Calculate isotropic-equivalent luminosity, flux or luminosity distance. Convert absolute magnitude using a matching luminosity reference; V/custom-band conversion requires the reference power for that band.
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Flux To Luminosity Formula
The following formula gives isotropic-equivalent luminosity from observed integrated energy flux and luminosity distance. Use bolometric flux for total luminosity; matching band flux gives band luminosity.
Variables:
- L is the luminosity (watts)
- F is the observed flux (watts per square meter)
- d is the luminosity distance in metres when F is in W/mยฒ and L is in watts
To calculate luminosity, multiply integrated energy flux by 4ฯ and the square of luminosity distance in metres. Extinction, K corrections and bolometric corrections must be handled separately.
| Flux (W/mยฒ) | Distance | Luminosity (Lโ) |
|---|---|---|
| 13.6 | 1 AU | 0.01 |
| 136 | 1 AU | 0.1 |
| 1.36e3 | 1 AU | 1 |
| 1.36e4 | 1 AU | 10 |
| 3.20e-10 | 1 pc | 0.01 |
| 3.20e-9 | 1 pc | 0.1 |
| 3.20e-8 | 1 pc | 1 |
| 3.20e-7 | 1 pc | 10 |
| 3.20e-12 | 10 pc | 0.01 |
| 3.20e-11 | 10 pc | 0.1 |
| 3.20e-10 | 10 pc | 1 |
| 3.20e-9 | 10 pc | 10 |
| 3.20e-16 | 1 kpc | 0.01 |
| 3.20e-15 | 1 kpc | 0.1 |
| 3.20e-14 | 1 kpc | 1 |
| 3.20e-13 | 1 kpc | 10 |
| 3.20e-22 | 1 Mpc | 0.01 |
| 3.20e-21 | 1 Mpc | 0.1 |
| 3.20e-20 | 1 Mpc | 1 |
| 3.20e-19 | 1 Mpc | 10 |
| * Values rounded to 3 significant figures. Uses L = 4ฯ dยฒ F. Constants: Lโ = 3.828ร10ยฒโถ W; 1 AU = 1.495978707ร10ยนยน m; 1 pc = 3.085677581491367ร10ยนโถ m; 1 kpc = 10ยณ pc; 1 Mpc = 10โถ pc. | ||
What is Luminosity?
Luminosity is the total amount of energy emitted by an object, such as a star or galaxy, per unit of time. It is an intrinsic property that does not depend on the object's distance from the observer. Luminosity is a fundamental parameter used in astronomy to understand the nature and evolution of celestial bodies.
How to Calculate Luminosity?
The following steps outline how to calculate the Luminosity.
- First, determine the observed flux (F) in watts per square meter.
- Next, determine the distance from the object (d) in parsecs.
- Convert the distance from parsecs to meters (1 parsec = 3.0857e+16 meters).
- Use the formula L = 4 * ฯ * d^2 * F to calculate the luminosity (L) in watts.
- After inserting the variables 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.
observed flux (F) = 3.2e-12 watts per square meter
distance from the object (d) = 100 parsecs
