⭐ Stellar Astrophysics & Stefan-Boltzmann Law
Stellar Luminosity & Stefan-Boltzmann Calculator
Compute stellar radiated luminosity ($L/L_\odot = (R/R_\odot)^2 (T/T_\odot)^4$), effective surface temperature ($T_{\text{eff}}$), radius ($R$), and Morgan-Keenan spectral classification.
☀️ Sun (1.0 R☉, 5,778 K)
✨ Sirius A (1.71 R☉, 9,940 K)
🔴 Betelgeuse (764 R☉, 3,600 K)
💎 Rigel (79 R☉, 12,100 K)
🪐 Proxima Centauri (0.15 R☉)
Stellar Physical Parameters
R☉ (Solar Radii)
Kelvin (K)
Radiated Stellar Luminosity (L)
1.000 L☉
Spectral Class
G-type (Yellow)
Absolute Mag ($M_v$)
+4.83 mag
Surface Flux ($\sigma T^4$)
63.2 MW/m²
💡 Stefan-Boltzmann Proportionality:
$$\frac{L}{L_\odot} = (1.00)^2 \times \left(\frac{5778}{5778}\right)^4 = 1.000\text{ }L_\odot$$
Stefan-Boltzmann Law in Astronomy
The total electromagnetic radiation power emitted by a spherical blackbody star is:
$$L = 4\pi R^2 \sigma T^4 \implies \frac{L}{L_\odot} = \left(\frac{R}{R_\odot}\right)^2 \left(\frac{T}{T_\odot}\right)^4$$
- Solar Constants: $L_\odot \approx 3.828 \times 10^{26}\text{ W}$, $R_\odot \approx 6.9634 \times 10^8\text{ m}$, $T_\odot \approx 5,778\text{ K}$.
- Spectral Types (H-R Diagram): O (>30,000 K), B (10,000–30,000 K), A (7,500–10,000 K), F (6,000–7,500 K), G (5,200–6,000 K), K (3,700–5,200 K), M (<3,700 K).