# Calculating stairs - formulas for calculating stairs

- Basics for the calculation
- Step 1 - Number of levels
- Step 2 - Exact step height
- Step 3 - Depth of the step
- Steepness of the stairs
- Run length of the stairs
- landing

- Regulations from DIN 18065
- Spiral stairs
- Diagonally staircase
- Stairs in the quadrant or semicircle
- Wendel-Steep staircase as a prefabricated staircase

You can not just build stairs as you like. To make a staircase both comfortable and safe, careful calculations are necessary. This is not difficult, if you know some basic concepts and the right formulas. In our article we show you how it works.

Whether a staircase is safe and comfortable to do depends on several factors: the width of the staircase, its pitch, and the width and height of the steps. All these factors have to interact in the right proportions. For stairs, there are also generally certain standards that should be adhered to. Although they can be disregarded in some cases (for example, if you only want to create two to three steps in a lower garden area). In general, however, this is not recommended, since unfavorably designed stairs, the risk of accidents is significantly higher. Even committing is then noticeably more uncomfortable.

## Basics for the calculation

In order to plan a staircase correctly and then calculate it, you first have to know some basic starting values. These apply to a straight staircase.

- Height of the stairs (H) - the height difference that a staircase should overcome
- Depth of stairs (T) - the length of the entire staircase construction at the bottom of the lower floor
- Length of the stairs (L) - the "diagonal" length of the stairs, which can be calculated from height and depth (right triangle)

These three values result from the available space that one has (or wants to use) for the stairs. The length of the stairs is for now only a trivial value.

### Step 1 - Number of levels

The number of steps can be easily determined by dividing the total height difference to be overcome by the desired step height. For the step height one should keep to the usual norm values:

- Missile stairs: 16 - 19 cm, optimal between 17 and 18 cm
- Basement stairs: 18 - 19 cm
- Attic stairs: 18 - 20 cm
- for administration buildings: 16 - 17 cm
- for commercial use: 17 - 19 cm
- for schools (children are much smaller than adults): 14 - 16 cm

Hint: So you can see that for most uses,18 cm isa very good average that you can roughly assume.This applies to both the interior and the exterior.The step height is sometimes referred to as "slope".

### Step 2 - Exact step height

Since you can not create "half steps" in the implementation of the stairs (in our example it would be 16.66 steps), you usually round up or down the number of steps. In this example, we rounded up to 17 levels. Now the exact step height has to be recalculated.

### Step 3 - Depth of the step

Important next to the step height but also the depth of the individual steps (appearance width). Only both together in the right proportions ensure a comfortable and safe walking on the steps.

There are formulas to calculate the optimal ratio. The so-called Blondel formula is used for this:

2 * step height + step depth = 63 cm stride length

**Step depth = 63 cm step length - 2 * step height**

The basis for this ratio is the average step length of adult people. Since people can be different in size, their stride also varies slightly, between 59 and 65 cm on average. The Blondel Rule, which is used in the entire staircase, takes as a value, however, step lengths of 62 - 64 cm. This fits very well for most people.

Tip: You always have to distinguish between the width of the step and the step width.The two do not necessarily have to be the same size, because the upper stage may be hanging over the underlying one.This is called supernatant.To get from the step width to the step width, you have to subtract the protrusion, because this protrusion area is not considered as actually usable width.

### Steepness of the stairs

However, the rule mentioned above only applies to stairs whose inclination angle is between 30 and 37 °. This is the case for most straight and easy stairs, so you do not have to worry about it. Only spiral staircases and other special staircase shapes (steep or ladder stairs) can have different inclinations here. There are always separate calculation methods.

### Run length of the stairs

Occasionally one reads also the term of the running length of the stairs. This value usually does not matter so much when planning a staircase, so let's just briefly mention it here. The run length is obtained by multiplying the available run width by the number of steps.

### landing

In general, staircase construction assumes that a staircase should not have more than 18 steps all the way through. If one uses conventional storey heights (up to about 3 meters), this is the case in most residential buildings.

If the staircase construction yields more steps, a plateau (landing, platform) is usually installed in the middle of the stairs. Also for its length, there is a fairly simple formula.

Platform length = width of step + number of steps * 65 cm

Tip: It is not completely fixed, you can freely choose the number of steps over the pedestal.However, it should definitely be an odd number so as not to interrupt the rhythm of the song.

## Regulations from DIN 18065

In the above part we have already determined optimal values for most stairs used in the house. If you can stick to these values, you definitely have an optimal, very safe and very comfortable straight staircase.

In some cases, this ideal size can not be kept exactly, or a slightly different dimension would take advantage of the available space for the stairs cheaper. For these cases, both the respective state building regulations and DIN 18065 provide a certain framework for possible deviations.

In particular, the DIN distinguishes but several building categories, and so-called "legally required stairs" and "unnecessary stairs".

Legally necessary stairs:

- is part of the escape route and essential for leaving the building

Not necessary for building law is:

- only an extra staircase
- no escape route
- a non-public connection in commercial buildings
- an attic stairs
- a ladder stairs
- every kind of steep stairs

An unnecessary staircase must, in comparison to stairs required by construction law, only have a minimum width of 50 cm. In contrast, stairs required by building law must be at least 80 cm wide (in multi-family houses with a maximum of 2 apartments in the house) and otherwise at least 100 cm wide. (For commercial buildings and multi-party buildings with several apartments, separate regulations apply)

TreppenArt | Permissible step height (= slope) | Permitted appearance width |

in principle | 14 - 19 cm | 26 - 37 cm |

Residential house (max 2 apartments) still allowed, also stairs within an apartment | 14 - 20 cm | 23 - 37 cm |

Not necessary stairs | 14 - 21 cm | 21 - 37 cm |

In this context, one can still move, if it makes constructive sense. Too far you should not deviate from the optimal ratio 18 cm / 26-28 cm, as this always causes a noticeable **loss of comfort** .

## Spiral stairs

While the calculation of a straight staircase is still relatively easy, it is much more difficult with spiral staircases.

### Diagonally staircase

A simple variant is to let two straight staircases m perpendicular to each other, and connect via a pedestal. This is especially recommended if the required depth is not available for a continuous staircase.

If you want to calculate such a staircase, you either go from the respective podium height and calculated first the stairs from the top to the pedestal, and then the stairs from the bottom to the pedestal.

In the case of lack of space you should expect from above, that is, existing depth and required platform width result in the number of upper levels and thus the required platform height.

Always keep in mind that the step height and the width of the steps should be the same for both stairs. If necessary, you can deviate from this if only a few steps lead to the podium, but in most cases it is not recommended.

### Stairs in the quadrant or semicircle

Such stairs can usually be calculated only with special programs, with manual calculations you can not go on here. Professionals usually use their own software for the calculation of such stairs, or the staircase dimensions are determined constructively. This too is a possibility, but rather expensive in practice. Nevertheless, it is still used by some staircase builders.

### Wendel-Steep staircase as a prefabricated staircase

Stairs within apartments are generally considered as structurally unnecessary stairs. If you want to install such a space-saving staircase, you can sit back and relax. The required dimensions are already fixed in such stairs almost always according to current regulations, they usually need only adjust the height and adjust the stairs accordingly. Complex calculations are not necessary for this.

**Tips for quick readers:**

- Step height and width must have a certain ratio
- Optimal values are 18 cm step height and 26 - 28 cm opening width
- more than 18 steps: pedestal necessary
- Legally necessary stairs must be at least 80 cm wide
- unnecessary stairs may also be narrower and steeper
- Spiral staircases can only be calculated by the professional