The Two Numbers That Matter
A stair is defined by its rise — the vertical height of each step — and its run, the horizontal depth of each tread. Everything else follows from those two and the total height to be climbed.
Number of risers = Total rise ÷ Target riser height, rounded to a whole number
Actual rise = Total rise ÷ Number of risers
Number of treads = Risers − 1
Total run = Treads × Tread depth
Stringer length = √(Total rise2 + Total run2)
Note the treads = risers − 1 relationship. The top riser lands on the upper floor, which serves as the final tread, so a stair with 15 risers has 14 treads.
Why Every Riser Must Be Equal
People climb stairs by rhythm, not by looking. Once the first two steps have set the expectation, the foot is placed by memory. A single riser differing by even 3/8 of an inch is a well-documented trip hazard, and building codes reflect this: the IRC allows a maximum variation of 3/8″ between the largest and smallest riser in a flight.
This is why you divide the total rise into equal parts rather than picking a round riser height and letting the last step take the remainder. The most common mistake in DIY stair building is a short or tall step at the top or bottom.
Code Limits
| Requirement | Residential (IRC) | Commercial (IBC) |
|---|---|---|
| Maximum riser height | 7¾″ | 7″ |
| Minimum tread depth | 10″ | 11″ |
| Minimum width | 36″ | 44″ |
| Minimum headroom | 6 ft 8″ | 6 ft 8″ |
| Maximum riser variation | 3/8″ | 3/8″ |
| Nosing projection | ¾″ to 1¼″ | ¾″ to 1¼″ |
| Handrail height | 34–38″ | 34–38″ |
Codes vary by jurisdiction and are periodically revised. Always confirm with the local building department before cutting stringers — a stair that fails inspection has to be rebuilt entirely.
The Comfort Rules
Three traditional formulas encode what feels comfortable underfoot. A well-proportioned stair satisfies all three.
| Rule | Target | Reasoning |
|---|---|---|
| 2 × Rise + Run | 24″ to 25″ | Matches the human stride; the oldest and most reliable rule |
| Rise + Run | 17″ to 18″ | Simple check for proportion |
| Rise × Run | 70″ to 75″ | Used in some European practice |
The 2R + T rule dates to the seventeenth-century French architect François Blondel, who observed that a person's stride shortens by roughly twice the height climbed. It has survived three centuries because it works.
Comfortable Combinations
| Rise | Run | 2R + T | Angle | Character |
|---|---|---|---|---|
| 6″ | 12″ | 24″ | 26.6° | Gentle, generous |
| 6.5″ | 11.5″ | 24.5″ | 29.5° | Comfortable |
| 7″ | 11″ | 25″ | 32.5° | The classic proportion |
| 7.25″ | 10.5″ | 25″ | 34.6° | Common in modern houses |
| 7.75″ | 10″ | 25.5″ | 37.8° | At the code limit; steep |
Space Requirements
Stairs consume more floor area than people expect. A standard 9-foot floor-to-floor height needs about 12 feet of horizontal run, plus landings top and bottom. Reducing the run to fit a tight space forces steeper risers, which quickly runs into the code limit and into discomfort.
Headroom is measured vertically from an imaginary line joining the tread nosings, and 6 ft 8 in is the minimum at every point. Openings in the floor above are the usual constraint.
Stringer Notes
- Deduct the tread thickness from the bottom riser when cutting stringers, or the first step will be too tall by exactly one tread thickness. This is the single most common cutting error.
- Use 2×12 stock for stringers; anything narrower leaves too little material after the notches.
- Space stringers 16″ on centre for typical residential loads, closer for wide stairs or heavy use.
- Nosing is not part of the run. The run is measured nosing to nosing; the overhang projects beyond it.
Frequently Asked Questions
How many steps for a 9-foot ceiling?
A 108-inch total rise at about 7.25″ per riser gives 15 risers of 7.2″ and 14 treads, running about 147 inches — just over 12 feet.
Can the last step be a different height?
No. Codes allow only 3/8″ variation across the whole flight, and an uneven step is a genuine hazard. Divide the total rise equally.
What is the most comfortable stair?
Around a 7″ rise with an 11″ run — 2R + T equals exactly 25″, and the angle is a little over 32°.
Do I measure floor to floor or floor to ceiling?
Floor to floor: from the finished lower floor to the finished upper floor, including the thickness of the upper floor structure. Using ceiling height alone omits the joists and gives a stair that lands short.