Signal-to-Noise Ratio (SNR) Calculator
Calculate SNR in decibels from power or amplitude ratios, or convert dB back to a linear ratio.
Includes quality tiers for audio, RF, and digital systems.
What signal-to-noise ratio measures
Signal-to-noise ratio (SNR) is the ratio of the desired signal power (or amplitude) to the background noise power, almost always expressed in decibels. A higher SNR means the signal is clearer above the noise floor. A lower SNR means the noise is eating into the signal.
Two equivalent formulas exist depending on whether you have power or amplitude values:
Power-based: SNR (dB) = 10 × log₁₀(P_signal / P_noise) Amplitude-based: SNR (dB) = 20 × log₁₀(A_signal / A_noise)
The factor changes from 10 to 20 because power scales with the square of amplitude (P ∝ A²), and log(A²) = 2 log(A). When in doubt, ask whether you have power values (watts, milliwatts) or amplitude values (volts, microvolts, sound pressure in pascals). For voltage measurements, use the amplitude formula.
Why decibels
Decibels are logarithmic, which is exactly what you want for SNR. Real-world signal-to-noise ratios span enormous ranges, from less than 10 for marginal voice communication to over 100 for studio digital audio. A logarithmic scale compresses these into a manageable 0 to 120 dB range. Each 10 dB step represents a 10× change in power ratio, and each 20 dB step represents a 10× change in amplitude ratio.
This compression is not just convenient. It also matches human perception. The ear responds logarithmically to sound intensity, so a 10 dB change feels roughly like a doubling of perceived loudness regardless of absolute level. SNR in decibels lines up with how engineers and listeners actually experience signal quality.
Quality tiers by application
| SNR (dB) | Quality | Typical application |
|---|---|---|
| > 90 dB | Excellent | 16-bit digital audio (CD: ~96 dB), professional studio recording |
| 60 to 90 dB | Very good | Hi-fi audio, FM broadcast, broadcast TV (audio), good telephone quality |
| 40 to 60 dB | Good | AM radio, telephone voice, video Internet streams, hearing aids |
| 20 to 40 dB | Fair | Marginal voice quality, weak FM reception, noisy environments |
| 10 to 20 dB | Poor | Voice intelligibility threshold (typical minimum ~12 dB) |
| < 10 dB | Unusable | Signal almost lost in noise; modern digital systems drop the connection here |
| 0 dB | Signal equals noise | The point where signal and noise have equal power |
| Negative dB | Noise exceeds signal | Possible only in heavy interference or completely lost signal conditions |
Worked example: hi-fi amplifier specification
A hi-fi amplifier datasheet lists an SNR of 105 dB (A-weighted, ref 1 W into 8 Ω). What does that mean in linear ratio?
105 dB = 10 × log₁₀(ratio), so ratio = 10^(105/10) = 10^10.5 ≈ 3.16 × 10^10
The signal is more than 30 billion times stronger in power than the noise floor. For voltage at the amplifier output, the ratio is the square root of that: about 178,000 times. At 1 W output, the noise floor is around 1 W / (3.16 × 10^10) ≈ 32 picowatts, or about 16 microvolts across 8 Ω. That is well below the threshold of human hearing in any normal listening environment.
Worked example: noise figure of a receiver
A radio receiver has signal input of 0.5 microvolts RMS and a noise floor of 0.1 microvolts RMS (at the input, referred to 50 Ω). The amplitude-based SNR:
SNR (dB) = 20 × log₁₀(0.5 / 0.1) = 20 × log₁₀(5) = 20 × 0.699 = 13.98 dB
Just above the voice intelligibility threshold. Adding a low-noise preamplifier could reduce the noise floor and pull this up to a comfortable 25 to 30 dB.
Where SNR shows up
In analog electronics, SNR limits how much signal detail you can recover before noise dominates. Op-amp datasheets list input noise voltage; sensor datasheets list noise equivalent power (NEP). Adding amplifier stages typically does not help SNR much, because each stage adds its own noise. The first stage (low-noise amplifier, LNA) sets the SNR for the entire chain through the Friis noise figure formula.
In digital communications, SNR determines the maximum data rate via the Shannon-Hartley theorem: C = B × log₂(1 + SNR), where C is channel capacity in bits per second and B is bandwidth in hertz. Doubling SNR adds roughly 1 bit per symbol of capacity. This is why 5G and Wi-Fi 6 push hard on improving SNR through beamforming, MIMO, and OFDM (multiple subcarriers).
In digital audio, SNR is fundamentally limited by the bit depth. Each additional bit gives about 6 dB more dynamic range. 16-bit audio yields about 96 dB SNR (the CD standard). 24-bit audio yields about 144 dB SNR, beyond the dynamic range of human hearing or any realistic recording environment, so the extra bits exist for headroom in mixing, not for final playback.
In ADC and DAC datasheets, related figures include SINAD (signal to noise and distortion), THD+N (total harmonic distortion plus noise), and ENOB (effective number of bits). ENOB = (SINAD − 1.76) / 6.02 converts a measured SINAD in dB into an equivalent perfect-converter bit depth.
Common misunderstandings
People sometimes assume a higher SNR is always better. For listening, yes; for measurement, it depends. A 100 dB SNR sensor might be wasted on a noisy environmental measurement where the source has 30 dB intrinsic variability. The bottleneck is wherever the noise is largest, not where it is smallest.
People also confuse SNR with signal-to-interference ratio (SIR) or signal to interference plus noise ratio (SINR). SNR considers only random background noise (thermal Johnson noise, shot noise, etc.). SIR adds deterministic interfering signals (other transmitters, crosstalk). SINR adds both. Wi-Fi and cellular link-quality reports often use SINR rather than SNR for this reason.
Quick conversions
To convert SNR in dB back to a linear power ratio: ratio = 10^(SNR/10). To a voltage ratio: ratio = 10^(SNR/20). To verify a measurement makes sense, the linear ratio should sit comfortably between 1 (0 dB, signal equals noise) and 10^12 (120 dB, signal one trillion times noise, an extraordinary specification only seen in laboratory-grade instruments).