How to Calculate Stairs
Calculating stairs starts with measuring the total rise -- the vertical distance from finished floor to finished floor. Divide that total rise by the ideal riser height (7.5 inches) to get the number of risers. Round to the nearest whole number, then recalculate the exact riser height by dividing total rise by the number of risers.
Risers = Round(Total Rise / 7.5")
Riser Height = Total Rise / Risers
Treads = Risers - 1
Total Run = Treads x Tread Depth
Stringer = sqrt(Rise² + Run²)
Worked example: Total rise = 108" (standard 9 ft floor-to-floor). 108 / 7.5 = 14.4, round to 14 risers. Riser height = 108 / 14 = 7.714" (7-11/16"). With 10" treads: total run = 13 x 10 = 130" (10'10"). Stringer = sqrt(108² + 130²) = 169" (14'1") -- buy 16 ft 2x12 stringers.
Stair Building Code Requirements (IRC Residential)
| Requirement | IRC Code | Notes |
|---|---|---|
| Max riser height | 7-3/4" (7.75") | Consistent within 3/8" variation |
| Min tread depth | 10" | Measured nosing to nosing |
| Nosing projection | 3/4" to 1-1/4" | Required if risers are solid |
| Min width | 36" | Clear width between walls/rails |
| Min headroom | 6'8" (80") | Measured vertically from tread nosing |
| Handrail height | 34" - 38" | Measured from stair nosing |
| Landing | Required top & bottom | Min 36" in direction of travel |
| Max riser variation | 3/8" | Between tallest and shortest riser |
The Riser + Tread Rule
The comfort of a staircase depends on the relationship between riser height and tread depth. The classic rule: Riser + Tread = 17" to 18". Another common formula: 2 x Riser + Tread = 24" to 25". A 7.5" riser with a 10" tread: 7.5 + 10 = 17.5" -- perfect.
Frequently Asked Questions
How many steps for an 8-foot ceiling?
With a standard 9 ft floor-to-floor height, you need 14 risers at 7.71" each, giving you 13 treads. Total run: about 10 ft 10 in.
What is the ideal stair angle?
Between 30 and 37 degrees for residential comfort. The standard 7.5" riser / 10" tread gives about 37 degrees.
Can I use 2x10s for stair stringers?
Not recommended. After cutting notches from a 2x10, the remaining wood may be less than 3.5". Always use 2x12s.