Stefan-Boltzmann Law Calculator
Calculate thermal radiation power using the Stefan-Boltzmann law for blackbody and real surface radiation
Calculate Using Stefan-Boltzmann Law
Absolute temperature of the radiating surface
Surface area of the radiating object
Emissivity ratio (0-1, where 1 = perfect blackbody)
Stefan-Boltzmann Law Results
Example: Solar Radiation Calculation
Solar Parameters
Surface Temperature: ~5778 K (5505°C)
Solar Radius: 6.96 × 10⁸ m
Surface Area: 4π × R² = 6.09 × 10¹⁸ m²
Emissivity: ~1 (near perfect blackbody)
Calculation
P = σ × ε × A × T⁴
P = (5.67×10⁻⁸) × 1 × (6.09×10¹⁸) × (5778)⁴
P = (5.67×10⁻⁸) × (6.09×10¹⁸) × (1.11×10¹⁵)
Solar Luminosity ≈ 3.83 × 10²⁶ W
Material Emissivity Values
Physical Constants
Temperature Examples
Room Temperature
~295 K (22°C, 72°F)
Incandescent Bulb
~2500 K (2227°C)
Sun Surface
~5778 K (5505°C)
Hot Blue Star
~30000 K (29727°C)
Understanding the Stefan-Boltzmann Law
What is the Stefan-Boltzmann Law?
The Stefan-Boltzmann law describes the power radiated from a blackbody in terms of its temperature. It states that the total energy radiated per unit surface area of a blackbody per unit time is proportional to the fourth power of the blackbody's temperature.
Key Applications
- •Stellar astronomy and luminosity calculations
- •Thermal engineering and heat transfer
- •Climate science and Earth's energy balance
- •Industrial furnace and oven design
Mathematical Formula
P = σ × ε × A × T⁴
- P: Total radiated power (Watts)
- σ: Stefan-Boltzmann constant (5.67×10⁻⁸ W/(m²·K⁴))
- ε: Emissivity (0 ≤ ε ≤ 1)
- A: Surface area (m²)
- T: Absolute temperature (Kelvin)
Important: Temperature must be in Kelvin for accurate calculations. The fourth power relationship means small temperature changes result in large power changes.
Understanding Emissivity
Emissivity (ε) is a measure of how efficiently a surface emits thermal radiation compared to a perfect blackbody. It ranges from 0 (perfect reflector) to 1 (perfect blackbody emitter). Real materials have emissivity values between these extremes, depending on their surface properties, temperature, and wavelength.
High Emissivity (ε > 0.8)
Materials that are good thermal radiators: carbon black, human skin, water, concrete
Medium Emissivity (0.3 < ε < 0.8)
Materials with moderate thermal radiation: glass, anodized aluminum, oxidized metals
Low Emissivity (ε < 0.3)
Highly reflective materials: polished metals, mirrors, shiny surfaces