How this works
Stair design is constrained by both safety codes and human comfort. The two key dimensions are riser (vertical rise per step) and tread (horizontal depth per step). Building codes set hard limits — the US IRC caps risers at 7.75 inches (197 mm) and minimum tread depth at 10 inches (254 mm); the UK Approved Document K limits risers to 220 mm and treads to a minimum of 220 mm. These keep the slope walkable and reduce trip hazards.
For comfort, builders use Blondel's formula: 2R + T should fall between 600 and 650 mm (about 24–26 inches), where R is the riser and T is the tread. A target of around 625 mm gives a stride that matches a typical adult walking pace. Steeper stairs (high R, short T) are exhausting; shallower stairs (low R, long T) take more horizontal space than usual but feel grand. Most residential staircases land at riser 175–195 mm and tread 250–280 mm.
The stringer is the diagonal board that supports the steps, and its length is just the Pythagorean hypotenuse of total rise and total run — sqrt(total_rise² + (steps × tread)²). Buy a stringer with at least 50 mm of margin since you'll trim to fit during install. Always cross-check this calculator's code result against your local building authority — the actual permitted dimensions vary by jurisdiction and by use (residential vs commercial vs egress vs spiral).
The formula
total_rise is the vertical distance from finished floor to finished floor. preferred_riser is your target riser height (typically 175–195 mm residential). The 625 mm Blondel target gives a comfortable stride. The code-check flags non-compliance with US IRC; for other jurisdictions, verify with the appropriate authority.
Example calculation
- Total rise 270 cm, preferred riser 18 cm.
- Steps = round(270/18) = 15. Actual riser = 270/15 = 18 cm. Tread = 625 − 2×180 = 265 mm. Stringer ≈ √(2700² + (15×265)²) ≈ 4793 mm. Angle ≈ 34.2°.
Frequently asked questions
What's a comfortable stair angle?
Around 30–37° is the sweet spot for residential stairs. Below 30° feels too shallow and takes excessive horizontal space; above 38° starts feeling steep and increases trip risk. Commercial stairs aim a touch shallower (28–35°). Spiral and ship's ladder stairs go up to 60–70° but are exempt from normal residential codes because of their specialised use.
Why does my staircase need a landing?
Most building codes require a landing every ~3.7 m (12 ft) of total rise — roughly every 16 steps for a 7-inch riser. Landings break long flights into manageable sections, give a place to rest mid-climb, and limit fall distance if someone trips. They also let direction changes happen safely. For long staircases in tall homes, plan for at least one landing; for short flights (under 12 steps) most codes allow continuous runs.