# Magnetic field of a static disk magnet

I have a magnetic disk (Radius R, height h) that creates magnetic field lines (axisymmetrical). I simulated the field lines, exported the data and am now trying to fit a function into the data to have a analytical solution for the magnetic flux density of my specific magnet. For several r's fixed I have the magnetic flux Density $B_z(z)$ as well as $B_r(z)$

I need functions of the following form: $B_z(r,z)$ and $B_r(r,z)$ since I think $B_\phi (r,z)$ is $0$. So I am wondering how I need to start. I found the following equation online but I think its only for the absolute value, not $B_z$ and $B_r$ how I need it:

$$B(r,z) = \frac{\mu_0 m}{4\pi (z^2+r^2)^{\frac{3}{2}}}\sqrt{1+\frac{3z^2}{z^2+r^2}}$$

Can someone help me how my function needs to look? I was thinking something like: $$B_z(r,z) = \frac{a}{b+((z+c)^2+(r+d)^2)^{\frac{3}{2}}}\sqrt{1+\frac{3z^2}{z^2+r^2}}$$ or am I completely off now? And furthermore, how would I change to cartesian coordinates then?