Compilating answers here and there, here's a complete set of arr tools to get the work done:
Function getArraySize(arr As Variant)
' returns array size for a n dimention array
' usage result(k) = size of the k-th dimension
Dim ndims As Long
Dim arrsize() As Variant
ndims = getDimensions(arr)
ReDim arrsize(ndims - 1)
For i = 1 To ndims
arrsize(i - 1) = getDimSize(arr, i)
Next i
getArraySize = arrsize
End Function
Function getDimSize(arr As Variant, dimension As Integer)
' returns size for the given dimension number
getDimSize = UBound(arr, dimension) - LBound(arr, dimension) + 1
End Function
Function getDimensions(arr As Variant) As Long
' returns number of dimension in an array (ex. sheet range = 2 dimensions)
On Error GoTo Err
Dim i As Long
Dim tmp As Long
i = 0
Do While True
i = i + 1
tmp = UBound(arr, i)
Loop
Err:
getDimensions = i - 1
End Function