How can I calculate the current through an LED?
Normally we speak of current through and voltage across a component.

The relationship of brightness to current is device dependent and can be done using the datasheet for your LED.  As far as I know, an equation that covered all devices would be too general for practical use. Some manufacturers give no information in the datasheet at all, but mostly you'll see a plot like this of a.u. vs mA: (p3): http://docs-asia.electrocomponents.com/webdocs/151e/0900766b8151e40a.pdf