Luminosity Calculator
Calculate stellar luminosity, absolute magnitude, and apparent magnitude
Calculate Stellar Luminosity
Radius of the star (1 R☉ = 695,700 km)
Surface temperature of the star (Sun: 5778 K)
Distance from Earth (for apparent magnitude calculation)
Calculation Results
Formula used: L/L☉ = (R/R☉)² × (T/T☉)⁴
Input values: R = 0 R☉, T = 0 K
Stefan-Boltzmann constant: σ = 5.670 × 10⁻⁸ W/(m²·K⁴)
Stellar Classification
Example Calculation
Vega (Alpha Lyrae)
Radius: 2.5 R☉
Temperature: 9,602 K
Distance: 25.04 light years
Calculation
L/L☉ = (R/R☉)² × (T/T☉)⁴
L/L☉ = (2.5)² × (9602/5778)⁴
L/L☉ = 6.25 × (1.662)⁴
L = 47.67 L☉
Absolute Magnitude: M = 0.58
Quick Reference
Famous Stars
Sun
1.0 L☉, 1.0 R☉, 5778 K
Vega
47.7 L☉, 2.5 R☉, 9602 K
Sirius A
25.4 L☉, 1.7 R☉, 9940 K
Betelgeuse
126,000 L☉, 640 R☉, 3590 K
Rigel
120,000 L☉, 78 R☉, 12100 K
Understanding Stellar Luminosity
What is Luminosity?
Luminosity is the total amount of electromagnetic energy emitted by a star per unit time. It's an intrinsic property that depends only on the star's radius and surface temperature, following the Stefan-Boltzmann law.
Key Relationships
- •Luminosity increases with the square of radius
- •Luminosity increases with fourth power of temperature
- •Hotter stars are much more luminous than cooler ones
- •Red giants are luminous due to large size
Mathematical Formulas
L = σ × A × T⁴
L/L☉ = (R/R☉)² × (T/T☉)⁴
M = -2.5 × log₁₀(L/L₀)
- L: Luminosity (Watts)
- σ: Stefan-Boltzmann constant
- A: Surface area (4πR²)
- T: Surface temperature (K)
- M: Absolute magnitude
- L₀: Zero-point luminosity
Note: Lower absolute magnitude means higher luminosity. The Sun's absolute magnitude is +4.74.