Stud count is wall length divided by spacing, plus one to close the end. Sixteen inches on centre is 1.333 feet, so a 20 foot wall is 15 bays and 16 studs before any openings.
Sixteen or twenty-four
Sixteen inches on centre is the residential standard and what most sheet goods are made for. Twenty-four is permitted for many non-bearing and some bearing walls, saves lumber, and leaves more room for insulation.
Twenty-four inch spacing needs thicker drywall on ceilings and can telegraph on walls. Check what your local code allows for the wall's role before deciding.
Plates are three times the length
A standard wall has a single bottom plate and a doubled top plate, so plate lumber is three times the wall length.
The upper top plate laps the joints in the lower one and ties intersecting walls together. That lap is structural, not optional.
Openings add more than people expect
A window needs two king studs, two jack studs, a header, and cripples above and below. That is five or six extra pieces for one opening.
Corners and partition intersections need backing to catch drywall. A California corner uses fewer studs than the old three-stud method and leaves room to insulate.
Blocking, backing and fire stops
Beyond studs and plates, a wall needs lumber that nothing in a stud count captures. Blocking between studs to catch the edges of drywall sheets, backing behind cabinets, grab bars and televisions, and fire blocking where codes require it.
Backing is the one people regret. Once the drywall is up, hanging anything heavy means finding a stud or opening the wall. Putting flat blocking where a cabinet or a television will go costs a few boards now.
Add roughly ten percent to the stud lumber for all of this, more on a wall with a lot of cabinetry.
Crowning and why walls end up wavy
Every stud has a slight bow along its length — the crown. Framed properly, all crowns face the same direction, so the wall has one consistent shallow curve rather than a series of in-and-out waves.
Sighting down each stud before nailing takes a second and is the difference between a flat wall and one that shows every stud under a coat of paint.
Badly bowed studs should go into short walls, into cripples over openings, or back on the pile. There are usually a few in every bundle.