Calculate Luminosity of Vega I want to calculate the Luminosity of a star e.g. Vega but can be any star and came across the formula for Luminosity at the University of Oregon (http://pages.uoregon.edu/soper/Light/luminosity.html).  

I'm not an expert on Maths, could anyone help me with the figures to put into the formula.  

$$L = (4\pi d^2)b$$ 

$d$ is the distance but the page doesn't say Parsecs or Light Years.

$b$ is the apparent brightness. 

I'm thinking 

$$L = ((4\times3.141) \times (25.04^2) ) \times 0.026 = 204.81 \mathrm{(light\ years)}$$ 

$$L = ((4\times3.141) \times (7.68^2)) \times 0.026 = 19.26 \mathrm{(parsecs)}$$

Which gives me 204.81 which is different to Luminosity which is quoted (40.12) on the Wikipedia page.  Is this the right formula for what I'm after.  Please no scientific equations like what you see on the page linked above.  Any calculations would need to be the type you would put into a non-scientific calculator.
The $b$ in your equation, brightness, is what we call a "Flux".  That's the amount of energy per unit area at a certain distance.  Flux can be calculated using the Stefan-Boltzmann law.
$$
J=\sigma T^4
$$
where $\sigma=5.670373\times10^{-8}\space W\space m^{-2}\space K^{-4}$is the Stefan-Boltzmann constant, This is measured in Watts per square meter.  That means that we will need our distance to be in meters, and we will get a luminosity in Watts.  We can go a little further and divide our answer by $3.828\times10^{26} \space W$ to get our final value in solar luminosities (L$_\odot$).

That will make our final equation:
$$
L=\frac{4\pi R^2 \sigma T^4}{L_\odot}
$$
Because we're using the Stefan-Boltzmann equation, instead of the distance to the star, we have to use its radius.  Vega's radius is $2.362 \space R_\odot$, which is $1.64\times10^9$ meters. Its surface temperature is 9,600 K.  Plugging in those numbers yields a luminosity of:
$$
L=42.7L_\odot
$$
This value is slightly different from the value quoted by Wikipedia, due to rounding, but is well within the acceptable range.