How this is calculated. The conductor in a via is the plated barrel — an annulus,
not the hole — so the cross-section is
π(router² − rinner²) where the inner radius is the drill
radius less the plating thickness. That area goes into the same IPC-2221 relation used for
traces,
I = k · ΔT0.44 · A0.725, with
k = 0.048: a via passes through the board and sheds heat more like an external
conductor than a buried one. Dividing the required current by the per-via capacity gives the
count, rounded up. Typical class 2 plating is 25 µm (1 mil); ask your fabricator rather than
assuming.
This is a thermal limit, not a current limit — vias rarely fail by melting,
they fail by cooking the laminate around them.
Check this geometry with your fabricator — an aspect ratio above about 10:1 is hard to plate evenly, and thin plating in the middle of the barrel is exactly where a via fails.