All about quantity surveying Mensuration applications

Mensuration is defined as ‘the act of measuring : MEASUREMENT’ or ‘geometry applied to the computation of lengths, areas, or volumes from given dimensions or angles’.

(merriam-webster dictionary).

So basically, mensuration is all about calculating the length, the area, the volume and so forth of something. They are Mathematical techniques that are practical and useful in calculating quantities from drawings.

And in construction we need to know the exact quantities of works that are required so we can budget and manage the entire process.

For example, in construction we need to know how many metres of skirting board we need to buy and install, we need to know how many roof tiles are required, how much concrete is need and so on.

If you don’t have the quantities then you cannot 1) budget for the correct amount of materials you will need 2) order the right amount of materials you need 3) agree payment between all parties about how much works are completed and eligible for payment and how much work is left to do.

Without correct quantities your project will quickly descend into budget and program over-runs and a whole scene of chaos on-site.

Mensuration techniques

There are many different mensuration or measurement applications that we can use to calculate definitive quantities for lengths, areas, volumes and so on.

The quantities that we are interested in are as follows:

Numerical quantity

These are the easiest to quantify as if you can count, you can quantify these totals:

• Windows
• External doors
• Internal doors
• Stairs
• Bathroom fittings
• Kitchens

So, we say 10 windows or 20 internal doors….easy!

Lengths

• Skirting boards
• Architraves
• Picture rails
• Drainage pipes
• Steel beams
• Steel columns
• Fencing
• Lengths of rafters
• Lengths of hips and valleys

Here we say 10 metres of fencing or 30 metres of skirting.

Areas

• Engineering brickwork
• Blockwork
• Insulation to cavity walls
• Insulation to floors, roof
• Face brickwork
• Floor finishes
• Underfloor heating
• Plasterboard to walls or ceilings
• Ceiling and wall finishes
• Pitched roof tiling
• Flat roof finish
• Ceramic tiling
• Cladding

In this case we say 100 metre squared (m2) of tiling or plasterboard

Volumes

• Concrete to foundations

With concrete we say 100 cubic metres (m3)

How do we measure lengths and areas?

You measure simple lengths such as skirting boards, architraves, picture rails using a scale ruler (or obviously now using readily available computer software).

Areas for brickwork, floor finishes, decoration, roofing, tiling are also measured using a scale ruler or computer software.  (you will need confirmation of the floor to ceiling heights).

How do we measure lengths of foundations, external walls ?

We measure the lengths of foundations and external walls using the girth (perimeter) measurement.

The Girth of a building is simply the perimeter of the property. So if you look at the ground floor plan of a building and run your pen along the length of the outside walls then that is the perimeter of the building.

• Rectangular buildings
• Buildings of irregular outline

How do we measure irregular areas ?

Most properties will not be a nice simple square. Instead they will often be irregular shapes.

• Trapezoids
• Segments
• Bellmouths

How do we measurement earthworks ?

• Measurement of earthworks
• Excavation
• Sloping site excavation
• Cuttings and embankments
• Scheduling

Mensuration formulae

Mensuration formulae are used to calculate areas from drawings using a scale ruler. Now, of course, thanks to the development of computer software we don’t need to use these formulae anymore. We simply use the software tools to click and select and the computer does the computations.

But its useful to know how these formula work so you are not just blindly selecting and clicking. A computer should be helping you do work that you don’t want to do or do it faster, not doing work you CANNOT do.

Traditional Mensuration formulae include:

• Square
• Rectangle
• Triangle
• Hexagon
• Octagon
• Trapezoid
• Circle
• Sector of circle
• Segment of circle
• Prism
• Cube
• Cylinder
• Sphere
• Segment of Sphere
• Pyramid
• Cone
• Frustum of Pyramid
• Frustum of cone
• Mid-ordinate rule
• Trapezoidal rule
• Simpsons rule
• Bellmouths
• Prismoidal rule