Definition of stair run: Stair run is the total horizontal distance traveled by a passenger using the staircase, from the first riser face to the last riser.

Definition of stair rise: The rise of a stairway is the total vertical height of a stairway between the running surface, which is just before the first stair tread or walk, and the beginning of the horizontal tread surface at the top of the staircase.

Working out stairs can sometimes be a bit hectic topic . In this article we are going to look at how to calculate stairs(riser, tread ,slope) the quick and easy way to work out your stair requirements.

How to Calculate Stairs:

Figure- 1: Staircase with details

In this example, let me consider a staircase with details shown in Figure 1.Basically, in architectural drawings , the levels such as FFL (floor finish level) or SSL (structural slab level) are already provided as per the design. In figure-1, i have shown two levels ,one at floor(+4000 mm) and other at landing(+1900 mm). I have shown these levels to give an idea when after completing your degrees in civil engineering ,you will work on site construction and it will help you as well.

1. Calculate the flight

Here i have considered two levels as you can see in the figure 1 above

Floor level= 1900 mm

Landing level= 4000 mm

Flight = 4000 - 1900 = 2100mm

So, staircase is  2100 mm high.

2.Calculate the number of steps that will be needed:

Considering an ideal riser of 150 mm, the height of the space is divided by the height of each step.

2100/150= 14 steps

3. Calculate the height of each riser and width of each tread:

The height of the space is divided by the number of steps that we have just obtained:

2100/14 = 150 mm height for each riser

So as per standard, we are providing 300 mm as tread length.

= 3800/300

= 13 No.s

we know that :(T+2R=600)

so, T + 2x150=600mm

Scope of the formula:

Nicolas Francois Blondel (1675–1683) was the first known person to establish the ergonomic relationship of tread and riser dimensions in the last volume of his Cours d'architecture.

He specified that 2 x riser + tread = step length.

Ideal requirements of stair

Step proportions:

T + 2R = 60-64 cm

T x R= 400-426 cm

2T + R = 40-45 cm

Standard values:

For residential building: T = 22-27 cm, R = 15-17 cm

For public building: T = 30 cm, R = ≤15 cm

How to work out the angle or slope of the stair?

Figure- 2: Slope of staircase

In order to work out our stair angle we can use a bit of basic trigonometry refer figure-2

Total rise =1940 mm

Total Run = 3800mm

1940 / 3800 = 0.51

Inverse Tangent of 0.51 =27 degrees

The angle or slope of staircase = 27 degrees

As per IS 456, the slope or pitch of stair should be between 25 degrees to 40 degrees.

Internal staircases should:

One flight between landings shall be designed for maximum number of people occupying that floor.

Not have any fire risk spaces opening directly on to staircase.

Have their external exit door at ground level, and should open directly to open spaces, or large lobby, if necessary.

Main stairs to be continuous from ground to terrace.

Should not have any combustible decoration.

Have clearly visible exit signs.

Show individual floors.

Be of non combustible material.

Be a self contained unit, enclosed, and with one side made of external wall.

Not be arranged around a lift shaft.

Not be of hollow combustible construction.

Not have gas piping or electrical panels along the stairway.

Can have ducting if it provides one hour of fire rating.

It has dimensions as:

minimum staircase width = 1.5 m

maximum riser height = 150mm

maximum 15 risers per flight

handrail height = 1.0m

External staircases are desirable for high rise buildings, and when provided shall comply to the following:

Spiral staircase can be employed but should be limited to a building not higher than 9m.

Designed for a low occupant load.

Not less than 1500 in diameter.

Designed for an adequate headroom.All external staircases should be directly connected to ground.

Entrance to external staircase shall be separate and remote from internal staircase.

No door or window opening shutter shall obstruct the staircase.

Should be kept in sound operable conditions.

Should be kept obstruction free.

The external staircase shall be constructed of non combustible materials, and any doorway leading to it shall have the required fire resistance.

No external staircase, used as a fire escape, shall be inclined at an angle greater than 45 deg. from the horizontal.

Some dimensions as:

Staircase flight width = 1250mm

Maximum riser = 190mm

Maximum risers per flight = 15