Stefan-Boltzmann Law (Blackbody Form)
Total power radiated by an ideal blackbody (emissivity ε = 1) is proportional to the fourth power of temperature. For real (gray) surfaces, use the general emissivity form P = εσAT⁴.
Variables
Your notes
Constants in this formula
Check value
Round inputs run through this page's calculator, with each constant at its tabulated value. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.
- σ = 5.670 374 419… × 10⁻⁸ W/(m²·K⁴) (Stefan-Boltzmann constant)
- A = 2 m² (Surface area)
- T = 3 K (Temperature)
Result: P = 9.186007 × 10⁻⁶ W
Where this formula is listed
- Modern Physics formulas, under Thermal Radiation.
- In the modern physics list it comes after Nuclear Radius and before Wien's Displacement Law.
- Modern Physics formula sheet, one of 41 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Stefan-Boltzmann Law (Blackbody Form) formula?
Stefan-Boltzmann Law (Blackbody Form) is written P = σAT⁴. Total power radiated by an ideal blackbody (emissivity ε = 1) is proportional to the fourth power of temperature. For real (gray) surfaces, use the general emissivity form P = εσAT⁴. It belongs to Modern Physics, under Thermal Radiation.
What are the units in P = σAT⁴?
In SI units, P is power radiated, measured in W; σ is stefan-boltzmann constant, measured in W/(m²·K⁴); A is surface area, measured in m²; T is temperature, measured in K.