Free stud calculator
Studs and plates for a wall, with corners and openings counted.
Studs = ⌈wall length ÷ spacing⌉ + 1 + 2 × (corners + openings + joining walls)
Openings also need headers, cripples and sills, which this count leaves out. For wall sheathing, use the plywood calculator.
Divide the wall length in inches by the stud spacing, round up and add one. Then add two for each corner, each wall that joins it and each door or window, and about 10% for waste. A 20 ft wall at 16" on centre with two corners and one window: 16 + 6 = 22, or 25 with waste.
It is a quick estimate that already covers corners, openings and waste for walls at 16" on centre. The calculator gives a closer count for your wall.
A load-bearing wall usually has one bottom plate and a double top plate — three times the wall length in plate stock. Non-bearing walls can use a single top plate.
16" on centre is standard for load-bearing walls and suits most drywall and sheathing. 24" is allowed for many walls under the IRC and saves lumber (advanced framing), but check your code and loads.