The Stefan-Boltzmann constant (σ) in SI units defines the total radiant heat power emitted per unit surface area of a black body per unit of temperature to the fourth power. It is derived from fundamental constants: σ = 2π⁵k⁴ / (15h³c²).
| Unit Name | Symbol | Value of σ | Application |
|---|---|---|---|
| Watts per sq meter-Kelvin⁴Current | W/(m²·K⁴) | 5.6704 × 10⁻⁸ | SI |
| Ergs per sq cm-second-Kelvin⁴ | erg/(cm²·s·K⁴) | 5.6704 × 10⁻⁵ | CGS |
| BTU per hr-sq ft-Rankine⁴ | Btu/(hr·ft²·°R⁴) | 0.1714 × 10⁻⁸ | Imperial |
| Kilocalories per hr-sq m-Kelvin⁴ | kcal/(hr·m²·K⁴) | 4.882 × 10⁻⁸ | Thermochemical |
| Watts per sq cm-Kelvin⁴ | W/(cm²·K⁴) | 5.6704 × 10⁻¹² | Astronomical |
| Kilowatts per sq meter-Kelvin⁴ | kW/(m²·K⁴) | 5.6704 × 10⁻¹¹ | SI Derived |
In the centimeter-gram-second (CGS) system, the Stefan-Boltzmann constant is expressed in ergs. This unit is historically significant in astrophysics and is still used in classical physics literature and stellar structure calculations.
| Unit Name | Symbol | Value of σ | Application |
|---|---|---|---|
| Watts per sq meter-Kelvin⁴ | W/(m²·K⁴) | 5.6704 × 10⁻⁸ | SI |
| Ergs per sq cm-second-Kelvin⁴Current | erg/(cm²·s·K⁴) | 5.6704 × 10⁻⁵ | CGS |
| BTU per hr-sq ft-Rankine⁴ | Btu/(hr·ft²·°R⁴) | 0.1714 × 10⁻⁸ | Imperial |
| Kilocalories per hr-sq m-Kelvin⁴ | kcal/(hr·m²·K⁴) | 4.882 × 10⁻⁸ | Thermochemical |
| Watts per sq cm-Kelvin⁴ | W/(cm²·K⁴) | 5.6704 × 10⁻¹² | Astronomical |
| Kilowatts per sq meter-Kelvin⁴ | kW/(m²·K⁴) | 5.6704 × 10⁻¹¹ | SI Derived |
The imperial form of the Stefan-Boltzmann constant uses British Thermal Units per hour per square foot per Rankine to the fourth power. It is essential for US-based HVAC design, furnace engineering, and industrial heat loss calculations.
| Unit Name | Symbol | Value of σ | Application |
|---|---|---|---|
| Watts per sq meter-Kelvin⁴ | W/(m²·K⁴) | 5.6704 × 10⁻⁸ | SI |
| Ergs per sq cm-second-Kelvin⁴ | erg/(cm²·s·K⁴) | 5.6704 × 10⁻⁵ | CGS |
| BTU per hr-sq ft-Rankine⁴Current | Btu/(hr·ft²·°R⁴) | 0.1714 × 10⁻⁸ | Imperial |
| Kilocalories per hr-sq m-Kelvin⁴ | kcal/(hr·m²·K⁴) | 4.882 × 10⁻⁸ | Thermochemical |
| Watts per sq cm-Kelvin⁴ | W/(cm²·K⁴) | 5.6704 × 10⁻¹² | Astronomical |
| Kilowatts per sq meter-Kelvin⁴ | kW/(m²·K⁴) | 5.6704 × 10⁻¹¹ | SI Derived |
Expressed in kilocalories per hour per square meter per Kelvin to the fourth power, this form is commonly found in European industrial engineering, particularly in furnace design, kiln calculations, and high-temperature process engineering.
| Unit Name | Symbol | Value of σ | Application |
|---|---|---|---|
| Watts per sq meter-Kelvin⁴ | W/(m²·K⁴) | 5.6704 × 10⁻⁸ | SI |
| Ergs per sq cm-second-Kelvin⁴ | erg/(cm²·s·K⁴) | 5.6704 × 10⁻⁵ | CGS |
| BTU per hr-sq ft-Rankine⁴ | Btu/(hr·ft²·°R⁴) | 0.1714 × 10⁻⁸ | Imperial |
| Kilocalories per hr-sq m-Kelvin⁴Current | kcal/(hr·m²·K⁴) | 4.882 × 10⁻⁸ | Thermochemical |
| Watts per sq cm-Kelvin⁴ | W/(cm²·K⁴) | 5.6704 × 10⁻¹² | Astronomical |
| Kilowatts per sq meter-Kelvin⁴ | kW/(m²·K⁴) | 5.6704 × 10⁻¹¹ | SI Derived |
Scaled to square centimeters for convenience in stellar physics, this representation is used when calculating the luminosity and effective temperature of stars, where surface areas are often expressed in cm² in CGS-adjacent astronomical conventions.
| Unit Name | Symbol | Value of σ | Application |
|---|---|---|---|
| Watts per sq meter-Kelvin⁴ | W/(m²·K⁴) | 5.6704 × 10⁻⁸ | SI |
| Ergs per sq cm-second-Kelvin⁴ | erg/(cm²·s·K⁴) | 5.6704 × 10⁻⁵ | CGS |
| BTU per hr-sq ft-Rankine⁴ | Btu/(hr·ft²·°R⁴) | 0.1714 × 10⁻⁸ | Imperial |
| Kilocalories per hr-sq m-Kelvin⁴ | kcal/(hr·m²·K⁴) | 4.882 × 10⁻⁸ | Thermochemical |
| Watts per sq cm-Kelvin⁴Current | W/(cm²·K⁴) | 5.6704 × 10⁻¹² | Astronomical |
| Kilowatts per sq meter-Kelvin⁴ | kW/(m²·K⁴) | 5.6704 × 10⁻¹¹ | SI Derived |