Stellar Luminosity Calculator
Calculate the luminosity of a star relative to the Sun using the Stefan-Boltzmann law, given its radius and surface temperature.
Results will appear here.
Formula
Stefan-Boltzmann Law:
L = 4π R² σ T⁴
Where:
- L = Stellar luminosity (Watts)
- R = Stellar radius (meters)
- σ = Stefan-Boltzmann constant = 5.6704 × 10⁻⁸ W m⁻² K⁻⁴
- T = Effective surface temperature (Kelvin)
Relative to the Sun:
L / L☉ = (R / R☉)² × (T / T☉)⁴
Where T☉ = 5,778 K and R☉ = 6.957 × 10⁸ m.
Bolometric Absolute Magnitude:
M_bol = 4.74 − 2.5 × log₁₀(L / L☉)
Assumptions & References
- The star is modelled as a perfect blackbody (ideal radiator).
- Solar luminosity L☉ = 3.828 × 10²⁶ W (IAU 2015 nominal value).
- Solar radius R☉ = 6.957 × 10⁸ m (IAU 2015 nominal value).
- Solar effective temperature T☉ = 5,778 K.
- Stefan-Boltzmann constant σ = 5.670374419 × 10⁻⁸ W m⁻² K⁻⁴ (CODATA 2018).
- Bolometric correction and interstellar extinction are not applied.
- Spectral classification boundaries follow the standard MK system.
- References: Carroll & Ostlie, Introduction to Modern Astrophysics; IAU 2015 Resolution B3.