Finding the angle of stair is very important in building designing as if the angle is higher than the recommended angle then it is very hard to climb the floor with stair a person may tired easily by climbing.

For residential stairs, the slope is usually between 30° and 42°,

TYPE 01 : If height & horizontal distance of a staircase is known :

Given data:

Height of landing = 1400mm.

Horizontal distance = 2200mm.

tanθ = [opposite ÷ adjacent]

        = [height ÷ horizontal distance]

         = [ 2000mm.÷ 1700mm.]

     = 0.85

θ = tan^-1 0.85

  = 40.36°

TYPE 02 : If Riser and Treade is known :

Riser = The Vertical part (|)in stair which help a person to climb.

Treade = The Horizontal part (__) in stair

Given data:

Riser = 150mm.

Tread = 260mm.

Slope 

     = [riser ÷ tread]

     = [ 150mm.÷ 260mm.]

     = 0.58

Here, slope = tanθ

So, 

tanθ = 0.58

θ = tan^-1 0.58

  = 30.00°

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