Luminosity Calculator
This tool helps astrophysicists and astronomy enthusiasts calculate the luminosity of stars based on their radius and temperature using the Stefan-Boltzmann Law.
Calculator
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Data Source and Methodology
All calculations are based on the Stefan-Boltzmann Law. For more information, refer to Stefan-Boltzmann Law. All calculations strictly adhere to the provided formulas and data.
The Formula Explained
The formula used is \( L = 4\pi R^2 \sigma T^4 \), where \( L \) is luminosity, \( R \) is radius, \( \sigma \) is the Stefan-Boltzmann constant, and \( T \) is temperature.
Glossary of Terms
- Radius (R): The radius of the star in solar radii.
- Temperature (T): The surface temperature of the star in Kelvin.
- Luminosity (L): The total energy output of the star, measured in solar luminosities.
Example Calculation
For a star with a radius of 2 solar radii and a temperature of 6000K, the luminosity is calculated as follows:
- Given: \( R = 2 \), \( T = 6000 \)
- Calculate \( L = 4\pi \times (2)^2 \times \sigma \times (6000)^4 \)
- Result: \( L ≈ 16 L☉ \) (solar luminosities)
Frequently Asked Questions (FAQ)
What is the Stefan-Boltzmann Law?
The Stefan-Boltzmann Law relates the total energy radiated by a black body to its temperature and surface area.
How does radius affect luminosity?
The luminosity of a star increases with the square of its radius. Doubling the radius increases luminosity by a factor of four.
Why is temperature important in calculating luminosity?
Temperature has a significant impact on luminosity, as it is raised to the fourth power in the Stefan-Boltzmann equation.
Can this calculator be used for non-stellar objects?
While primarily designed for stars, the calculator can be adapted for other astronomical objects by adjusting input units.
What units should be used?
Radius should be in solar radii, and temperature should be in Kelvin for accurate results.
Formula (LaTeX) + variables + units
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The formula used is \( L = 4\pi R^2 \sigma T^4 \), where \( L \) is luminosity, \( R \) is radius, \( \sigma \) is the Stefan-Boltzmann constant, and \( T \) is temperature.
- No variables provided in audit spec.
- Stefan-Boltzmann Law — en.wikipedia.org · Accessed 2026-01-19
https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.