What Is a Stairs Angle Calculator?

A Stairs Angle Calculator determines the angle or slope of a staircase based on the vertical height (rise) and the horizontal depth (run). The angle is crucial for:

• Ensuring compliance with building codes.
• Designing a staircase that is safe and comfortable to use.
• Balancing the steepness and usability of stairs.

Formula for Stair Angle

The formula to calculate the angle of a staircase is:

$\text{Angle} = \arctan\left(\frac{\text{Rise}}{\text{Run}}\right)$

Here:

• Rise = the total vertical height of the staircase.
• Run = the total horizontal length of the staircase.

This formula uses the arctangent function (inverse tangent) to calculate the angle.

Example

Suppose the staircase has:

• Rise = 120 inches
• Run = 144 inches

The angle is calculated as:

$\text{Angle} = \arctan\left(\frac{120}{144}\right)$

$\text{Angle} \approx 39.8^\circ$