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How to calculate stairs

When designing Straight stairs, Quarter Landing Stairs, or Half Landing Stairs we deal with straight flights and generally speaking it is not difficult to make a calculation of configuration, as well as of the arrangement of steps in the flight.

 

 

 

 

 

 

 

 

Example Calculation for Stairs with a Straight Flight

Let us describe the calculation process of the stairs with a straight flight as an example.

 

 

 

Suppose we build a staircase from the ground to the second floor. Floor to Floor Height is equal to 2600 mm. As a result we want to receive the stairs with correlation of the riser height and going 17/29 (you may read how select a correlation of the riser height and going in the section How to build stairs). To estimate the number of risers we should divide the Floor to Floor Height by the riser height which we take from the correlation of the riser height and going 2600 mm ÷ 170 mm = 15.29. Since the number of risers shall be a whole number, we round down the value received and get 15 risers. Now to figure out the precise value of the riser height we shall divide the Floor to Floor Height by the number of risers, that is 2,600 mm ÷ 15 = 173.33 mm. We have to round down the value received to 173 mm, because it is impossible to measure out the value of 173.33 mm by hand marking.
But now if we multiple 173 mm by 15 risers we receive the value of 2,595 mm. The difference can make either low or considerable values. As you have already understood, the accuracy in size is of crucial significance here. Ignoring even tenths after the decimal point at one step leads in the aggregate to the difference between the Floor to Floor Height and the stairs height. That’s why we recommend to execute the marking as accurately as possible and to use a beam compass if necessary. In the example set above the value of 5 mm can be compensated if you slightly level up the stairs, or if you increase the height of the last riser. You shall remember about the maximum allowable difference in the riser heights of the flight (you can read about it in the section How to build stairs). But the best thing is to avoid such situations.
The drawings proposed in the section Stairs Plans are made to a high precision, and the value of the height of stairs which you choose corresponds to the actual height of stairs.

Thus, we receive the following parameters for the stairs:
Number of risers - 15
Riser height - 173 mm
Going - 290 mm

When laying out the steps and choosing the correlation of the riser height and going for the stairs, you shall always take into consideration the dimensions of the existing aperture and remember about the headroom of stairs and its minimal size. You can figure out the headroom even on the top plan view.
For this purpose the dimensions of the existing aperture are plotted on the plan of the staircase. Then we determine on which step the edge of the aperture and the stairs overlap. Then subtract the total height of steps up to the overlapping from the floor-to-ceiling height. The value received will constitute the headroom of the stairs. As you already know from the section How to build stairs, the minimal size of the headroom makes 2,100 mm.

 

 

 


As you see it rarely happens to receive the exact match of values of correlation of the riser height and going given in the section How to build stairs. You can only get them if the floor-to-floor height is even divisible by the riser height. Therefore we have to round the received values in favor of these correlations.
You mark off the received values on the closed string or open string upwards and sidewards, and do not forget to adhere to parallel and perpendicular alignment of the steps. When marking take minimal sizes of closed and open strings into account (read about it in the section Stairs Models).

 

Example Calculation for Winder Stairs

When designing Single Winder Stairs or Double Winder Stairs, to calculate and determine the shape of treads in the flight is rather difficult. The shape of winder treads cannot be chosen at random. To provide for safety, convenience of usage, and also to receive a harmonic bend of the flight, special care must be used to evenly increase the depth of the treads from the tread with the narrowest going and up to the next square tread in the flight. At that the going of the largest winder tread at the distance of 305 mm from the edge shall not exceed the going of the smallest winder tread for more than 10 mm. Besides, the minimal size of the going at the distance of 305 mm from the edge shall be not less than 255 mm. The middle winder tread, that is the tread with the narrowest going, shall be positioned symmetrically to the axis going from the vertex of the turn angle of the flight to the point constituting the center of rounding of the inner part of the flight. The minimal going for any tread at the narrowest point shall make 152 mm according to American standards, and 120 mm according to European standards.
To receive a harmonic bend and to adhere to the minimal sizes mentioned above, the number of winder treads in the flight shall be from 7 to 9.

Fig. Minimal sizes of treads
 

 

 

 

part1 | part 2

 

 

 

Related Content :

- Stairs Types

- How to build stairs

- Stairs Models