# Scale and the models of the hyperbolic plane

I was reading somewhere (sorry I always forget where) that the scale of the Poincare Half plane is y (the vertical)

So at the boundary line the scale is $0$ or $( 1 : \infty )$.

at the horocycle $y = 1$ the scale is $1:1$ and

at $y = \infty$ the scale is $\infty$ and all vertical lines and hypercycles meet .

now I was wondering what is the scale function for the other models of the hyperbolic plane, escpecially for the Poincare disk model and the Klein disk model?