Signal-to-Noise Ratio (SNR) Calculator
Calculate signal-to-noise ratio from signal and noise power (or voltage). Convert dB ↔ ratio. Estimate effective bits (ENOB) and link budget margin.
How to Use
- Enter signal and noise levels as power (W) or voltage (V).
- SNR is computed in dB; for ADC inputs this converts to ENOB.
- Higher SNR means cleaner signal; audio CD-quality ≈ 96 dB.
- For systems with fixed-bit ADCs, SNR is often limited by analog noise rather than resolution.
Show Work
Formulas
History of Signal-to-Noise Analysis
The concept of signal-to-noise ratio became quantitative with Harry Nyquist\'s 1928 paper describing thermal ("Johnson") noise in resistors — a fundamental noise floor set by the random thermal motion of electrons. John B. Johnson at Bell Labs measured this noise that same year; the formula Vn = √(4kTRB) has borne his name ever since. This established a physical limit below which no amount of electronic cleverness could reduce noise.
Claude Shannon\'s 1948 paper "A Mathematical Theory of Communication" made SNR the central parameter of information theory. His capacity formula C = B·log2(1 + SNR) gives the maximum bits-per-second achievable through a noisy channel — a direct trade-off between bandwidth and SNR. Modern LTE/5G radio systems push near this Shannon limit through sophisticated modulation and forward-error correction.
Practical SNR improvement techniques span decades: careful PCB layout and shielding (1960s), correlated double sampling for CCD imagers (1970s), digital averaging (always, but easier with DSP from the 1980s), chopper-stabilized amplifiers for µV-level offsets (1980s), and lock-in amplification for sub-noise-floor coherent signals (since the 1940s). Modern instrumentation — gravitational-wave detectors, radio astronomy, quantum-noise-limited optical sensors — approaches the thermal noise floor within a few dB.
About This Calculator
Enter signal and noise levels as either power (watts) or voltage. The tool returns SNR in dB, the linear ratio, ENOB (effective number of bits for an ADC system), and a categorical rating. Presets cover common benchmarks: 20 dB (marginal), 40 dB (adequate), 96 dB (CD audio), 120 dB (studio-quality).
For RF and telecom, noise is usually quoted as a power (dBm or W); for analog audio and instrumentation, voltage (µV RMS) is more common. Both are handled here — pick the measurement type that matches your data and the tool returns consistent dB. Everything runs client-side.
Frequently Asked Questions
What is SNR?
Ratio of signal to noise amplitude or power, expressed in dB. Higher = cleaner signal. An audiophile headphone amp might have 120 dB SNR; a cheap radio 40 dB. Tells you how much fine detail survives in a noisy environment.
Power vs voltage SNR?
Both give the same dB value: P_ratio = 10·log(Ps/Pn), V_ratio = 20·log(Vs/Vn). Voltages use 20× because P ∝ V². Either works — pick whichever matches your measurements.
What's ENOB?
Effective Number Of Bits. A 12-bit ADC has 72 dB theoretical SNR; if real SNR is 60 dB, ENOB ≈ 10 bits. ENOB = (SNR_dB − 1.76) / 6.02. Tells you the effective resolution after noise.
What SNR do I need?
Depends on the application. Audio: CD is 96 dB, high-end is 120+. Vision sensors: 40-60 dB. Scientific instrumentation: 100+ dB. ADC datasheets list SNR at specific input amplitudes and frequencies.
How do I improve SNR?
Increase signal (if possible) or reduce noise. For noise: shielding, better grounding, lower-noise amplifiers, careful layout, cooling, averaging. Often easier to reduce noise than to boost signal.
Common Use Cases
Audio Recording
Pro studio mic + preamp: 120 dB SNR. Voice recording has 50-60 dB SNR naturally (noise floor relative to max level).
RF Link Budget
If received signal is −80 dBm and noise floor is −110 dBm, SNR = 30 dB — good for digital modulation.
ADC Performance
16-bit ADC with 80 dB SNR has ENOB = 13 bits. Noise floor dominates the lower 3 bits.
Thermal Noise
Resistor Johnson noise: 4kT·R·Δf. A 1 MΩ resistor at room temperature, 10 kHz BW: ~13 µV RMS.
Shannon Capacity
Channel capacity = BW × log₂(1 + SNR). Higher SNR = more bits per second possible on a given bandwidth.
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