For Horizontal Axis Wind turbines (HAWTS), there is a formula for calculating the expected power output. IT is:
efficiency * air density * swept area * windspeed ^3
For a HAWT, since it is sorta flat, the swept area is simply pi r^2 (r=radius).
However, for a VAWT (vertical AWT), the blades can be as high as they want.
How do you calculate the swept area in this case?
If you look at a vawt from the side, the swept area will be the diameter of the rotor, times the height of the blades. It will describe a rectangle.
However most VAWT constructions I've seen have the blades only effectively working on the downwind side, so halve the area calculated above.
Then, consider that the effort isn't equal - the blades provide most power when they're at right angles to the wind, and progressively less (cosine?) of the angle as they come closer to the line of the wind. So take away some more
And finally, when the blades are on the upwind side, they'll actually be providing drag and losing power, so take off a bit more again!
I guess I'm saying the calculation for "swept area" is probably straightforward, but determining the POWER you can get from the wind for a given "swept area" will be far more complex than with a hawt.