Signal-to-Noise Ratio
SNR = 10 × log₁₀(Ps/Pn)
Quick answer
This calculator solves SNR = 10 × log₁₀(Psignal / Pnoise) for SNR. With Signal Power 10 W, Noise Power 100 µW, the result is 50 dB. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Signal-to-noise ratio measures how much stronger the desired signal is compared to the background noise, expressed in decibels. Higher SNR means cleaner signal quality. In digital communications, minimum SNR thresholds determine the achievable data rate and modulation scheme. In audio, SNR defines the dynamic range available. Thermal noise (Johnson-Nyquist noise) in resistors sets a fundamental noise floor: P_noise = kTB, where k is Boltzmann's constant, T is temperature in Kelvin, and B is bandwidth in Hz.
Variables
- SNR — Signal-to-noise ratio (dB)
- Psignal — Signal power (W)
- Pnoise — Noise power (W)
Practical Notes
Typical SNR requirements: telephone quality audio 30 dB, CD quality audio 96 dB, WiFi (OFDM 64-QAM) 25 dB, cellular LTE 15-25 dB depending on modulation. Op-amp circuits typically achieve 60-100 dB SNR. To improve SNR, either increase signal power or reduce noise bandwidth through filtering.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| SNR | SNR | dB | dB |
| Ps | Signal Power | W | µW, mW, W, kW |
| Pn | Noise Power | µW | µW, mW, W, kW |
Step by step
- 1. What you know: Signal Power 10 W, Noise Power 100 µW
- 2. The relation: SNR = 10 × log₁₀(Psignal / Pnoise)
- 3. Substitute: Ps = 10 W, Pn = 100 µW
- 4. Result: SNR = 50 dB
Worked examples
Minimum range
Given: Signal Power 10 mW, Noise Power 0.1 µW
Result: SNR = 50 dB
Low range
Given: Signal Power 100 mW, Noise Power 1 µW
Result: SNR = 50 dB
Typical
Given: Signal Power 10 W, Noise Power 100 µW
Result: SNR = 50 dB
High range
Given: Signal Power 1 kW, Noise Power 0.5 mW
Result: SNR = 63.01 dB
Maximum range
Given: Signal Power 10 kW, Noise Power 5 mW
Result: SNR = 63.01 dB
Solving for each variable
Solve for SNR
Signal Power 10 mW, Noise Power 0.1 µW → 50 dB
Solve for Signal Power
SNR 0.3 dB, Noise Power 0.1 µW → 0.1072 µW
Solve for Noise Power
SNR 0.3 dB, Signal Power 10 mW → 9.333 mW
How SNR changes with Signal Power
| Signal Power (input) | SNR (result) |
|---|---|
| 1 W | 40 dB |
| 2.5 W | 43.98 dB |
| 5 W | 46.99 dB |
| 7.5 W | 48.75 dB |
| 10 W | 50 dB |
| 15 W | 51.76 dB |
| 20 W | 53.01 dB |
| 40 W | 56.02 dB |
| 70 W | 58.45 dB |
| 100 W | 60 dB |
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<p><a href="https://vbatpower.com/formulas/snr/">Signal-to-Noise Ratio</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Signal-to-Noise Ratio?
Use SNR = 10 × log₁₀(Psignal / Pnoise). With Signal Power 10 W, Noise Power 100 µW, SNR works out to 50 dB.
What is the formula for Signal-to-Noise Ratio?
The formula is SNR = 10 × log₁₀(Psignal / Pnoise). Signal-to-noise ratio measures how much stronger the desired signal is compared to the background noise, expressed in decibels.
How do you find Signal Power when you know the other values?
Rearrange for Signal Power: with SNR 0.3 dB, Noise Power 0.1 µW, Signal Power is 0.1072 µW.
How do you find Noise Power when you know the other values?
Rearrange for Noise Power: with SNR 0.3 dB, Signal Power 10 mW, Noise Power is 9.333 mW.
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