It's easy to do in a few of steps.

File/Import & Export
Export to a file
Choose Excel
Select 'Contacts'
Do it.

Open and then scroll down the Excel file to get the final line number of contacts you have.

Note: if you want total email addresses you have in the address book for your contacts, you will need to scroll across to 'Email2Address' and Email3Address' and do a sum for those cells that are populated and add to the total.