References: This is based off a formula that I found in the article “The Design of Fast Ocean Steamers” by EW DeRusset contained within the November 1908 edition of Cassier's Magazine; with suitable modifications.

Where:

Length_WL: Hull Length (at Waterline)
Beam: Hull Beam
Depth: Hull Depth
BC: Block Coefficient
WC: Weight Coefficient

Workable Weight Coefficients are:

Destroyer Hulls (Long Tons): 214

Notes: Very accurate across a spectrum from DD-1 to DL-2 from data in Norman Friedman's US Destroyers: An Illustrated Design History.

Destroyer Fittings (Long Tons): 1300

Notes: Not that accurate, really more of a baseline to get you into the rough ballpark, with wide variations observed from data in Norman Friedman's US Destroyers: An Illustrated Design History.