A fillet weld is the triangle of metal deposited into the corner where two plates meet, and it is measured by its leg — the length of each side of that triangle along the plates. The quoted size flatters the working section: load shears a fillet across its narrowest dimension, the diagonal throat, which for the standard 45-degree fillet is the leg times sin 45°, so a 1/4-in fillet is structurally a 0.177-in-thick strip of weld metal. Every strength comparison against the allowable weld stress Fw happens on that throat, and sizing a weld from a computed demand means dividing by 0.707·Fw at the end.
Practical fillet design postpones choosing the size by treating each weld as a line of unit throat, whose "area" is simply its length. A group of such lines has a total length Lw, a length-weighted centroid, line moments of inertia Ix and Iy, and a polar moment J = Ix + Iy. A vertical load P at an eccentricity e produces a uniform direct shear flow P/Lw plus a torsion T = P·e whose shear flow grows linearly with distance from the centroid, so the corner farthest from the centroid governs. The elastic (vector) method sums both components there and converts the worst resultant into a required leg — the analysis AISC 360 and Eurocode 3 EN 1993-1-8 frame for eccentrically loaded weld groups.