Well done on progress so far.
Establishing tonnes per square metres is my least favourite calculation because of the variable quality of manure, and of how one measures its depth. For example cow manure tends to hold more moisture than horse and therefore weighs more per volume. Then a 5cm layer becomes 3cm after one month in many cases, depending also on how fluffy the manure was.
Bering that in mind, about three tonnes is my best estimate. However I tend to over-order as I have space to store any spare, and prefer that to running out. So two tonnes may do it.