How to calculate the stairs ?

Calculating stairs involves several steps to ensure that they are safe, comfortable, and fit the intended space. Here is a detailed guide on how to calculate stairs:

Step by step guide to calculating stairs

1. Determine total rise (H)

   • Measure the total height from the lower floor to the upper floor, including the finished flooring.

2. Decide on riser height (h)

   • The comfortable height for a riser is usually between 17 cm and 19 cm. For safety and comfort, it should not exceed this range.

3. Calculate number of risers (n)

   • Use the formula:

   $n = \frac{H}{h}$

   • Round the result to the nearest whole number to get the number of risers.

4. Adjust riser height

   • Recalculate the exact riser height using the total rise and the whole number of risers:

   $h = \frac{H}{n}$

5. Determine tread depth (s)

   • The tread depth should be between 25 cm and 30 cm for comfort. Use the standard stair formula:

   $2h+s\approx 63cm$

   • Rearrange to solve for s:

   $s \approx 63 - 2h$

6. Calculate the total run (L)

   • Total run is the horizontal length of the stairway and is calculated by multiplying the number of treads (one less than the number of risers) by the tread depth:

   $L = s \times (n - 1)$

Example calculation

Let's consider a room with a total rise of 270 cm and a preferred riser height of 18 cm:

1. Total rise (H): 270 cm
2. Preferred riser height (h): 18 cm

Calculate number of risers (n):

$n = \frac{270}{18} = 15$

Adjust riser height:

Since 15 is a whole number, the riser height remains 18 cm.

Determine tread depth (s):

$s \approx 63 - 2 \times 18 = 27 \, \text{cm}$

Calculate the total run (L):

$L = 27 \times (15 - 1) = 27 \times 14 = 378 \, \text{cm}$

$\text{By following these steps, you can calculate the dimensions of a staircase that is both safe and comfortable to use. This process involves measuring the total rise, deciding on an appropriate riser height, calculating the number of risers and tread depth, and finally determining the total run. Adjustments may be necessary to fit specific spatial constraints and design preferences and regulations in your country.}$