Apologies for the necro, but after racking my brain for quite some time, I just couldn't get the same number as the in-game UI was presenting for various weapons.
I came across this thread, which helped me with my calculations.
Specifically redlynx's linked spreadsheet, which included some steps I was entirely not considering.
I just wanted to voice my appreciation.
For anyone wanting the formula for Excel (to be used in the weapon_data.csv), here it is:
=(([@[damage/shot]]*(MAX(1,[@[burst size]]))*(1/([@chargeup]+[@chargedown]+([@[burst size]]-1)*[@[burst delay]]))))
Thanks again, and hopefully this helps someone else who is looking for this information in the future.
Note this is for "damage per shot" weapons, with no ammo regen calculations.
I haven't figured out how to properly calculate the sustained and beam damages correctly.