I am having trouble figuring the height of a point on any given quad. Is there some way of calculating this using the coordinates of the 4 corners?

I have the 4 coordinates of the corners, and the x and z values of the point on the quad..I want to find the y value of that point.

The quad is in 3d space, and is planar.

I think I'm having trouble posting, not sure but my replies arent showing up.

Yes.

How many dimensions are we working in? (It's a bit easier in 2D than 3D). If in 3D, are we guaranteed that the quad is actually planar, and that the point is in the same plane?

what information are you starting with and what do you want to end up with?

The quad is in 3 dimensions.
It is planar.
I have the 4 corners of the quad, and the x and z values of some point on that quad..what I want is the y value of that point on the quad.

if the vertices of the quad are A, B, C, D then (A-B) x (D-B) gives you the quad's plane's normal, and a vertical line through the point is (X,0,Z) + k(0,1,0). Then you can do a standard line-plane intersection.

More simply than the plane/line thing, just plug x & z straight into the plane equation, and solve for y (which is the only remaining unknown).