Drywall

Which drywall screw — length by board thickness, thread by framing material

Two separate choices. Length = board thickness + ≥⅝″ of bite into the framing (1¼″ for ½″ board, 1⅝″ for ⅝″). Thread = the framing material: coarse #6 for wood, fine for steel. The wrong thread strips out.

Source: ASTM C840 (screw length + penetration); coarse vs. fine thread by framing
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What this diagram shows

A two-part selection guide for drywall screws. Length is set by the board thickness plus grip: a half-inch board takes a 1¼-inch screw and a five-eighths-inch board takes a 1⅝-inch screw, because the screw must bite at least five-eighths inch into the wood framing beyond the board. Thread is set by the framing material: a coarse #6 thread with deep, widely-spaced threads is for wood studs, while a fine thread is for steel studs, where the fine threads tap and hold in metal. Using the wrong thread strips out — a coarse thread spins in steel and a fine thread will not bite wood. The #6 coarse-thread screw is the drywall default for wood framing.

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