Sampling Rate Calculator Formula

Understand the math behind the sampling rate calculator. Each variable explained with a worked example.

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Formulas Used

Minimum Sampling Rate (Nyquist)

min_sampling_rate = 2 * max_signal_freq_hz

Practical Sampling Rate

practical_rate = oversampling_ratio * max_signal_freq_hz

Data Rate (16-bit mono)

data_rate_16bit = oversampling_ratio * max_signal_freq_hz * 16

Variables

VariableDescriptionDefault
max_signal_freq_hzMaximum Signal Frequency(Hz)20000
oversampling_ratioOversampling Ratio2

How It Works

How to Determine Sampling Rate

The Nyquist theorem states the minimum sampling rate is twice the highest signal frequency.

Formulas

f_sample_min = 2 x f_max

f_sample_practical = Oversampling Ratio x f_max

In practice, engineers oversample (4x to 8x or more) because:

  • Perfect brick-wall anti-aliasing filters do not exist
  • Oversampling reduces quantization noise
  • It allows simpler, cheaper analog filters

    • Worked Example

    Capture audio up to 20 kHz with 2x oversampling.

    max_signal_freq_hz = 20000oversampling_ratio = 2
    1. 01Minimum (Nyquist): 2 x 20,000 = 40,000 Hz
    2. 02Practical rate: 2 x 20,000 = 40,000 Hz
    3. 03Data rate (16-bit): 40,000 x 16 = 640,000 bits/s = 640 kbps

    Ready to run the numbers?

    Open Sampling Rate Calculator