Signal to Noise Ratio Calculator
Calculate the signal-to-noise ratio (SNR) in decibels from signal and noise power levels. Enter values in milliwatts or decibels to determine signal quality. See also our Decibel Calculator and Sound Converter.
How to Calculate Signal to Noise Ratio
Signal-to-noise ratio (SNR or S/N) is a measure that compares the level of a desired signal to the level of background noise. It is one of the most important parameters in communications, audio engineering, electronics, and scientific measurement. A higher SNR indicates a cleaner signal with less noise contamination, while a lower SNR means the signal is harder to distinguish from the noise floor.
To calculate SNR, divide the signal power by the noise power and express the result in decibels. When both values are in linear units (watts or milliwatts), use SNR = 10 × log₁₀(Ps/Pn). When both values are already in decibels, simply subtract: SNR = Signal(dB) - Noise(dB). The result tells you how many decibels the signal is above the noise floor.
In practice, SNR determines the quality and reliability of a communication link, the fidelity of an audio recording, the sensitivity of a scientific instrument, and the bit error rate of a digital system. Shannon's theorem relates SNR directly to channel capacity: C = B × log₂(1 + SNR), showing that higher SNR allows higher data rates for a given bandwidth.
SNR Formulas
Basic SNR (from power):
SNR(dB) = 10 × log₁₀(P_signal / P_noise)
SNR from dB values:
SNR(dB) = Signal(dBm) - Noise(dBm)
SNR from voltage (same impedance):
SNR(dB) = 20 × log₁₀(V_signal / V_noise)
Shannon Capacity:
C = B × log₂(1 + SNR_linear)
C = channel capacity (bits/s)
B = bandwidth (Hz)
Noise Figure:
NF(dB) = SNR_input(dB) - SNR_output(dB)
Example Calculation
A wireless receiver measures a signal power of 100 mW and a noise power of 1 mW. Calculate the SNR:
Given: P_signal = 100 mW, P_noise = 1 mW
SNR = 10 × log₁₀(100/1) = 10 × log₁₀(100)
SNR = 10 × 2 = 20 dB
Linear ratio: 100:1
In dBm: Signal = 10×log₁₀(100) = 20 dBm
Noise = 10×log₁₀(1) = 0 dBm
SNR = 20 - 0 = 20 dB ✓
Shannon capacity (10 MHz bandwidth):
C = 10×10⁶ × log₂(1+100) = 66.6 Mbps
SNR Quality Reference Table
| SNR (dB) | Linear Ratio | Quality |
|---|---|---|
| 0 dB | 1 | Signal equals noise |
| 3 dB | 2 | Signal is 2× noise |
| 6 dB | 4 | Minimum for digital comm |
| 10 dB | 10 | Acceptable voice quality |
| 15 dB | 31.6 | Good AM radio |
| 20 dB | 100 | Good quality audio |
| 30 dB | 1000 | Very good quality |
| 40 dB | 10000 | Excellent / FM radio |
| 50 dB | 100000 | High-fidelity audio |
| 60 dB | 1000000 | CD quality audio |
| 80 dB | 100000000 | Professional studio |
| 96 dB | 4×10⁹ | 16-bit digital audio |
Frequently Asked Questions
What is signal-to-noise ratio?
Signal-to-noise ratio (SNR) is the ratio of desired signal power to unwanted noise power, usually expressed in decibels. It quantifies how much a signal has been corrupted by noise. An SNR of 0 dB means signal and noise are equal; positive values mean the signal dominates; negative values mean noise dominates. Higher SNR always means better signal quality.
What is a good SNR value?
It depends on the application. For Wi-Fi: 20+ dB is good, 40+ dB is excellent. For audio: 60+ dB is acceptable, 90+ dB is high-fidelity. For digital communications: the required SNR depends on the modulation scheme — BPSK needs about 10 dB for low error rates, while 256-QAM needs 30+ dB. Generally, more complex signals require higher SNR.
How does SNR relate to bit error rate?
Higher SNR means lower bit error rate (BER) in digital communications. The exact relationship depends on the modulation scheme. For BPSK: BER ≈ 0.5 × erfc(√(Eb/N0)), where Eb/N0 is the energy per bit to noise density ratio (related to SNR). Each modulation scheme has a characteristic BER vs SNR curve that determines the minimum SNR for reliable communication.
What is noise figure and how does it relate to SNR?
Noise figure (NF) measures how much a device degrades the SNR: NF = SNR_in / SNR_out (in linear) or NF(dB) = SNR_in(dB) - SNR_out(dB). An ideal noiseless device has NF = 0 dB. Real amplifiers have NF of 1-10 dB. In a receiver chain, the first amplifier's noise figure dominates the overall system noise figure (Friis formula).
How can I improve SNR?
Increase signal power (higher transmit power, better antenna gain), reduce noise (better shielding, lower noise figure amplifiers, cooling), reduce bandwidth (narrower filters pass less noise), use signal averaging (N averages improve SNR by √N), use error-correcting codes, or use spread-spectrum techniques. The best approach depends on the specific constraints of your system.
What is the difference between SNR and SINAD?
SNR compares signal to noise only, while SINAD (Signal to Noise and Distortion) includes harmonic distortion in the denominator: SINAD = Signal / (Noise + Distortion). SINAD is always less than or equal to SNR. For ADCs, SINAD determines the effective number of bits (ENOB): ENOB = (SINAD - 1.76) / 6.02. SINAD is a more complete measure of signal quality.
SNR in Different Applications
In wireless communications, SNR determines the maximum data rate achievable over a channel (Shannon limit). In medical imaging (MRI, CT), SNR determines image quality and diagnostic capability. In photography, SNR relates to ISO sensitivity and image noise. In financial analysis, SNR concepts are applied to distinguish market signals from random fluctuations. In radar systems, SNR determines detection range and probability of detection versus false alarm rate.
Thermal Noise and Noise Floor
The fundamental noise limit in electronic systems is thermal noise (Johnson-Nyquist noise), generated by random thermal motion of electrons. The thermal noise power is: P_noise = kTB, where k is Boltzmann's constant (1.38×10⁻²³ J/K), T is temperature in Kelvin, and B is bandwidth in Hz. At room temperature (290K), the noise power spectral density is -174 dBm/Hz. This sets the absolute minimum noise floor for any electronic system and determines the maximum achievable SNR for a given signal power and bandwidth.