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Stefan-Boltzmann Law Radiated Power Calculator

All matter at a temperature above absolute zero continuously radiates energy as electromagnetic waves governed by the Stefan-Boltzmann law (P = ε·σ·A·T⁴).

Operating surface temperature in Celsius (converted internally to Kelvin).

Effective radiating geometric surface area in square meters.

Surface emissivity between 0 and 1.0 (blackbody = 1.0; oxidized metal/human skin ≈ 0.9–0.98; polished aluminum ≈ 0.05).

Temperature of the enclosing ambient surroundings in Celsius.

Calculated Result
1.23 kW

Net Radiated Thermal Power

Gross Emitted Power

1,978.9 W

Absorbed Ambient Power

753.8 W

Emissive Flux

989.4 W/m²

Surface Emissivity

0.9

Calculation Breakdown

  1. Absolute Kelvin Thermodynamic TemperaturesT_s = 373.15 K, \quad T_a = 293.15 KTs=Ts(°C)+273.15,Ta=Ta(°C)+273.15T_s = T_s(°C) + 273.15, \quad T_a = T_a(°C) + 273.15
  2. Stefan-Boltzmann Fourth-Power Emission1,978.87 Watts (Emissive Flux: 989.4 W/m²)Pemit=εσATs4P_{\text{emit}} = \varepsilon \sigma A T_s^4
  3. Ambient Back-Radiation Absorption753.78 WattsPabs=εσATa4P_{\text{abs}} = \varepsilon \sigma A T_a^4
  4. Net Radiation Heat Transfer Rate1,225.09 Watts (1.225 kW)Pnet=εσA(Ts4−Ta4)P_{\text{net}} = \varepsilon \sigma A (T_s^4 - T_a^4)

Radiated Power vs Surface Temperature (2 m², ε = 0.9, Tamb = 20°C)

Interactive visualization based on your current inputs

Power (W)
0.02.5k4.9k7.4k9.8k50°C100°C150°C200°C300°CTemperature (°C)Net Power (W)

What Is the Stefan-Boltzmann Law Radiated Power Calculator?

The Stefan-Boltzmann Law describes the total radiant heat power emitted by a body as electromagnetic waves across all wavelengths.

Formulated experimentally by Jožef Stefan in 1879 and derived theoretically by Ludwig Boltzmann in 1884, it forms the bedrock of thermal radiative transfer.

How Does the Stefan-Boltzmann Law Radiated Power Calculator Work?

Every object radiates heat proportionally to its surface area, emissivity factor, and the fourth power of absolute temperature (T⁴).

At the same time, the object absorbs radiation from surrounding walls at temperature T_ambient.

The difference between emitted and absorbed power yields the net radiative heat loss.

Stefan-Boltzmann Law Radiated Power Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

Pnet=εσA(Ts4−Ta4)P_{\text{net}} = \varepsilon \sigma A \left(T_s^4 - T_a^4\right)

The Stefan-Boltzmann constant σ couples temperature to radiant electromagnetic flux. Temperatures must always be evaluated in absolute Kelvin.

How to Use the Stefan-Boltzmann Law Radiated Power Calculator

  1. Enter the emitter surface temperature in Celsius.
  2. Enter the surface area in square meters.
  3. Select emissivity (0.95 for rubber, paint, glass, concrete; 0.1 for polished metals).
  4. Provide ambient environmental enclosure temperature.

Step-by-Step Example Calculation

100°C Industrial Radiator Panel

Input Values:

tempSurface:100
area:2
emissivity:0.9
tempAmbient:20
Worked Steps: A 2 m² panel at 100°C (373.15 K) emits 1974.7 W and absorbs 753.5 W from 20°C surroundings, shedding a net 1221.2 W of thermal radiation.

Understanding Your Result

Net Radiated Power: Net heat rate leaving the object (Watts or kW).

Emissive Power: Radiant flux density per unit area (W/m²).

Emitted vs Absorbed: Breakdown of gross outward and inward radiation.

Factors That Affect the Result

  • Temperature: Fourth-power dependence makes temperature by far the most potent variable.
  • Emissivity: Direct linear scaling factor.

When Should You Use This Calculator?

  • Spacecraft thermal control and radiator sizing.
  • Industrial furnaces, boiler firebox design, and electronic heat sinks.

Assumptions & Limitations

  • Assumes a diffuse greybody surface where emissivity equals absorptivity (Kirchhoff’s law).
  • Assumes the object is completely enclosed by large isothermal surroundings.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Standard radiative heat transfer formulation utilizing CODATA Stefan-Boltzmann constant.

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