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Do you mean the total number or rows by "visible rows", or do you actually mean only the rows that are visible in the grid viewport (and not all rows that the user can scroll to)?
For the first, you (as in the application developer) are responsible of knowing how much data you have in the grid, by specifying the grid.size property (if you are using a function/remote data source). If you are using an array data source, then you should also know the size of that array.
Once you know the number, then it’s straightforward to place the number in the footer row using the JS API.