1.1 Units of measurement

A unit of measurement is an agreed standard quantity used to express the size of something, such as a length, mass, area, volume or time, so that everyone who reads the figure understands it the same way. Without common units, drawings, orders, quotations and payments would be confusing, and costly mistakes would follow, such as ordering cement in the wrong quantity or cutting timber to the wrong length. Kenya uses the International System of Units (SI), also called the metric system, in which every quantity has one standard unit and larger or smaller sizes are shown with prefixes such as kilo and milli. Example: a site supervisor for a contractor building staff houses at a county referral hospital in Meru read all wall lengths on the drawings in millimetres, measured them on site in metres, ordered sand in cubic metres and cement in 50 kg bags, and every quantity matched because everyone used the same SI units.

SI Base Units

The SI system is built on seven base units, from which all other units are made.

Derived Units

Derived units are formed by combining base units through multiplication or division, and they describe quantities such as area, volume, speed and pressure.

SI Prefixes

Prefixes are placed before a unit to show multiples or fractions of it in powers of ten, which keeps numbers short and easy to read.

Rules for Writing Units Correctly

• Use the correct case: Unit symbols are written in lower case, such as m, kg and s, except those named after a person, such as N (Newton) and W (Watt), and the litre, which may be written L to avoid confusion with the number 1.
• Leave a space between number and unit: Write 25 kg and 3.6 m, not 25kg or 3.6m, except for the degree sign in angles (90°).
• Do not add an s for plurals: Symbols never take a plural, so write 50 kg, not 50 kgs, and 12 m, not 12 ms.
• Do not put a full stop after a symbol: Write 15 mm, not 15 mm., unless it ends a sentence.
• Do not mix units in one figure: Write 2.45 m or 2,450 mm, not 2 m 450 mm, so that the figure can be read and calculated easily.
• Use only one prefix at a time: Write 1 Mg or 1 t (tonne), not 1 kkg.
• Group long numbers clearly: Separate thousands with a space or comma, such as 12 500 or 12,500, so that large figures are not misread.

Units Commonly Used in Construction and Technical Work

• Millimetres (mm) on drawings: Building and engineering drawings give dimensions in millimetres so that small sizes, such as a 225 mm wall or a 12 mm bar, are shown without decimals.
• Metres (m) for site measurement: Lengths of walls, trenches, pipes and roads are measured and recorded in metres, often to two or three decimal places.
• Square metres (m²) for areas: Floor tiles, plastering, painting, roofing sheets and land plots are measured and priced by area.
• Cubic metres (m³) for volumes: Excavation, concrete, hardcore, sand and ballast are measured by volume.
• Kilograms (kg) and tonnes (t) for mass: Cement is sold in 50 kg bags, steel reinforcement is ordered by the tonne, and loads on structures are calculated from mass.
• Litres (L) for liquids: Paint, water, fuel and admixtures are measured in litres, where 1,000 L = 1 m³.
• Number (No.) for items: Doors, windows, sockets and sanitary fittings are counted individually and priced per item.
• Hours and days for time: Labour, plant hire and curing periods are measured in hours or days, for example plant hired at a daily rate.
• Hectares (ha) and acres for land: Large land areas are given in hectares, although many Kenyan title deeds and land sales still use acres.

Imperial Units Still Encountered

Although Kenya uses the SI system officially, some older units remain common in trade, especially for timber, land and some materials, so workers must be able to convert them.

Measuring Tools and Instruments

Steps to Convert Between Units

1. Identify the given unit: Read the figure carefully and note the unit it is in, such as millimetres or acres.
2. Identify the required unit: Decide which unit the answer must be in, for example metres for a site measurement or hectares for a land record.
3. Find the conversion factor: Use the prefix table or the imperial conversion table to find how many of one unit make the other, for example 1 m = 1,000 mm.
4. Decide whether to multiply or divide: Multiply when converting to a smaller unit (more of them) and divide when converting to a larger unit (fewer of them).
5. Remember squared and cubed units: For areas, square the length factor (1 m² = 1,000,000 mm²) and for volumes cube it (1 m³ = 1,000,000,000 mm³).
6. Carry out the calculation: Work out the result step by step, writing the units at every line.
7. Check that the answer is sensible: A conversion to a smaller unit must give a bigger number, and vice versa, which helps catch errors.
8. Round appropriately: Round the answer to a sensible accuracy for the purpose, such as the nearest millimetre for cutting or two decimal places for metres.

Worked Examples

Converting Millimetres to Metres

A wall on the drawing for a classroom block at a primary school in Kitui is shown as 7,450 mm long.

Length (m) = Length (mm) ÷ 1,000

Length = 7,450 mm ÷ 1,000

Length = 7.45 m

Calculating an Area and Its Cost

The floor of a banking hall at a bank branch in Nakuru measures 12.5 m by 8.4 m and is to be tiled at Ksh 1,350 per m².

Area = Length × Width

Area = 12.5 m × 8.4 m

Area = 105 m²

Cost = Area × Rate per m²

Cost = 105 m² × Ksh 1,350/m²

Cost = Ksh 141,750

Calculating a Volume and Converting to Litres

A water tank base for a SACCO office in Embu is 3 m long, 2 m wide and 0.15 m thick, and a rectangular water tank on site measures 2 m by 1.5 m by 1.2 m.

Volume of base = Length × Width × Thickness

Volume = 3 m × 2 m × 0.15 m

Volume = 0.9 m³

Capacity of tank (L) = Volume (m³) × 1,000

Volume of tank = 2 m × 1.5 m × 1.2 m = 3.6 m³

Capacity = 3.6 m³ × 1,000

Capacity = 3,600 L

Converting Acres to Hectares

A farmers' cooperative in Kitale owns a 25 acre demonstration farm and must record its area in hectares.

Area (ha) = Area (acres) × 0.4047

Area = 25 acres × 0.4047

Area = 10.1175 ha

Area ≈ 10.12 ha

Converting Imperial Timber Sizes to Millimetres

A hotel in Nanyuki orders roof rafters described as 2" x 6".

Size (mm) = Size (inches) × 25.4

Width = 2 in × 25.4 = 50.8 mm

Depth = 6 in × 25.4 = 152.4 mm

Size ≈ 50 mm x 150 mm (nominal metric size)

Chapter Summary

This chapter introduced the fundamental units of measurement essential for mensuration, covering both standard and metric systems used in civil engineering contexts. It then focused on converting between these units accurately to ensure correct calculations in practical applications. The chapter progressed to calculating perimeters and areas of various plane figures, emphasizing their relevance in determining boundaries and surfaces. It further explored the computation of volume and surface area for common solids, providing techniques to quantify three-dimensional spaces and surfaces. The final topic addressed methods for finding the area of irregular figures, equipping students with strategies to handle non-standard shapes encountered on site. Throughout, the chapter combined theoretical concepts with step-by-step calculation methods to build a strong foundation in mensuration for engineering tasks.