Sample Rate & Nyquist Calculator
Calculate the Nyquist frequency (maximum reproducible frequency) for any audio sample rate. The Nyquist limit is exactly half the sample rate.
How to use this tool
- Enter sample rate in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your nyquist frequency and the full breakdown beneath it.
Find the highest frequency that can be represented at a given sample rate (Nyquist theorem).
Formula
Nyquist frequency (Hz) = sample rate (Hz) ÷ 2
Nyquist frequency (kHz) = Nyquist frequency (Hz) ÷ 1000
How it works
This calculator applies the Nyquist–Shannon sampling theorem, which states that the highest frequency a digital audio system can accurately reproduce is exactly half its sample rate. Any audio content above this limit must be filtered out before conversion to avoid aliasing artefacts.
The calculation is a simple division and is mathematically exact. In practice, real anti-aliasing filters roll off slightly below the Nyquist limit, so usable bandwidth is marginally less than the theoretical maximum.
Worked example
Worked example
- Standard CD audio sample rate = 44 100 Hz.
- Nyquist frequency = 44 100 / 2 = 22 050 Hz.
- Convert to kHz: 22 050 / 1000 = 22.05 kHz.
Nyquist frequency: 22 050 Hz | 22.05 kHz
Key terms
- Sample rate
- The number of audio samples captured per second, measured in Hz. Common values are 44 100 Hz (CD), 48 000 Hz (video), and 96 000 Hz (high-resolution audio).
- Nyquist frequency
- Half the sample rate; the theoretical upper limit of reproducible frequency for a given digital audio system.
- Nyquist–Shannon sampling theorem
- A fundamental principle stating that a signal can be perfectly reconstructed from discrete samples if the sample rate is at least twice the highest frequency present.
- Aliasing
- A distortion artefact that occurs when audio frequencies above the Nyquist limit are sampled, causing them to 'fold back' and appear as spurious low-frequency content.
- Anti-aliasing filter
- A low-pass filter applied before analogue-to-digital conversion to remove frequencies above the Nyquist limit and prevent aliasing.
Frequently asked questions
- What is the Nyquist frequency?
- The Nyquist frequency is half the sample rate — the highest frequency that can be accurately reproduced without aliasing.
- Why is CD audio 44,100 Hz?
- 44,100 Hz gives a Nyquist limit of 22,050 Hz, safely above the 20 kHz upper limit of human hearing.