Signal to Noise Ratio to Resolution Conversion Calculator

Convert Signal to Noise Ratio (SNR) in decibels (dB) to the equivalent digital resolution in bits. This calculator is useful for audio systems, imaging equipment, and other applications where resolution and noise performance need to be understood in relation to each other.

Input Parameters

Calculation Results

Resolution in Bits

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Calculation Formula

Resolution (bits) = log₂(10^(SNR/10))

Where:
- SNR is the Signal to Noise Ratio in decibels
- log₂ is the logarithm to base 2
- 10^(SNR/10) converts SNR from dB to linear scale

Signal to Noise Ratio to Resolution Conversion Calculator Usage Guide

Learn how to use the calculator and understand the relationship between SNR and resolution.

How to Use This Calculator

  1. Enter the Signal to Noise Ratio (SNR) in decibels (dB) in the input field. For example, a CD-quality audio system typically has an SNR of around 96 dB.
  2. Click the "Calculate" button to compute the equivalent digital resolution in bits.
  3. The result will be displayed in bits. For example, an SNR of 96 dB corresponds to approximately 20.05 bits of resolution.

Understanding the Relationship Between SNR and Resolution

The Signal to Noise Ratio (SNR) in decibels is related to the resolution in bits through logarithmic scaling. The formula used is:

Resolution (bits) = log₂(10^(SNR/10))

This formula works because:

  • SNR in dB is converted from linear to logarithmic scale using 10^(SNR/10)
  • Then the logarithm to base 2 is taken to convert the linear scale to bits of resolution

Practical Examples

  • 16-bit audio: Has approximately 98.99 dB SNR
  • 24-bit audio: Has approximately 144.77 dB SNR
  • DSD (Direct Stream Digital): Theoretical SNR is around 120-130 dB, resulting in approximately 24-26 bits of resolution

Note: This calculator provides an approximate conversion between SNR and resolution. Real-world systems may have additional factors affecting the actual resolution.