Does ShipStation Calculate Shipping Cost?

Yes, and it will act on the answer if you ask it to.

Per order, on demand. The rate calculator shows you the cost of the service currently on a shipment alongside the other services available from your connected carriers, so you can compare and choose.

Automatically, for every shipment. Rate Shopper fetches live rates when it runs and applies the cheapest qualifying service. Attach it to an automation rule and the strategy is assigned at import without anyone opening the order; the pricing then runs again whenever the rate is asked for and immediately before the label is bought, against whatever package is on the order. You can also apply it by hand to one order or in bulk to a selection. You choose one of the standard strategies — Cheapest, Fastest, Best Value — or, on the Advanced plan, build a custom rate shopper around your own service collection and transit time thresholds. Attach it to an automation rule with the Set Rate Shopper action and it is assigned at import. How Rate Shopper works and how to configure it well.

One thing to get right first: the rate is calculated for the package on the order, so the package has to be correct before the rate means anything. ShipStation’s own setup documentation has the dimensions rule running before the Rate Shopper rule for exactly this reason: “The dimensions rule must come first to ensure that all orders generate the appropriate rate.” Which is also why a flat-rate box can never win once you have packed into your own carton. Product Defaults handle that well for single-item orders with stable packaging. Automating package dimensions covers the rest.