Signal-to-Noise Ratio (SNR) Calculator

General Physics

Determine the quality of a signal by comparing its level to the level of background noise. This tool calculates SNR from power or amplitude values.

Practical Examples

Explore these real-world scenarios to understand how the SNR calculator is applied in various fields.

High-Fidelity Audio System

audio

An amplifier outputs a signal with a power of 50 Watts, while the background noise power is 0.005 Watts.

Signal: 50, Noise: 0.005

Type: power

Wireless Communication Link

telecom

A received radio signal has a voltage of 10 microvolts (0.00001 V), and the noise voltage is 2 microvolts (0.000002 V).

Signal: 0.00001, Noise: 0.000002

Type: amplitude

Medical MRI Scan

imaging

In a medical image, the signal intensity from tissue is measured at 800 units, while the background noise intensity is 50 units. These are amplitude-like measurements.

Signal: 800, Noise: 50

Type: amplitude

Basic Electronics Lab

lab

A circuit has a signal power of 2 Watts and a noise power of 0.5 Watts.

Signal: 2, Noise: 0.5

Type: power

Other Titles
Understanding Signal-to-Noise Ratio (SNR): A Comprehensive Guide
Dive deep into the principles of SNR, its calculation, applications, and the science behind it.

What is Signal-to-Noise Ratio (SNR)?

  • Defining SNR
  • Why SNR is Important
  • SNR in Different Contexts
Signal-to-Noise Ratio, often abbreviated as SNR or S/N, is a fundamental measure used in science and engineering that compares the level of a desired signal to the level of background noise. It is a critical metric for assessing the quality of a signal, whether it's an audio recording, a wireless transmission, a medical image, or an electrical circuit's output. A higher SNR indicates a cleaner, higher-quality signal, where the desired information is strong relative to unwanted interference. Conversely, a low SNR means the noise is significant, potentially obscuring or corrupting the signal.
The Decibel (dB) Scale
SNR is almost always expressed in decibels (dB), which is a logarithmic unit. The logarithmic scale is convenient because it can represent very large or very small ratios in a more manageable range of numbers. It also aligns better with human perception of stimuli like sound and light.

Step-by-Step Guide to Using the SNR Calculator

  • Inputting Your Values
  • Choosing the Correct Input Type
  • Interpreting the Results
Our calculator simplifies the process of finding SNR. Follow these steps for an accurate calculation:
1. Enter Signal and Noise Values
In the 'Signal Value' field, enter the measured level of your desired signal. In the 'Noise Value' field, enter the measured level of the background noise. Ensure both values are in the same units (e.g., Watts for power, Volts for amplitude).
2. Select Input Type: Power or Amplitude
This is a critical step. If your values are measurements of power (e.g., Watts, milliwatts), select 'Power'. If they are measurements of amplitude (e.g., Voltage, current, pressure), select 'Amplitude'. The calculator uses a different formula for each.
3. Interpret the Output
The calculator provides two results: SNR in dB (the standard logarithmic measure) and SNR as a simple ratio (Signal Value / Noise Value). A dB value greater than 0 indicates the signal is stronger than the noise.

Real-World Applications of SNR

  • Telecommunications and Networking
  • Audio and Video Engineering
  • Medical Imaging and Analytics
SNR is not just a theoretical concept; it has crucial practical applications across many industries.
Audio Engineering
In audio, a high SNR for a microphone or recording means less audible hiss and hum, resulting in a cleaner sound. For example, a professional microphone might have an SNR of 70 dB or more.
Wireless Communications
For Wi-Fi, cellular, and satellite communications, a higher SNR at the receiver allows for faster data rates and fewer errors. Internet service providers constantly monitor SNR to ensure reliable connections.
Medical Imaging
In MRI and CT scans, a high SNR is essential for producing clear images that allow doctors to make accurate diagnoses. Low SNR can result in grainy images where important details are lost.

Mathematical Derivation and Formulas

  • The Power-Based SNR Formula
  • The Amplitude-Based SNR Formula
  • Converting Between Ratio and dB
The calculation of SNR in decibels depends on whether you are working with power or amplitude quantities.
Formula for Power
When using power quantities (P), such as Watts, the SNR in dB is calculated as: SNR (dB) = 10 * log10(Psignal / Pnoise). The factor of 10 is used for power ratios.
Formula for Amplitude
When using amplitude quantities (A), such as voltage or pressure, the SNR in dB is calculated as: SNR (dB) = 20 log10(Asignal / Anoise). The factor of 20 is used because power is proportional to the square of the amplitude (P ∝ A²). The logarithm property log(x²) = 2log(x) brings the '2' out front, making the multiplier 20 instead of 10.

Calculation Walkthrough

  • Power Example: If Signal Power is 2W and Noise Power is 0.1W, the ratio is 2/0.1 = 20. SNR(dB) = 10 * log10(20) ≈ 10 * 1.301 = 13.01 dB.
  • Amplitude Example: If Signal Voltage is 5V and Noise Voltage is 0.2V, the ratio is 5/0.2 = 25. SNR(dB) = 20 * log10(25) ≈ 20 * 1.398 = 27.96 dB.

Common Misconceptions and Best Practices

  • Confusing Power and Amplitude
  • Ignoring Units
  • What Constitutes a 'Good' SNR?
Understanding common pitfalls can help ensure you use SNR correctly.
Misconception: All SNR Calculations Use 10*log10
A frequent error is to always use the 10log10 formula. Remember to use 20log10 for amplitude measurements to get the correct dB value that corresponds to the underlying power ratio.
Best Practice: Keep Units Consistent
The SNR calculation is based on a ratio, so the absolute units cancel out. However, the signal and noise values must be in the same units for the ratio to be meaningful (e.g., Volts and Volts, not Volts and microvolts).
Context is Key for 'Good' SNR
A 'good' SNR is highly context-dependent. An SNR of 20 dB might be excellent for a wireless link but poor for high-fidelity audio. Always refer to the standards and requirements of your specific application.