{
    "name": "Signal-to-Noise Ratio Calculator",
    "url": "https://calculators.geekmidst.com/calculators/signal-to-noise-ratio-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/signal-to-noise-ratio-calculator.md",
    "category": "Science & engineering",
    "description": "Calculate signal-to-noise ratio in decibels from signal and noise powers, RMS voltages or dBm levels, with the equivalent power and amplitude ratios.",
    "summary": "SNR compares the wanted signal with the background noise. In decibels it is 10 log₁₀ of the power ratio, or 20 log₁₀ of the RMS voltage ratio.",
    "also_called": [
        "SNR calculator"
    ],
    "applies_to": "Worldwide",
    "last_updated": "2026-10-29",
    "computation": "Results are computed in the visitor’s browser on the HTML page. This API describes the calculator; it does not compute results.",
    "inputs": [
        {
            "name": "type",
            "label": "Values are",
            "type": "segmented",
            "default": "power",
            "options": {
                "power": "Powers",
                "amplitude": "RMS voltages",
                "dbm": "Levels in dBm"
            }
        },
        {
            "name": "signal",
            "label": "Signal",
            "type": "number",
            "default": "10"
        },
        {
            "name": "noise",
            "label": "Noise",
            "type": "number",
            "default": "0.01"
        }
    ],
    "outputs": [
        {
            "key": "snr_db",
            "label": "SNR",
            "format": "number"
        },
        {
            "key": "power_ratio",
            "label": "Power ratio",
            "format": "multiple"
        },
        {
            "key": "amplitude_ratio",
            "label": "Amplitude (voltage) ratio",
            "format": "multiple"
        }
    ],
    "formula": {
        "text": "SNR(dB) = 10 log₁₀(P_s ÷ P_n) = 20 log₁₀(V_s ÷ V_n);  from dBm: SNR = L_s − L_n",
        "variables": {
            "P_s, P_n": "signal and noise power",
            "V_s, V_n": "signal and noise RMS voltage across the same impedance",
            "L_s, L_n": "signal and noise levels in dBm"
        }
    },
    "worked_example": {
        "inputs": {
            "type": "power",
            "signal": "10",
            "noise": "0.01"
        },
        "steps": [
            "Power ratio = 10 ÷ 0.01 = 1,000.",
            "SNR = 10 × log₁₀(1,000) = 10 × 3 = 30 dB."
        ],
        "result": "A 10 mW signal over 0.01 mW of noise has an SNR of 30 dB, a power ratio of 1,000."
    },
    "interpretation": "Every 10 dB is a further factor of 10 in power. As a rough guide, voice links need 10–20 dB, CD audio has a theoretical 96 dB, and a positive SNR at least means the signal is stronger than the noise.",
    "assumptions": [
        "Signal and noise are measured over the same bandwidth; voltages are RMS across the same impedance."
    ],
    "limitations": [
        "If the measured “signal” includes noise (signal + noise), the true SNR is slightly lower, noticeably so below about 10 dB."
    ],
    "rules": null,
    "faqs": [
        {
            "question": "Why 20 log for voltage?",
            "answer": "Power is proportional to voltage squared, and log(V²) = 2 log V, so 10 log of the power ratio equals 20 log of the voltage ratio."
        },
        {
            "question": "Can SNR be negative?",
            "answer": "Yes. Negative SNR means the noise is stronger than the signal; spread-spectrum systems such as GPS still work below 0 dB."
        }
    ],
    "sources": [],
    "related": [
        {
            "name": "Decibel to Power Ratio Converter",
            "url": "https://calculators.geekmidst.com/calculators/decibels-power-ratio-calculator"
        },
        {
            "name": "Nyquist Rate Calculator",
            "url": "https://calculators.geekmidst.com/calculators/sampling-nyquist-rate-calculator"
        },
        {
            "name": "FFT Frequency Bin Calculator",
            "url": "https://calculators.geekmidst.com/calculators/fourier-frequency-bin-calculator"
        }
    ],
    "disclaimer": null,
    "publisher": "GM¹X CalcVerse"
}