Enter your signal and noise values to get instant results in both linear and decibel forms.
SNR (Linear Ratio)
100.00
SNR (Decibels)
20.00 dB
What is Signal-to-Noise Ratio (SNR)?
Signal-to-Noise Ratio (SNR) is a fundamental metric used in science and engineering to compare the level of a desired signal to the level of background noise. It is defined as the ratio of signal power to noise power, often expressed in decibels (dB). A higher SNR indicates a clearer, higher-quality signal, while a lower SNR suggests that the signal is being obscured by noise.
Common SNR Formulas
The formula you use depends on the type of signal you are measuring (power vs. voltage).
Linear Ratio Formula
This is the simplest form, expressing the ratio directly.
$$ SNR = P_{signal} / P_{noise} $$
Decibel (dB) Formula (Power)
Use this formula when working with power measurements (e.g., Watts).
$$ SNR(dB) = 10 \cdot \log_{10}(P_{signal} / P_{noise}) $$
Decibel (dB) Formula (Voltage)
Use this formula for voltage measurements (e.g., Volts), as power is proportional to voltage squared.
$$ SNR(dB) = 20 \cdot \log_{10}(V_{signal} / V_{noise}) $$
Where is SNR Used?
- Audio Engineering: Used to measure the quality of audio recordings and sound systems. A high SNR means less hiss and background hum.
- Digital Imaging: In photography and medical imaging, SNR measures the quality of a sensor's output. A higher SNR results in a clearer, less grainy image.
- Telecommunications: Used to determine the reliability of a signal transmitted over a network. A high SNR is crucial for stable Wi-Fi, radio, and cellular connections.
- Scientific Measurement: Used to evaluate the precision of lab instruments and experiments by quantifying how much of the measured value is true signal vs. random fluctuation.
What is a Good SNR?
The definition of a "good" SNR is highly dependent on the application. Here are some common benchmarks:
| Application | SNR Range (dB) | Interpretation |
|---|---|---|
| Wireless Communications | 10-15 dB | Poor/Unreliable connection |
| 25-40 dB | Good/Stable connection | |
| High-fidelity Audio | > 90 dB | Excellent, professional quality |
| Digital Photography | ~ 30 dB | Average quality |
| > 40 dB | Excellent quality, low noise |
Common Mistakes & Pitfalls
- Units Mismatch: A common error is using different units for the signal and noise values. Always ensure both values are in the same units (e.g., Watts and Watts, not Watts and milliwatts) before calculating.
- Using the Wrong Formula: Remember that the decibel formulas for power and voltage are different. Power calculations use
10 * log10, while voltage calculations use20 * log10. - Ignoring Hidden Noise Sources: Many systems have multiple noise sources (e.g., thermal noise, shot noise). Failing to account for all of them will result in an inaccurate SNR value.
