This sheet lays out a 6 ft (72") 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: 13 balusters
72" ÷ (1-1/2" + gap) fits 13 balusters with 14 equal gaps of 3-3/4" (3.750"), 5-1/4" on centre level and 6-9/16" along the rail.
From the post face the leading edges fall at 4-11/16", 11-1/4", 17-13/16", 24-3/8" and on in 6-9/16" steps. Buy 15 to allow 10% for splits and miscuts.
3/4" metal: 16 balusters
Thinner balusters need more of them: 16 at 3-1/2"+ gaps, 4-1/4" on centre (5-3/8" along the rail). The first four marks: 4-7/16", 9-3/4", 15-1/8", 20-7/16".
1" metal or composite takes 15 at 3-9/16"; 3-1/2" flat pickets take 10 at 3-3/8".
The 36.9° rake
On a 7-1/2" rise and 10" run the rail climbs 54" over this 72" run and measures 90" 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 4-11/16" for wood or 4-7/16" 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 6' 3-1/2" apart, past the 6'-0" DCA 6 limit for prescriptive guard posts. Add 0 intermediate post (1 bays of about 72" 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).