Start by measuring the final packed dimensions and the actual weight after packing. Carriers often price furniture by dim weight when boxes are large, so oversized packaging can raise the cost even if the item is not very heavy.
For a reliable estimate, use these inputs:
packed length, width, height for each box or crate
actual weight after packing
pickup and destination postal codes
delivery type such as residential, liftgate, or inside placement
declared value for customs paperwork
To lower costs, reduce empty space and use the smallest box that still allows proper packaging.