# Luminosity Calculator

Simply type the radius of the star, the temperature to calculate the luminosity, and the distance from the earth to the star, then press the calculate button to receive the apparent magnitude details in less time.

### What is the definition of Luminosity and its Equation?

The energy generated by an object, such as a star or galaxy, is measured in luminosity. The luminosity of main-sequence stars is proportional to their temperature; the hotter a star is, the brighter it shines. Cooler stars, on the other hand, release less energy, making them harder to discern in the night sky.

The Stefan-Boltzmann law can be used to derive the formula for star luminosity. This law states that the
energy radiated per unit time by a black body: **P = σ*A*T ^{4}**

- Where, σ be the Stefan Boltzmann constant, the value is equal to 5.670367 * 10
^{-8} - A be the surface area of the body (equal to A = 4πR
^{2}for spherical objects) - T be the temperature of the body measured in Kelvins

The radiant power emitted by a light-emitting object is measured in luminosity, which is an absolute measure of radiated electromagnetic power. It is determined by the temperature and radius of the object.

The formula for luminosity is as follows: **L/L☉ = (R/R☉) ^{2}(T/T☉)^{4}.**

- Where, the star luminosity is L
- L☉ is the luminosity of the sun and is equal to 3.828 x 10
^{26}W - Radius is R
- T is the temperature of the star in Kelvins
- R☉ is the radius of the sun and equal to 695700 km
- T is the star temperature
- T☉ is the temperature of the sun and it is 5778 K

### Absolute and Apparent Magnitude

You can use this tool to compute absolute magnitudes. The luminosity can also be measured using absolute
magnitude. It can be displayed on a logarithmic scale rather than in watts. The term absolute magnitude
refers to a method of determining luminosity. It is calculated on a logarithmic scale. The absolute
magnitude formula is M = -2.5 x log^{10}(L/L^{₀})

The apparent magnitude of a star, on the other hand, is a measure of its brightness as seen from Earth.
**m = M-5 + 5*log _{₁₀}(D)**

- Where, The apparent magnitude of the star is denoted by m
- The absolute magnitude of the star is denoted as M
- D is the distance between the star and Earth, measured in parsecs.

For more concepts check out physicscalculatorpro.com to get quick answers by using this free tool.

### How to find Luminosity with Temperature and Radius?

- Determine the radius first. Calculate the star radius
- Determine the temperature next. Calculate the star's surface temperature.
- Calculate the luminosity at the end. using the equation above, calculate the star's luminosity.

### Luminosity Calculation Examples

**Question 1:** Find Luminosity and Absolute magnitude where the star radius is 80km at the
temperature 225k.

**Solution:**

Consider the question,

Star Radius, R = 80km

Star Temperature, T = 225K

We know that, The Luminosity formula is **L/L☉ = (R/R☉) ^{2}*(T/T☉)^{4}**

Absolute magnitude formula is **M = -2.5 x log ^{10}(L/L^{₀})**

L= 3.828 * 10^{26}*(80 / 695700)^{2}(225 /5778)^{4}

Luminosity(L) = 11639.32563799216 GW

M = -2.5 * log_{10}(11639.32563799216 / 3.828 *10^{26})

Absolute magnitude(M) = 38.53260620971615

Therefore,The Luminosity is is 11639.32563799216 GW and Absolute magnitude is 38.53260620971615.

### FAQs on Luminosity Calculator

**1. What is the formula for calculating luminosity?**

They can determine the luminosity of a star if they know its brightness and distance from
this: [luminosity = brightness x 12.57 x (distance)^{2}]. The size of a star is also related to
its luminosity. The larger star emits more energy and the more luminous.

**2. What is the relationship between the size of a star and its
brightness?**

The Luminosity of a star increases as its size grows. Consider this: a bigger star has a larger surface area. Because of the larger surface area, more light and energy may be emitted.

**3. What is the luminosity formula and how to use it?**

The luminosity equation is used to calculate how much energy a body emits per unit time.
The Stefan-Boltzmann law can be used to derive it. The luminosity formula is **L/L☉ =
(R/R☉) ^{2}*(T/T☉)^{4}**

**4. What is a luminosity example?**

The condition of being bright or having light is defined as luminosity. The sun is an
example of something with luminosity.The sun's luminosity value is **3.828 x 1026 W**.