How Does the Stair Length Calculator Work?

To understand how the calculator works, let’s break down the formula that calculates the stair length.

The total stair length is essentially the hypotenuse (diagonal length) of a right triangle where:

• The vertical rise is the total height of all steps combined.
• The horizontal run is the total depth of all steps combined.

Using the Pythagorean theorem, we can calculate this diagonal length, or stair length.

Formula for Calculating Total Stair Length

Let’s go step-by-step through the formula:

Calculate Total Rise (Vertical Distance):

Multiply the number of steps (N) by the rise height per step (H) to get the total rise.

$\text{Total Rise} = N \times H$

Calculate Total Run (Horizontal Distance):

Multiply the number of steps (N) by the run depth per step (D) to get the total run.

$\text{Total Run} = N \times D$

Calculate Total Stair Length:

Using the Pythagorean theorem, combine the total rise and total run to get the total stair length (L).

$L = \sqrt{(N \times H)^2 + (N \times D)^2}$

Example Calculation

Let’s say you’re designing a staircase with:

• 20 steps
• Rise height of each step = 7 inches
• Run depth of each step = 10 inches

Using the formula, we can calculate the total stair length.

Calculate Total Rise:

$\text{Total Rise} = 20 \times 7 = 140 \text{ inches}$

Calculate Total Run:

$\text{Total Run} = 20 \times 10 = 200 \text{ inches}$

Calculate Total Stair Length:

$L = \sqrt{(140)^2 + (200)^2}$

$L = \sqrt{19600 + 40000}$

$L = \sqrt{59600} \approx 244 \text{ inches}$

So, the total stair length for this staircase would be approximately 244 inches.