Stair Calculator

To design building stairs using this tool, follow these steps:

1. Total Rise: Enter the vertical floor-to-floor height (the distance from the lower finished floor level to the upper finished floor level).
2. Stair Standard: Select from Residential (IRC), Commercial/Public (IBC), or Custom. This sets maximum riser height and minimum tread depth guidelines.
3. Target Riser & Tread: Input the preferred riser height and tread depth. Default values are set to typical standards (e.g. 170 mm riser and 280 mm tread).
4. Advanced Settings: Toggle these to include nosing, stair width, a landing run length, or to input your own custom code thresholds.

Stair rise and run are the two primary dimensions of a staircase step:

• Riser Height (R): The vertical height between two consecutive tread surfaces.
• Tread Depth (T): The horizontal surface width of a single step, measured from the front edge to the riser, excluding the nosing.
• Total Rise: The absolute vertical height spanned by the entire flight of stairs.
• Total Run: The total horizontal footprint length of the staircase flight from the face of the first riser to the face of the last riser.

Architects and builders calculate stair geometry using these standard mathematical formulas:

• Number of Risers: Calculated by dividing the total rise by the target riser height and rounding to the nearest whole step:
  Number of Risers = Round(Total Rise ÷ Target Riser Height)
• Actual Riser Height: Calculated by dividing the total rise by the rounded number of risers:
  Actual Riser Height = Total Rise ÷ Number of Risers
• Number of Treads: In a straight flight of stairs, the number of treads is always one less than the number of risers:
  Number of Treads = Number of Risers - 1
• Total Run: The total horizontal footprint length, including landing lengths if applicable:
  Total Run = (Number of Treads × Tread Depth) + (Landing Length × Landings)
• Stringer Length: The diagonal structural board supporting the treads and risers (calculated using the Pythagorean theorem):
  Stringer Length = √(Total Rise² + (Number of Treads × Tread Depth)²)

Climber comfort is assessed using Blondel's stride formula, which establishes an ergonomic relationship between step rise and tread run:

If the sum of twice the riser plus one tread is below 600 mm, the stairs feel too shallow and the stride feels unnaturally short. If it exceeds 640 mm, it requires an excessive stride length, leading to fatigue and tripping hazards.

In addition, the ideal pitch angle for standard staircases is between 30 and 37 degrees. Slopes steeper than 40 degrees are dangerous for typical public occupancy, while slopes below 20 degrees are too shallow and should be replaced by a ramp.

To clarify how these steps and equations work in practice, let's walk through a typical design example for a residential building.

Stairway safety codes differ significantly between residential and public buildings to balance space efficiency and crowd accessibility:

• Residential (IRC): Stairs in private single-family homes can be steeper to save footprint. The maximum riser height is 7.75 inches (196.8 mm), and the minimum tread depth is 10 inches (254 mm).
• Commercial (IBC): Stairs in public spaces require flatter runs for crowd safety, egress speed, and accessibility. The maximum riser height is 7 inches (177.8 mm), the minimum riser height is 4 inches (101.6 mm), and the minimum tread depth is 11 inches (279.4 mm).

Stair layouts must prioritize occupant safety and conform to local design codes. Remember that minor changes in riser or tread dimensions can significantly impact the ease of climbing and local compliance.