Staircase Calculator
Calculate stair dimensions — enter floor height to find the number of steps, riser height, tread depth, total run, and stringer length.
Staircase Dimensions
Enter your staircase dimensions and click Calculate.
How Does the Formula Work?
The staircase calculator determines every dimension you need to build a safe, comfortable stairway. You enter the total floor-to-floor height and your preferred riser and tread dimensions, and the tool calculates the exact number of steps, the actual riser height (adjusted so all steps are equal), the total horizontal run, the stringer length, and the stair angle. It also runs the Blondel comfort check to tell you whether the proportions feel natural to climb.
Actual Riser = Total Rise ÷ Risers
Treads = Risers − 1
Total Run = Treads × Tread Depth
Stringer = √(Rise² + Run²)
Angle = atan(Rise / Run)
Comfort = 2 × Riser + Tread (ideal 24–25 in / 60–65 cm)
The critical insight is that the total rise must be evenly divided among all risers. If you have 108 inches of total rise and want 7.5-inch risers, you get 14.4 — which rounds to 14 risers of 7.714 inches each. Every riser must be identical; the IRC allows a maximum variance of only 3/8 inch between the tallest and shortest riser in a flight. Unequal risers are the leading cause of stair falls.
IRC Building Code Requirements (2021)
The International Residential Code (IRC R311.7) governs residential stairs in the United States and sets strict limits. Maximum riser height is 7-3/4 inches (196 mm). Minimum tread depth is 10 inches (254 mm), measured from nosing to nosing. Minimum stair width is 36 inches above the handrail and 31-1/2 inches at and below handrail height. Maximum nosing projection is 1-1/4 inches. Headroom must be at least 6 feet 8 inches measured vertically from the nosing line. Landings must be at least as deep as the stair is wide, with a minimum of 36 inches.
The Blondel Comfort Formula
In 1675, French architect François Blondel established that comfortable stairs follow the rule 2R + T = 24 to 25 inches (60 to 65 cm), where R is riser height and T is tread depth. This approximates the average human stride on an incline. A 7.5-inch riser with a 10-inch tread gives 2(7.5) + 10 = 25 inches — right in the comfort zone. Values below 24 inches indicate stairs that are too steep (high risers, short treads), while values above 25 indicate stairs that are too shallow (short risers, deep treads). Both extremes cause fatigue and increase trip risk.
Stringer Sizing
The stringer is the diagonal structural member supporting the treads and risers. Its length equals the hypotenuse of the rise-run triangle. For a typical 9-foot floor with 13 treads at 10 inches, the run is 130 inches and the stringer length is about 170 inches (14.2 feet). At Home Depot and Lowes, dimensional lumber comes in 2-foot increments — buy the next size up. Standard stringer stock is a 2x12 board; after cutting the notches, at least 3.5 inches of solid wood must remain below the notch line for structural integrity. For wide stairs over 36 inches, use three stringers instead of two. Southern yellow pine and Douglas fir are the preferred species for stringers in the US market.
Stair Angle and Comfort
Residential stairs typically fall between 30 and 37 degrees. Below 30 degrees, the staircase takes up too much floor space and feels more like a ramp. Above 37 degrees, it becomes tiring to climb and dangerous to descend. Ship ladders and attic stairs can be steeper (up to 45 degrees) but are not code-compliant for primary access. ADA-accessible ramps are 1:12 slope (about 4.8 degrees) — a completely different calculation. The ideal residential angle is around 33 to 35 degrees, which corresponds to a 7–7.5 inch riser with a 10–11 inch tread.
Common Mistakes
The most frequent error is measuring total rise incorrectly. Total rise means finished floor to finished floor — not subfloor to subfloor. If you have 3/4-inch hardwood on the upper floor and tile on the lower floor, account for both finish thicknesses. A second common mistake is forgetting that the number of treads is one less than the number of risers. The bottom floor acts as the first tread, and the top landing acts as the last tread. If you cut equal numbers of risers and treads on your stringer, you will have one tread too many.
ADA and Universal Design
The Americans with Disabilities Act (ADA) sets strict requirements for commercial and public stairs. Risers must be between 4 and 7 inches, treads at least 11 inches deep, and nosings must not project more than 1.5 inches. Handrails are required on both sides at 34 to 38 inches height. For residential accessibility, wider treads (12 inches), shallower risers (6 to 7 inches), and a minimum stair width of 36 inches improve safety for elderly residents and people with mobility challenges. Universal design principles recommend consistent riser heights throughout — even a quarter-inch variation between steps increases the risk of tripping significantly.
For outdoor stairs, consider weather-resistant materials and non-slip surfaces. Composite decking treads from Trex or TimberTech resist rot and provide built-in traction. Concrete steps should have a broom finish or applied non-slip coating for wet weather safety.
Tips & Recommendations
Total rise means finished surface to finished surface — include tile, hardwood, or carpet thickness at both levels.
IRC allows max 3/8-inch variance between risers. Unequal risers are the number one cause of stair falls in homes.
The landing counts as the last tread. Do not cut an extra tread on your stringer or the top step will be too short.
Aim for 24–25 inches. Outside this range, stairs feel either too steep or too shallow and cause fatigue.
Frequently Asked Questions
How many steps for a 9 ft floor height?
With a 7.5-inch riser: 9 ft = 108 in ÷ 7.5 = 14.4, rounded to 14 risers. Actual riser = 108 ÷ 14 = 7.71 in (under the IRC 7.75 in max). You get 13 treads.
What is the 2R + T rule?
The Blondel formula: twice the riser plus the tread should equal 24–25 inches (60–65 cm). A 7.5 in riser + 10 in tread gives 2(7.5)+10 = 25 — ideal comfort.
What is the minimum stair width?
IRC requires 36 inches minimum clear width above the handrail and 31.5 inches at/below handrail height for residential stairs.
How long is the stringer?
Stringer = √(rise² + run²). For 9 ft rise and 108.3 in run: √(108² + 108.3²) ≈ 152.9 in = 12.7 ft. Buy 14 ft lumber.
What about landings?
IRC requires a landing at least as deep as the stair width (min 36 in) at the top and bottom. For runs longer than 12 ft, add an intermediate landing.
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