The simple formula is
length × width × depth × density = mass. For example, if you have an empty lightbox cabinet made from .080" aluminum that measures 10'x2'x8", you just add up the 5 sides of the box using that formula:
Rear: 120" × 24" × .08" = 230.4 in³
L/R sides: 8" × 24" × .08" × 2 sides = 30.72 in³
Top/Bottom: 120" × 8" × .08" x 2 sides = 153.6 in³
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Total: 230.4 + 30.72 + 153.6 = 414.72 in³
Now I can swap
length × width × depth for the total volume of aluminum I just calculated, and multiply it by
density.
414.72 in³ × 0.1 lb/in³ = 41.5 lb total cabinet weight.
Obviously that's just the aluminum cabinet, not including the
sign face, frame extrusions, ballasts, etc., but it gives you a good starting point. You can easily make a spreadsheet to automate this.