Should I use shipping estimate calculator on product page?

It's almost like common sense (at least by observing many different online stores) to show a shipping estimate cost on the shopping cart page. With this, the user have the information of how much the full purchase will cost before entering the checkout process, where he will finally complete the transaction.

But... How about the product page. Does it make sense to show the same shipping calculator also on the product page?

If the user is only selecting one product, It seems fine. The final shipping cost will be the same in the cart page. However, if the user already has other products on the shopping cart, the shipping estimate on the product page would return a cheaper value than the full shopping cart.

Is there any other thing to consider to decide wether or not to put it on the product page.