Shopify doesn't have support for that. We use an app called boxify, it could be useful if they have the shipping integrations you need.
As it is mentioned, Shopify only allows you to add product weight and not dimensions. If you would like to calculate the rates based on both product weight & dimensions, you will have to use an app like our Multi Carrier Shipping Label app. The app helps you add product weight & dimensions, and also integrate with multiple shipping carriers and calculate the shipping rates.
How is that even possible!?!?! Every vendor has multiple products and multiple box sizes. It would just be another field to enter the information under each product. If you don't purchase an after market app is there a workaround so you can still use Shopify's shipping discounts since every carrier computes shipping rates that include box dimensions?