This sheet lays out a 4 ft (48") 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: 9 balusters
48" ÷ (1-1/2" + gap) fits 9 balusters with 10 equal gaps of 3-7/16" (3.450"), 4-15/16" on centre level and 6-3/16" along the rail.
From the post face the leading edges fall at 4-5/16", 10-1/2", 16-11/16", 22-7/8" and on in 6-3/16" steps. Buy 10 to allow 10% for splits and miscuts.
3/4" metal: 10 balusters
Thinner balusters need more of them: 10 at 3-11/16" gaps, 4-7/16" on centre (5-9/16" along the rail). The first four marks: 4-5/8", 10-1/8", 15-11/16", 21-1/4".
1" metal or composite takes 10 at 3-7/16"; 3-1/2" flat pickets take 7 at 2-15/16".
The 36.9° rake
On a 7-1/2" rise and 10" run the rail climbs 36" over this 48" run and measures 60" 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 4-5/16" for wood or 4-5/8" 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.
Posts and heights
With 4x4 posts the centres are 51-1/2" apart, inside the 6'-0" DCA 6 limit for guard posts.
The rail sits 34" above the nosings (34" to 38" where it is also the handrail).