How long should screws be to fasten 3/4" thick cabinets to studs covered with 1/2" drywall?

To effectively fasten 3/4" thick cabinets to studs that are covered with 1/2" drywall, the length of the screws must adequately penetrate both materials to ensure a secure connection.

In this scenario, the total thickness that the screw needs to penetrate is the combined thickness of the drywall (1/2") and the cabinets (3/4"). This gives a total thickness of 1 1/4" (1/2" + 3/4"). However, to ensure that the screw is long enough to securely anchor into the studs behind the drywall, it's important to add a little extra length.

By selecting screws that are 2 1/4" long, you provide the necessary depth to penetrate through the drywall and into the stud sufficiently. Specifically, 2 1/4" of screw length allows for 1 1/4" to accommodate the thickness of both the drywall and the cabinet material, and leaves an additional inch for anchoring solidly into the stud, promoting a strong and stable installation. Thus, 2 1/4" screws are the appropriate length to ensure the cabinets are fastened securely to the studs.