you will probably have to pay for a service to achieve this. Sales tax can be very complicated because it often varies by county, and even by municipality. Also, tax rates across the country change regularly.
Usually, sales tax is not required unless your business has a "nexus" in the state that the product is being shipped to.
(Caveat - I've been out of that loop for about three years now.)
A service is required for accurate results. For example, many counties just had a sales tax holiday for certain goods for "Back to School". For example, many residents of the county my firm is in aren't even aware that sales tax is only 6% over $5k; otherwise it's 7%. These rules vary by quite a bit in the over 10k jurisdictions that comprise the U.S. We fully integrated our manufacturing solution "Kosmas" with Avalara AvaTax API, so we have quite a bit of experience with it, though not many people want to pay for it since it's not cheap. Avalara uses transactional pricing based on an estimated number of calls paid in advance. It also requires the client to setup their products/services and classify them. On top of that, Avalara doesn't assume any liability for incorrect classification, so it recommends clients use tax lawyers to set it up. Hope some of this helps.