This sheet lays out an 8 ft (96") stair railing between post faces, measured level along a 7-1/2" × 10" stair. It compares 1-1/2" wood with 3/4" metal, gives every mark from one hook of the tape, and checks the 4-3/8" sphere rule and post spacing.
1-1/2" wood: 18 balusters
96" ÷ (1-1/2" + gap) fits 18 balusters with 19 equal gaps of 3-5/8" (3.632"), 5-1/8" on centre level and 6-7/16" along the rail.
From the post face the leading edges fall at 4-9/16", 10-15/16", 17-3/8", 23-13/16" and on in 6-7/16" steps. Buy 20 to allow 10% for splits and miscuts.
3/4" metal: 21 balusters
Thinner balusters need more of them: 21 at 3-5/8"+ gaps, 4-3/8" on centre (5-1/2" along the rail). The first four marks: 4-9/16", 10-1/16", 15-9/16", 21-1/16".
1" metal or composite takes 20 at 3-5/8"; 3-1/2" flat pickets take 13 at 3-5/8".
The 36.9° rake
On a 7-1/2" rise and 10" run the rail climbs 72" over this 96" run and measures 120" along its length. Clear gaps are measured level, square to the plumb balusters; every tape mark along the rail is the level distance ÷ cos 36.9° = × 1.2500.
Cut fillet strips to 4-9/16" for wood or 4-9/16" for metal, with 36.9° on both ends. Keep the bottom rail within 1-1/2" of the nosing line so the tread-riser triangle stays under a 6" sphere.
This span needs a middle post
With 4x4 posts the centres would be 8' 3-1/2" apart, past the 6'-0" DCA 6 limit for prescriptive guard posts. Add 1 intermediate post (2 bays of about 46-1/4" clear), or use a railing kit rated for this section length.
The rail sits 34" above the nosings (34" to 38" where it is also the handrail).