### How to calculate the concrete volume of a staircase?/ Volume of concrete in a staircase.

Let us now calculate the volume of concrete in a staircase flight & landing as shown in the below drawings.

Let us calculate the concrete volume of the landing slab, steps, & waist slab separately for easy understanding.

#### 1. Landing slab:

Given data :

Landing thickness = 200mm.= 0.2m.

Landing width = 0.9m.

Landing length = 1.0m.

The concrete volume of the landing slab

= [2nos.× length × width × thickness]

= [2nos. × 1m. × 0.9m. × 0.2m.]

= 0.36 cum.

#### 2. Steps:

Given data:

No. of steps = 8 nos.

Width of the step = 1m. {length ( l ) }

Riser = 166.66mm. = 0.1667m. { height ( h ) }

Tread = 250mm. = 0.25m. { base ( b ) }

The individual step forms a triangular prism as shown in the above drawing.

The formula to calculate the volume of a triangular prism is [1/2 × b × h × l]

The concrete volume of the total staircase steps

= 8nos.× [ 1/2 × base × height × length ]

= 8nos. × [ 1/2 × 0.25m. × 0.1667m. × 1m.]

= 8nos. × 0.0208

= 0.1667 cum.

#### 2. The waist slab:

Given data:

The thickness of the waist slab = 150mm = 0.15m.

Width of the waist slab = 1m.

Let us draw a triangle ABC, joining the two ends of the waist slab as shown above.

By Pythagoras theorem,

AC2=AB2 + BC2

From the staircase drawing,

The horizontal distance AB = 2m, &

The vertical distance BC

= [landing height + bottom landing thickness.]

= [1.3m + 0.2m.] = 1.5m.

AC2 = 22 + 1.52

AC = √22 + 1.52

AC = √6.25

Length AC = 2.5m.

Now, the concrete volume of the waist slab

= [length × width × thickness.]

= [2.5m × 1m. × 0.15m.]

= 0.375cum.

The concrete volume of the staircase

= [The volume of landing + the volume of steps + the volume of waist slab.]

= [0.36 cum. + 0.1667 cum + 0.375 cum.]

= 0.902 cum.

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