaries above.

Finding the Nyquist Zone Number

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

z = \left\lfloor \frac{2f}{f_s} \right\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:

f_N = \frac{150}{2} = 75 \text{ Hz}

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

f_s = 2(12 \text{ MHz}) = 24 \text{ MHz}

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

\frac{f_s}{2} = \frac{100 \text{ MHz}}{2} = 50 \text{ 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.
f_s \ge 2f_{max}

Use the formula above when designing a system around a signal’s highest frequency content. 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.