It costs as little as $149.99/month for a 12-foot moving container and $159.99/month for a 16-foot moving container. Additional costs include truck rental, mileage, insurance, and more, which means that you’re looking at a minimum of an $800 cost for an out-of-state moving container move. The exact cost depends on the size of the moving container, how long you’re renting it, how far you’re moving, and other factors.