Stair Stringer Calculator

Compute structural stair riser heights, total tread runs, and stringer lengths accurately.

Total Rise Profile

Computed Stringer Blueprint

Exact Step Count 6 Steps
Exact Riser Height 7.00 in
Total Run Footprint 52.50 in
Min Stringer Length 67.23 in

Stair Geometry & The Pythagorean Theorem

To establish equal step margins, the step count is derived by dividing total elevation rise by target step increments. The exact uncut raw board stringer length uses the Pythagorean theorem:

$$\text{Stringer Length} = \sqrt{(\text{Total Rise})^2 + (\text{Total Run})^2}$$

Geometric Safety Layouts for Stair Construction

Designing comfortable, safe stairways requires precisely balancing rise heights and tread runs within strict building code limits. Even minor layout variations between steps create serious trip hazards and will fail local building inspections.

The Standard Rise/Run Ratio

To maintain standard walking gaits, carpenters follow the traditional rule of thumb: Rise + Run should equal roughly 17 to 18 inches. Residential building codes generally limit the maximum individual step rise to 7-3/4 inches, alongside a minimum horizontal tread run of 10 inches.

Allowing for Tread Thickness

When cutting out your timber stringer notches, remember to trim off a thickness equal to one tread from the bottom foot layout point. This adjustment ensures your very first step matches the exact height of the remaining steps once the finished treads are installed.

Stair Construction Code Property IRC Standard Threshold Limit Primary Field Safety Application
Maximum Step Rise Limit 7.75 Inches Maximum Prevents steep, vertical step heights
Minimum Horizontal Tread Run 10.00 Inches Minimum Ensures safe, full foot placement on steps