# Wave energy ~ wave height squ. or wave amplitude squ.?

Hello,
I've found different formulas regarding wave energy.

1) Wave energy is proportional to wave length $$\lambda$$ times wave height squared

2) Wave energy is proportional to wave period T times wave amplitude squared

From what I've read, wave period is equivalent to wave length.
But wave height does not equal wave amplitude (for a sinusoidal wave: h=2a) so shouldn't it be 4a?

I think I'm mixing up a few things.