Do you provide API to calculate shipping cost?

No. We do not offer API to calculate shipping cost. Most of the shopping carts has the real time shipping rate calculator integrated with USPS/ UPS/ FedEx. You have to setup an account with these carriers and use that account information in the shopping cart's rate calculating API and enable this feature. If you have developed custom shopping cart, you have to contact these carriers to integrate with their API . If you don't want to use real time shipping calculator, you may add shipping table in your custom shopping cart and manually find the shipping cost and  pre-populate.