I wasn't aware that they had any specific dimensions... the one the drystone walling association did at Brodie Castle was four foot.

The Ha-ha is an expression in garden design that refers to a trench, in which is a fence concealed from view. Alternatively it can be used to mean a ditch the one side of which is vertical and faced with stone, the other face sloped and turfed, making the trench, in effect, a retaining wall. The ha-ha is designed not to interrupt the view from a garden, pleasure-ground, or park, while maintaining a physical barrier at least in one direction. I found this definition which suggests to me it can be any dimension you require depending on the reason for it?

Normal only used in big country gardens so that the view right across the countryside is not obscured.

It just needs to be a suitable height (depth?) to stop livestock jumping over or out of it.
The amusing thing about the one at Brodie Castle, though, is that being open to the public they have had to put a fence in front of the HaHa to stop children falling into it!

Ha -Ha!