In this Stefan-Boltzmann Law guide, we will show you how to calculate the total radiated power of an object in a matter of seconds.
We will also help you understand the Stefan-Boltzmann law, its formula, and what each variable means while we’re at it.
What is the Stefan-Boltzmann Law?
Why does temperature and surface area affect the radiation of an object? H
ow to apply this law in real-world situations? Find all the answers here!
Stefan-Boltzmann Law Calculator
Calculate the total radiated power of an object using P = ε σ A T⁴
Stefan-Boltzmann Law: Formula Explanation
The Stefan-Boltzmann Law describes how much power (P) an object radiates based on its surface area (A), temperature (T), and emissivity (ε). The formula is:
P = ε σ A T⁴
- P: Total Radiated Power (Watts, W)
- A: Surface Area of the object (m²)
- ε: Emissivity of the material (0 to 1)
- σ: Stefan-Boltzmann Constant (5.670374419 × 10⁻⁸ W/m²·K⁴)
- T: Temperature in Kelvin (K)
Real-World Applications
Solar Panels
Used to calculate the thermal radiation emitted by the panel at high temperatures.
Astrophysics
Determines the luminosity of stars based on their surface temperature and size.
Industrial Heating
Used to estimate heat loss from furnaces or radiators to optimize efficiency.
Solved Example: Step-by-Step
Problem: Calculate the total radiated power of an object with surface area 2 m², emissivity 0.8, and temperature 500 K.
A = 2 m², ε = 0.8, T = 500 K, σ = 5.670374419 × 10⁻⁸ W/m²·K⁴
P = ε × σ × A × T⁴
P = 0.8 × (5.670374419 × 10⁻⁸) × 2 × (500)⁴
500⁴ = 62,500,000,000
P = 0.8 × 5.670374419 × 10⁻⁸ × 2 × 62,500,000,000
P ≈ 5663.5 W
The object radiates approximately 5663.5 Watts of power.
Reference Table: Stefan-Boltzmann Law
| Variable | Meaning | Typical Values / Notes |
|---|---|---|
| P | Total Radiated Power | Watts (W) |
| A | Surface Area of Object | m² (e.g., 1 – 10 m²) |
| ε | Emissivity of Material | 0 – 1 (0 = perfect reflector, 1 = perfect emitter) |
| σ | Stefan-Boltzmann Constant | 5.670374419 × 10⁻⁸ W/m²·K⁴ |
| T | Temperature | Kelvin (K), e.g., 300 K – 6000 K |
| Applications | Where the formula is useful | Astrophysics, Solar Panels, Industrial Heating |
FAQs
What is the Stefan-Boltzmann Law?
In simple words, it tells us how much power an object radiates based on its temperature, surface area, and material.
What does emissivity mean?
Emissivity (ε) shows how good a material is at radiating heat. It ranges from 0 (no radiation) to 1 (perfect radiator).
Why is this law important?
It helps us understand how objects like stars, furnaces, and solar panels emit heat or light based on temperature.