What is the Blondel formula?

2 x riser + tread = 24-25 inches. It describes the relationship for comfortable walking rhythm.

Can I build stairs with different riser heights?

No. Maximum variation between adjacent risers must not exceed 3/8 inch (residential) or 3/16 inch (commercial).

The projecting edge of a tread that extends beyond the riser below it, typically 3/4 to 1-1/4 inches.

What is the minimum landing size?

Landings must be at least as wide as the stairway and at least 36 inches in the direction of travel.

How do I build stairs for an exterior deck?

Treads should be sloped slightly to shed water. Use pressure-treated lumber and allow for drainage gaps.

What is the maximum number of risers before a landing is required?

IRC requires a landing at every 12 feet of vertical rise, which corresponds to approximately 18 risers at the maximum 7.75 inch riser height. IBC requires a landing after every 12 feet of horizontal travel. Intermediate landings provide a resting point and reduce the severity of a fall.

How do I calculate stair stringer length accurately?

The stringer is the structural support that runs diagonally under the steps. Its length is calculated using the Pythagorean theorem: square root of (total rise squared plus total run squared). Account for the thickness of tread material when cutting stringer notches — the actual cut dimension for each step is riser height minus tread thickness, and tread depth minus nosing projection.

Stair Calculator

Unit

Total Rise (in)

Introduction

Stairs are fundamental architectural elements that connect different levels of a building while providing safe, comfortable, and code-compliant passage between floors. Designing stairs requires careful attention to the relationship between riser height (the vertical component of each step), tread depth (the horizontal walking surface), and total rise (the overall vertical distance between finished floors). Getting these proportions right is essential for safety — stairs with risers that are too high or treads that are too shallow are a leading cause of falls.

Building codes in most jurisdictions specify acceptable ranges for riser height and tread depth. The International Residential Code (IRC) requires a maximum riser height of 7.75 inches (197 mm) and a minimum tread depth of 10 inches (254 mm). The relationship between riser and tread is often guided by the "Blondel formula": two risers plus one tread should equal approximately 24 to 25 inches.

This Stair Calculator helps determine the number of risers, riser height, tread depth, and approximate stringer length for a given total rise and desired run. It provides values consistent with commonly recommended ranges for comfortable and safe stair design.

The design of safe and comfortable stairs involves balancing multiple variables within code-required constraints. The riser height determines how much effort is required to climb each step — higher risers are more fatiguing and potentially dangerous, especially for elderly individuals and children. The tread depth determines how securely the foot is placed — deeper treads provide more stability but require more horizontal space. The relationship between these two dimensions, expressed by the Blondel formula (2R + T = 24-25 inches), has been empirically validated over centuries as producing the most comfortable stair geometry for the average adult human gait.

Building code compliance is not merely a matter of safety — it is a legal requirement for any permitted construction project. The International Residential Code (IRC) and International Building Code (IBC) provide specific dimensional requirements that vary slightly between residential and commercial applications. Local jurisdictions may adopt amendments with stricter requirements, particularly in areas with cold climates where snow and ice on exterior stairs require additional considerations. This calculator provides dimensions based on commonly adopted code ranges, but always verify against your local code before ordering materials.

How to Use

Enter the total rise — vertical height from lower to upper finished floor.
Enter the total run — horizontal distance available for the staircase.
Optionally enter a preferred riser height or target tread depth.
Press Calculate to receive: number of risers, riser height, tread depth, stringer length, and stair angle.
Review results for compliance with local building code.

Measuring Total Rise Correctly: The total rise is the vertical distance from the finished floor of the lower level to the finished floor of the upper level. This is not simply the distance from subfloor to subfloor — you must account for the thickness of finished flooring materials on both levels. For example, if the upper level has 3/4 inch hardwood flooring and the lower level has 1/2 inch tile, the total rise changes by the difference in these thicknesses. Always measure after flooring is installed or account for the planned flooring thickness in your measurements.

Formulas and Calculations

Number of Risers

n = round(\frac{R_{total}}{h_{target}})

where R_total is total rise and h_target is target riser height.

Actual Riser Height

h = \frac{R_{total}}{n}

where R_total is total rise and n is the number of risers.

Tread Depth

d = \frac{T_{total}}{n - 1}

where T_total is total horizontal run and n is the number of risers.

Stringer Length

L = sqrt(R_{total}^2 + T_{total}^2)

using the Pythagorean theorem (See Pythagorean Theorem for detailed calculations).

Blondel Formula

2h + d = \text{24 to 25 inches}

for comfortable walking, where h is riser height and d is tread depth.

Stair Angle

theta = arctan(R_{total} / T_{total})

where R_total is total rise and T_total is total run.

Reference Tables

Standard Stair Dimensions by Building Code

Parameter	IRC (Residential)	IBC (Commercial)
Max riser height	7.75 in (197 mm)	7 in (178 mm)
Min tread depth	10 in (254 mm)	11 in (279 mm)
Min stair width	36 in (914 mm)	44 in (1118 mm)
Max variation between risers	3/8 in (9.5 mm)	3/16 in (4.8 mm)
Min headroom	80 in (2032 mm)	80 in (2032 mm)
Handrail height	34-38 in (864-965 mm)	34-38 in (864-965 mm)

Practical Tips

Check Your Local Code: Building codes vary by jurisdiction. Always verify that your calculated stair dimensions meet local requirements before cutting materials.

Account for Finish Flooring: The total rise must be measured from finished floor to finished floor. Account for the thickness of flooring materials on both levels.

Frequently Asked Questions

What is the Blondel formula?: 2 x riser + tread = 24-25 inches. It describes the relationship for comfortable walking rhythm.
Can I build stairs with different riser heights?: No. Maximum variation between adjacent risers must not exceed 3/8 inch (residential) or 3/16 inch (commercial).
What is a nosing?: The projecting edge of a tread that extends beyond the riser below it, typically 3/4 to 1-1/4 inches.
What is the minimum landing size?: Landings must be at least as wide as the stairway and at least 36 inches in the direction of travel.
How do I build stairs for an exterior deck?: Treads should be sloped slightly to shed water. Use pressure-treated lumber and allow for drainage gaps.
What is the maximum number of risers before a landing is required?: IRC requires a landing at every 12 feet of vertical rise, which corresponds to approximately 18 risers at the maximum 7.75 inch riser height. IBC requires a landing after every 12 feet of horizontal travel. Intermediate landings provide a resting point and reduce the severity of a fall.
How do I calculate stair stringer length accurately?: The stringer is the structural support that runs diagonally under the steps. Its length is calculated using the Pythagorean theorem: square root of (total rise squared plus total run squared). Account for the thickness of tread material when cutting stringer notches — the actual cut dimension for each step is riser height minus tread thickness, and tread depth minus nosing projection.

Limitations

This tool is a design aid and does not replace local building codes or professional structural calculations.
Complex staircases (winders, landings, spiral stairs) require specialized design.
Stringer length is calculated for a simple straight flight only.
Assumes uniform riser height and tread depth throughout the flight.
Handrail, guardrail, and landing requirements are not addressed.
Does not account for stair width or multiple flights.
Spiral and winding stairs have fundamentally different geometry not supported by this calculator.

Additional Stair Design Considerations

Beyond the basic dimensional calculations that this tool provides, several other factors affect stair safety and comfort. Headroom clearance must be at least 80 inches (2032 mm) measured vertically from a line connecting the stair nosings to any overhead obstruction — insufficient headroom is a common issue in basement stair conversions and attic access staircases. Handrail requirements include a specific gripping profile (type I or type II per IBC), a height of 34-38 inches measured from the stair nosing, and continuous extension beyond the top and bottom risers. Guardrails are required on open sides where the drop exceeds 30 inches.

Landings are required at the top and bottom of every stair flight and at every 12 feet of vertical rise (IRC) or every 12 feet of horizontal travel (IBC). Landings must be at least as wide as the stairway and a minimum of 36 inches in the direction of travel. For curved or spiral staircases, additional code requirements govern minimum tread depth at the walk line (typically 12 inches from the inside handrail) and maximum variation in tread depth. Winders (tapered treads) have specific dimensional constraints that require careful layout and are not supported by this basic calculator.

References

International Residential Code (IRC) — Section R311.7
International Building Code (IBC) — Section 1011
Architectural Graphic Standards (12th ed.), AIA
"Stair Design and Layout" — Fine Homebuilding Magazine

Last updated: May 24, 2026