Staircase Calculator

Total Height

Number of Steps

Step Depth (Optional)

Riser Height

unit

Tread Depth

unit

Total Run

unit

Stringer Length

unit

How to Calculate Stair Dimensions

The design of a staircase involves understanding the relationship between the total height, number of steps, and depth of each step. Here’s how to calculate the key components:

Riser Height:
The riser height is the vertical distance between two consecutive steps and is calculated using the formula:
$\text{Riser Height} = \frac{\text{Total Height}}{\text{Number of Steps}}$
Tread Depth:
The tread depth is the horizontal distance of the step. It can be specified or derived based on a 2:1 ratio with the riser height for standard comfort.
Total Run:
The total run is the sum of the tread depths for all steps, excluding the top step, and is calculated as:
$\text{Total Run} = \text{Tread Depth} \times (\text{Number of Steps} - 1)$
Stringer Length:
The stringer length is the diagonal distance from the base to the top of the staircase. Using the Pythagorean theorem:
$\text{Stringer Length} = \sqrt{(\text{Total Height})^2 + (\text{Total Run})^2}$

Example:

You need to build a staircase for a deck with a total height of 2.4 meters (240 cm). You want 12 steps and have no specific preference for tread depth.

Total height = 240 cm.
Number of steps = 12.
Calculate riser height:
$\text{Riser Height} = \frac{240}{12} = 20 \, \text{cm}$
Calculate tread depth: Assume 2:1 ratio with riser height:
$\text{Tread Depth} = 2 \times 20 \, \text{cm} = 40 \, \text{cm}$
Total run = $40 \times 11 = 440 \, \text{cm}$ .
Stringer length:
$\text{Stringer Length} = \sqrt{240^2 + 440^2} = 502.4 \, \text{cm}.$

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