This sheet lays out a 5 ft (60") 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: 11 balusters
60" ÷ (1-1/2" + gap) fits 11 balusters with 12 equal gaps of 3-5/8" (3.625"), 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", 23-3/4" and on in 6-7/16" steps. Buy 13 to allow 10% for splits and miscuts.
3/4" metal: 13 balusters
Thinner balusters need more of them: 13 at 3-9/16"+ gaps, 4-5/16" on centre (5-7/16" along the rail). The first four marks: 4-1/2", 9-15/16", 15-5/16", 20-3/4".
1" metal or composite takes 12 at 3-11/16"; 3-1/2" flat pickets take 8 at 3-9/16".
The 36.9° rake
On a 7-1/2" rise and 10" run the rail climbs 45" over this 60" run and measures 75" 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 4-1/2" 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 63-1/2" 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).