Look at the two lines the calculator counts as is. Sheet metal cannot be crafted at any bench, so every sheet comes from crates, road runs and the recycler. Gears are a Level 3 craft while the ballista's own blueprint sits at Level 2, so for most of a wipe the gear is loot too. Crafting it yourself adds 100 scrap that would otherwise go into research.
Those sheets have another buyer. Every craft of high external stone walls takes one, and a duo with three sheets in the box chooses between a ring of walls and a ballista behind it. Walls usually come first: without them, attackers simply walk past the ballista to your door.
Tip
Learn the incendiary bolt in the same research run. It takes no sulfur and no high quality metal, so the ballista is loaded the day it stands.
Still unsure whether you will defend or raid? Look at the mounted ballista first: the same bill, on wheels.
Questions
Ballista ×10: how many resources?
Metal Fragments ×2,500, Gears ×10, Sheet Metal ×20.