{
    "name": "Stefan–Boltzmann Radiation Calculator",
    "url": "https://calculators.geekmidst.com/calculators/radiation-stefan-boltzmann-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/radiation-stefan-boltzmann-calculator.md",
    "category": "Science & engineering",
    "description": "Calculate net thermal radiation between a grey surface and large surroundings with Q = εσA(Ts⁴ − Tsur⁴), plus emitted power and radiative coefficient.",
    "summary": "Every surface radiates in proportion to the fourth power of its absolute temperature. The net exchange with large surroundings is εσA(T_s⁴ − T_sur⁴).",
    "also_called": [
        "Radiant heat calculator",
        "Stefan–Boltzmann law 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": "emissivity",
            "label": "Emissivity (ε)",
            "type": "number",
            "default": "0.9"
        },
        {
            "name": "area",
            "label": "Surface area",
            "type": "number",
            "default": "1.5",
            "unit": "m²"
        },
        {
            "name": "t_surface",
            "label": "Surface temperature",
            "type": "number",
            "default": "60",
            "unit": "°C"
        },
        {
            "name": "t_surroundings",
            "label": "Surroundings temperature",
            "type": "number",
            "default": "20",
            "unit": "°C"
        }
    ],
    "outputs": [
        {
            "key": "net_w",
            "label": "Net radiant heat loss",
            "format": "number"
        },
        {
            "key": "emitted_w",
            "label": "Emitted by the surface",
            "format": "number"
        },
        {
            "key": "absorbed_w",
            "label": "Absorbed from the surroundings",
            "format": "number"
        },
        {
            "key": "h_rad",
            "label": "Radiative heat transfer coefficient",
            "format": "number"
        }
    ],
    "formula": {
        "text": "Q̇ = ε × σ × A × (T_s⁴ − T_sur⁴);  h_rad = εσ(T_s + T_sur)(T_s² + T_sur²)",
        "variables": {
            "ε": "emissivity (0–1)",
            "σ": "Stefan–Boltzmann constant, 5.670374419 × 10⁻⁸ W/(m²·K⁴)",
            "A": "surface area",
            "T_s, T_sur": "absolute temperatures in K"
        }
    },
    "worked_example": {
        "inputs": {
            "emissivity": "0.9",
            "area": "1.5",
            "t_surface": "60",
            "t_surroundings": "20"
        },
        "steps": [
            "T_s = 333.15 K, T_sur = 293.15 K.",
            "Emitted = 0.9 × 5.670374419e-8 × 1.5 × 333.15⁴ = 942.99 W; absorbed = 0.9 × σ × 1.5 × 293.15⁴ = 565.33 W.",
            "Net = 942.99 − 565.33 = 377.65 W."
        ],
        "result": "A 1.5 m² painted surface at 60 °C in a 20 °C room loses about 378 W by radiation."
    },
    "interpretation": "Because of the fourth power, radiation dominates at high temperatures. The radiative coefficient lets you add radiation to convection: total h ≈ h_conv + h_rad.",
    "assumptions": [
        "Grey, diffuse surface that is small compared with surroundings at a uniform temperature.",
        "Emissivity equals absorptivity."
    ],
    "limitations": [
        "View factors between two finite surfaces are not included.",
        "Solar or other directed radiation is not included."
    ],
    "rules": null,
    "faqs": [
        {
            "question": "Why must temperatures be in kelvin?",
            "answer": "The law depends on T⁴ measured from absolute zero; the calculator converts your °C values for you."
        },
        {
            "question": "Does a shiny surface lose less heat?",
            "answer": "Yes. Low-emissivity surfaces such as polished metal or low-e glass radiate far less, which is why survival blankets are shiny."
        }
    ],
    "sources": [
        {
            "title": "NIST: fundamental physical constants (CODATA)",
            "url": "https://www.nist.gov/"
        }
    ],
    "related": [
        {
            "name": "Convection Heat Transfer Calculator",
            "url": "https://calculators.geekmidst.com/calculators/convection-heat-transfer-calculator"
        },
        {
            "name": "Conduction Heat Flow Calculator",
            "url": "https://calculators.geekmidst.com/calculators/conduction-heat-flow-calculator"
        },
        {
            "name": "Temperature Converter",
            "url": "https://calculators.geekmidst.com/calculators/temperature-converter"
        }
    ],
    "disclaimer": null,
    "publisher": "GM¹X CalcVerse"
}