Enclosed space and living space are two of the most important parameters that are repeatedly used in a wide variety of subject areas to define a building. While the living space can be determined quite easily, the cubature, on the other hand, always causes difficulties. What does it include and what is neglected in the calculation? We explain step by step how you can safely get a reliable result.
What is the cubature?
The term "cubature" comes from the Latin "cube" and directly describes a body. In the case of buildings, however, this body means the volume that the house takes up as a whole. Generally speaking, this includes the sum of the different volumes that add up to the total volume:
- Net volume: Volume of all usable rooms, "air volume" in the building
- Construction volume: Volume of all components of a building, i.e. walls, ceilings, roof, etc.
While the cubature is still omnipresent in technical terminology, the more modern expression "enclosed space" can be found in current regulations, which basically describes the same thing.
What is the built-in space for?
With laypeople, the question arises again and again why such an override is made around the cubature calculation at all. A look at the various uses of this value quickly shows its meaning:
- Cost planning and monitoring
- Parameter for the assessment under construction planning law
- Mortgage lending
- Basis for determining the fair value
- Individual aspects
NOTE: Again and again one reads about the so-called "building mass" in specialist literature, case law and regulations. Depending on the set of rules, the determination can be something
vary, but ultimately it is also about the volume or the enclosed space.The DIN277-1 as a basis for calculation
In contrast to the determination of the residential or Usable area, where several determination methods are equally available, the basis of the cubature calculation is clear and simple. In Germany there is a binding set of rules that contains all the requirements for determining the cubature: DIN 277-1 "Floor areas and spatial contents in construction - Part 1: Building construction". This regulation even goes back to the year 1934, when for the first time a uniform stipulation was made to determine the volume, which was officially called cubature at that time. After several changes and revisions, the current version of this DIN standard from 2016 applies today.
ATTENTION: Although DIN 277-1 is not a law, but rather a standard that is not generally mandatory, it is now generally recognized and therefore practically binding. As a technical rule, it is now part of the recognized state of the art and is also used as a reference by courts in the event of a dispute. If the enclosed space is calculated differently, this is possible, but in the event of a dispute it entails an enormous amount of effort in terms of justification and proof of equivalence.
What is taken into account, what is left out?
A look at the DIN makes it clear very quickly what belongs to the cubature and what does not. The introductory sentence of Section 7 "Determination of the volume of the building" clearly reflects the essential content:
"The gross volume (BRI) includes the volume of all rooms and building structures that are located above the gross floor area (GFA) of the building."
It is also defined
that the gross volume, another synonym for enclosed space or the cubature, is formed by the outer boundary surfaces of building floors, outer walls and roofs with dormer windows. Simply put, this means that the roof surface, the outer edge of the outer wall and the floor slab form the boundaries of the volume under consideration. The question now rightly arises how this is dealt with in detail. Because, in individual cases, a house has a large number of details which, depending on the design of the DIN, may or may not result in additional volume. In order to create clarity here, it is clearly regulated which building components are explicitly not included in the cubature calculation:- Deep and shallow foundations, i.e. foundations and floor slabs
- Light shafts
- Outside stairs and ramps if they are not structurally connected to the building
- Entrance canopies
- Roof overhangs
- Cantilever sun protection systems
- Chimneys, exhaust and ventilation pipes that protrude over the roof cladding
- Skylight domes with a volume above the roof covering of no more than one cubic meter
- Pergolas
- Fixed outdoor seating or terraces, even if protruding from the surface of the terrain
The special case
Parts of the building that are not completely enclosed have a somewhat special position when calculating the volume. Examples of this are, for example, canopies on columns that do not have closed walls. Attics or balcony parapets, that is, vertical wall segments that lack the upper "cover" in the form of a roof, are also frequently found. Here the DIN clearly stipulates that so-called fictitious components can and must also be used to delimit space.
What does that mean?
This simply means that the upper edge of an attic represents the upper limit of the volume created in this way. In the case of a roofing, the fictitious outer walls are either defined by the supports or - if they are cantilevered without supports, by the edge of the roof.
NOTE: The demarcation of the roof edge and roofing is not very easy, as a certain section of the roof edge is often enlarged and thus forms the terrace roof. Here you can normally use 0.50 meters as the limit value. If a roof overhang is larger, it is viewed as a space-forming roof. Up to 0.50 meters it is a roof edge that has not been taken into account.
The calculation using the example step by step
Now let's take a look at the volume calculation using a specific example. As an object of our volume determination, we imagine a typical single-family house with the following
- Length 10 meters
- Width 8.5 meters
- Eaves height (height of the intersection of the outer wall with the roof cladding = 3.50 meters from the terrain
- Ridge height 6.00 meters
- Basement, upper edge of floor slab 3.00 meters below ground
- Roof shape gable roof
- Roof overhang 0.30 meters
- Extension vestibule 1.00 meters wide, 1.50 meters deep, from the site 3.00 meters high, flat roof
- Extension of terrace roof, post spacing 3.00 meters from the house edge and 3.00 meters in width, flat roof, height from the terrain 2.50 meters
Step by step
1. Thoughtful breakdown into tangible sub-volumes:
- Body of the house from the top of the floor slab to the height of the eaves
- Roof eaves height to ridge height
- Vestibule
- Patio roof
2. Definition of the mathematical formulas for calculating the volume of the sub-structures:
a. House body: length x WIDTH X HEIGHT
b. Roof: Length x width x height x 0.5
c. Vestibule: length x WIDTH X HEIGHT
d. Patio roof: length x WIDTH X HEIGHT
3. Calculation of the volume:
a. House body: 10.00m x 8.50m x (3.50m + 3.00m) = 552.50m³
b. Roof: 10.00m x 8.50m x (6.00m - 3.50m) x 0.5 = 212.00m³
c. Vestibule: 1.50m x 1.00m x 3.00m = 4.50m³
d. Patio roof: 3.00mx 3.00mx 2.50m = 22.50m³
e. Sum a. to d. = 791.50m³
Notes on calculation
The example clearly shows that a cubature calculation is actually very easy with the right approach. These hints and tips will help you to achieve your goal without errors:
Disassembly
Break down the structure to be calculated into individual volumes that are as easy to calculate as possible. The formulas for cuboids or triangular bodies known from school days can almost always be used.
Roof pitch
No matter how steep a roof is and whether it is a symmetrical or asymmetrical roof, sloping roofs can always be calculated using the formula length x width x height x 0.5. Even monopitch roofs can be calculated in this way, if one understands it as a special form of the gable roof with a roof surface with an incline of 90 degrees.
Lower edge for special components
Whether a vestibule or a patio roof, whenever there is no structural lower edge, the terrain surface can be viewed as the lower limit of the volume. For example, if there is a vestibule in sloping terrain, use the terrain height at the entrance door as the relevant height.