Enter the luminosity, radius, and temperature into the calculator to determine the missing variable.

Luminosity Radius Temperature Calculator

Enter any 2 values to calculate the missing variable





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Luminosity Radius Temperature Formula

The following formula is used to calculate the luminosity, radius, or temperature of a star. 

L = 4πR²σT⁴

Variables:

  • L is the luminosity in watts (W)
  • R is the radius in meters (m)
  • T is the temperature in kelvin (K)
  • σ is the Stefan-Boltzmann constant, approximately 5.67 × 10⁻⁸ W/m²K⁴

To calculate the luminosity, multiply 4π by the square of the radius, the Stefan-Boltzmann constant, and the fourth power of the temperature.

What is the Luminosity Radius Temperature Relationship?

The luminosity radius temperature relationship is a fundamental concept in astrophysics that describes how the luminosity (total energy output) of a star is related to its radius and surface temperature. This relationship is crucial for understanding the properties and behavior of stars. The formula L = 4πR²σT⁴ shows that the luminosity of a star is directly proportional to the square of its radius and the fourth power of its surface temperature. This means that even small changes in temperature can result in significant changes in luminosity. This relationship helps astronomers determine the size, temperature, and energy output of stars based on observable data.

How to Calculate Luminosity, Radius, or Temperature?

The following steps outline how to calculate the luminosity, radius, or temperature of a star.

  1. First, determine the two known variables (e.g., radius and temperature).
  2. Next, use the formula L = 4πR²σT⁴ to solve for the unknown variable.
  3. If solving for luminosity, multiply 4π by the square of the radius, the Stefan-Boltzmann constant, and the fourth power of the temperature.
  4. If solving for radius, rearrange the formula to R = √(L / (4πσT⁴)).
  5. If solving for temperature, rearrange the formula to T = (L / (4πR²σ))^(1/4).
  6. After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Luminosity (L) = 3.828 x 10²⁶ W

Radius (R) = 6.96 x 10⁸ m

Temperature (T) = 5778 K