Measurements and calculations are an important part of each stage of a furniture project, from the original design idea through to final construction and finishing.
In this chapter we will look at:
Measurements provide the link that allows you to convert a working drawing into a furniture project. Obtaining accurate measurements will help to ensure that the furniture piece you are making finishes up the required size and in the correct proportions. Accurate measurements are also necessary for sound construction and to ensure that the components of your project fit together neatly.
A measurement is obtained by:
Refer to "Hand Tools - Measuring & Marking Tools" for information about common measuring devices such as folding rules, steel rules and measuring tapes. Scale drawings and the use of scale rules are explained in "Drawing & Setting Out - Scaling a Drawing".
Wherever possible, use dimensioned measurements from the working drawing when marking out your furniture project or when making a full size setout on a rod. If the detail isn’t dimensioned on the drawing, use a scale rule in preference to other rules or measuring tapes to take a measurement from the scale drawing.
The main disadvantage of using an ordinary rule for taking measurements off a scale drawing is that you need to make a calculation for each measurement. For example, if the drawing scale is 1:5 and you take a measurement of 13mm off the drawing, you need to calculate 13 x 5 = 65 to find the full size measurement.
Always double check measurements you have obtained before you apply them to your project. If you mark something the wrong length it will be cut to the wrong length. Measurement mistakes result in wasted time and wasted material.
When you have confirmed your measurements write them down. Measurements could be recorded on the working drawing, on a rough sketch or written lightly on the components of your project.
Remember it is your responsibility to know the standard of work that is expected. Inaccurate measurement will affect the standard of work you produce, so you will need to have a good understanding of tolerances that are allowed under your employer’s quality assurance requirements or the specifications for the project.
For example, the clearance or gap between the doors of the cabinet illustrated on the right might be specified as ‘1·0mm to 1·5mm’.
These stated tolerances tell you how accurate the measurement, construction and fitting of the doors will need to be.
In the Furnishing Industry linear measurements are in millimetres (mm) and metres (m). There are 1000 millimetres in 1 metre.
Working drawings used in furniture construction are generally dimensioned in millimetres. You will notice that the unit symbol mm is not shown on dimensioned drawings. Very long measurements are sometimes shown in metres. A decimal point is used to indicate a measurement in metres.
Converting millimetres to metres, or metres to millimetres simply requires the decimal point to be removed or inserted, for example:
When you are working out a timber list or ordering material for a furniture project you will generally need to obtain linear measurements and perform some basic calculations. This task is made easier if you understand how timber is sold and how a timber list is usually written.
Timber is sold in metres with standard lengths starting at 1·8m and generally increasing in increments of 0·3m, for example 1·8m, 2·1m, 2·4m, 2·7m and 3·0m.
The photograph on the right shows how standard lengths of timber are stored in racks at a timber merchant’s yard.
A timber list should include:
A quantity of 68x19 dressed meranti is required for your furniture project. Allowing a few millimetres on each piece for cutting and wastage, you have worked out that you will need 6 pieces 900mm long, 6 pieces 600mm long, 3 pieces 700mm long and 2 pieces 1200mm long.
This is how you would write the timber list:
68x19 DAR meranti 2/1200 6/900 3/700 6/600
Note that the lengths are listed in order from the longest to the shortest. If you were telling someone your timber list you would say:
68 by 19 dressed all round meranti, 2 at 12 hundred, 6 at 9 hundred, 3 at 7 hundred and 6 at 6 hundred.
When you buy timber for your project you need to calculate the most economical way to get the pieces you require out of standard lengths. For example, 3/700 will cut neatly out of a 2·1m length. For the timber list above you could order:
68x19 DAR meranti 2/2·7 1/2·4 1/2·1 2/1·8
Note: You could also get the pieces of timber you require for your project out of other combinations of standard lengths.
Furniture manufacturers generally purchase large quantities of rough sawn timber which is cut and dressed as required. In a small workshop you might have to rip, dock and dress the timber for your own projects. In a larger furniture factory machinists are generally given the cutting lists to prepare.
Before leaving this page, think of what you've just been reading, and test yourself with these questions.
[[ mc /r /f ][ Converting 2.3m to mm should result in: ][ 2300mm ][ * 230mm ][ * 23mm ][ * 0.23mm ][ The unit gets smaller by a factor of 1000, so the quantity gets bigger by the same factor. ]]
[[ mc /r /f ][ Standard lengths of timber get bigger or smaller in increments of: ][ 0.3m ][ * 0.5m ][ * 0.1m ][ * 0.6m ][ Timber is sold in 1.8m, 2.1m, 2.4m , 2.7m, 3.0m lengths. ]]
[[ mr /f ][ What info should be included in a timber order: ][ The section size and shape. ][ The type of timber. ][ The type of finish. ][ * The straightness of the timber. ][ The number of pieces. ][ Hopefully, the timber supplied will be straight enough to do the job. ]]
You may need to perform basic calculations at any stage of a furniture project using addition, subtraction, multiplication and division, for example, when you are setting out details from a scale drawing or working out material quantities and costs.
Some of the calculations you perform may require the use of a special formula. One example to follow uses the formula for finding the perimeter of a rectangle. Another uses the formula for finding the circumference of a circle. Make sure you always choose the correct formula and write it as the first line of your solution.
[[ sh /n ][ Linear Calculations ]]Calculate the total linear metres in the following timber order:
68x19 DAR meranti 4/2·7 12/2·4 7/2·1 14/1·8.
Linear Metres = (4 x 2·7) + (12 x 2·4) + (7 x 2·1) + (14 x 1.8)
= 10·8 + 28·8 + 14·7 + 25·2
= 79·5 m
The photograph above shows a rectangular table. The 1800 x 900 top is edged with ABS plastic edging. How many metres of ABS plastic edging would be required for a batch of 6 table tops? Round up to the next whole metre. (Measurements must be converted from millimetres to metres.)
Perimeter of rectangle = (Length + Width) x 2
= (1·8 + 0·9) x 2
= 2·7 x 2
Edging for 1 table top = 5·4 m
Edging for 6 table tops = 5·4 x 6
= 32·4
= 33 m
The photograph below shows a circular table. The table top is 1200 in diameter and is edged with ABS plastic edging. How much ABS plastic edging will be required to finish the table top? Give your answer in metres and round up to two decimal places.
Before leaving this page, think of what you've just been reading, and test yourself with these questions.
[[ mc /r /f ][ Calculate the total linear metres for this order: 68x19 DAR Beech 6/2·7 4/2·4 12/2·1 6/1·8. ][ 61.8 m. ][ * 28 m. ][ * 37 m. ][ * 46.6 m. ][ * 16.8 m. ][ 6 x 2.7 + 4 x 2.4 + 12 x 2.1 + 6 x 1.8 = 16.2 + 9.6 + 25.2 + 10.8 = 61.8 m. ]]
[[ mc /r /f ][ What length of ABS plastic edging will be required to finish a table top that is circular with a diameter of 0.9 m? ][ 2.83 m. ][ * 1.44 m. ][ * 3.14 m. ][ * 0.81 m. ][ * 1.8 m. ][ P = π x D = 3.14 x 0.9 = 2.83 m. ]]
In larger scale furniture production, quantities of materials such as manufactured boards are often estimated on the basis of total surface area plus an allowance for cutting or waste. When the total area is calculated the material can then be costed by applying a unit rate or dollar value for every unit of area.
The unit of area used in the Furnishing Industry is the square metre. If you imagine a piece of MDF or plywood that has been cut perfectly square and measures exactly 1·000 x 1·000, its surface area is one square metre. The symbol used to denote square metres is m2.
Many different surface shapes can be used in the design of furniture as illustrated in the photograph of the office desk below.
Surface shapes are usually simple plane figures such as rectangles, squares, quadrilaterals, triangles and circles. Complex shapes can generally be made up from a combination of simple shapes.
You will need to know how to calculate the surface area of various shapes when you are estimating quantities and costs of materials such as particleboard, MDF, contact adhesive and finishing materials.
Trade prices for large quantities of manufactured boards are sometimes stated as a price per square metre, so you will need to calculate the number of square metres required to work out the total cost of the material.
Manufacturers of products such as contact adhesive, lacquer and paint provide an estimate of coverage in square metres on the container, for example, 14 square metres per litre. Once again you will need to know the area to be covered so you can calculate quantities and costs of these materials.
Example 1
The top of the cafe table shown on the right measures 890 x 890 and is constructed from standard particleboard 25mm thick, faced and edged with plastic laminate.
How many square metres of the particleboard would be required for a batch of 20 table tops?
Area of Square = side2
Area of 1 Top = 0·89 x 0·89
= 0·792 m2
Area of 20 Tops = 0·792 m2 x 20
= 15·84 m2
Example 2
The supports (legs) of the table shown above are constructed from two pieces of 18mm whiteboard 890 x 700 slotted together. How many square metres of whiteboard would be required for the batch of 20 tables?
Area of Rectangle = Length x Width
Area of 1 Support = 0·89 x 0·7
= 0·623 m2
Area of 40 Supports = 0·623 m2 x 40
= 24·92 m2
Example 3
Find the total surface area (upper surface only) of a batch of 15 circular table tops each with a diameter of 1.2 metres. Round the total up to whole square metres.
Area of a Circle = πR2 (R = radius = half diameter = 0·6m)
Area of 1 Top = 3.14 x 0.6 x 0.6 (3.14 is a close approximation for π)
= 1·13 m2 (rounded to two decimal places)
Area of 15 Tops = 1·13 x 15
= 16·95
= 17 m2 (whole square metres)
Triangles often form part of complex shapes while some shapes can be divided into two or more triangles. This is called triangulation and is a handy way of finding the area of rectilinear shapes. Think of a triangle as half a rectangle.
The formula for finding the area of a triangle is as follows:
Example 4
a. The illustration below represents the shape of a large function room that is to have carpet laid on the floor.
The shaded areas illustrate that the shape of the floor is made up of a square and a triangle. Calculate the area of the room in square metres.
Area of room = Area of square + Area of triangle
= Side2 + (Base x Perp Width ÷ 2)
= (25 x 25) + (25 x 10 ÷ 2)
= 625 m2 + 125 m2
= 750 m2
b. The illustrations below show that shapes bounded by four or more straight lines can be divided into triangles.
Rectilinear shapes can be divided into triangles.
Area of the shape equals the sum of the areas of the triangles.
Before you could calculate the area of these shapes you would need to measure the base and perpendicular width of each triangle.
Before leaving this page, think of what you've just been reading, and test yourself with these questions.
[[ mc /r /f ][ Which of these is not a plane shape? ][ * Square. ][ * Rectangle. ][ * Triangle. ][ Cone. ][ * Circle. ][ A cone is a solid or 3-dimensional shape. ]]
[[ mc /r /f ][ What is the standard unit of area in the general construction industry? ][ Square metres. ][ * Square millimetres. ][ * Metres. ][ * Millimetres. ][ Square metres (m2) are the industry standard unit for area. ]]
[[ mc /r /f ][ A kitchen cabinet is to have rectangular front doors measuring 600 mm by 200 mm. If the kitchen requires 16 of these doors to be manufactured, what is the total timber area of the doors? ][ 1.92 m2 ][ * 16.0m2 ][ * 192m2 ][ * 1.60m2 ][ 0.6 x 0.2 x 16 = 1.92 m2 ]]
[[ mc /r /f ][ If you have to make a circular tabletop with a diameter of 800 mm, what will be the area of this tabletop? ][ 0.50 m2 ][ * 0.64 m2 ][ * 0.16m2 ][ * 0.80m2 ][ Radius = 0.4 m : Area = πr2 = 3.14 x 0.4 x 0.4 = 0.50 m2 (to 2 decimal places). ]]
When you estimate quantities of materials you may need to make an allowance for waste and other discrepancies. For example, when a number of panel sizes and shapes are cut out of standard size sheets, there is usually a certain amount of waste.
The allowance for waste could be, for example, an extra 10% of the material. There are two simple methods for including a waste allowance or cutting allowance in your calculations; adding the waste allowance to the net amount of material or multiplying the net amount of material by a waste allowance factor.
Let’s imagine the material for a furniture project includes a number of rectangular and triangular panels. We have calculated the net amount of material to be 40m2 and our Company Procedures Manual tells us we should allow 10% extra for cutting.
Net amount of material = 40 m2
10% cutting allowance = 4 m2 (10% or one tenth of 40)
Total material required = 40 + 4
= 44 m2
Another way to calculate the total is to multiply the net amount by a waste allowance factor. For example, the factor for a waste allowance of 15% is 1·15, 10% is 1·10 and 5% is 1·05. The numeral 1 represents the net amount and the waste allowance is added after the decimal point.
You’ll find that multiplying the net amount of material by a waste allowance factor is a very convenient method, particularly when you are using a calculator. Now let’s do the calculation again but this time we’ll multiply the net amount by the waste allowance factor.
Net amount of material = 40 m2
Waste allowance factor = 1.1 (1 + 10% or one tenth = 1.1)
Total material required = 40 x 1.1
= 44 m2
Before leaving this page, think of what you've just been reading, and test yourself with these questions.
[[ mc /r /f ][ If you have calculated that you need 36 m of timber for a job, how much should you order to allow 15% for wastage? ][ 42 m. ][ * 40 m. ][ * 39.6 m. ][ * 37.8 m. ][ * 38 m. ][ 36 x 1.15 = 41.4 = 42 m. ]]
In the Furnishing Industry bulk quantities of timber are generally ordered by volume. Other items purchased by volume would include adhesives and liquid finishing materials.
The unit of volume measurement generally used for bulk orders of timber is the cubic metre.
Imagine a square box (cube) which measures 1·000 x 1·000 x 1·000. The amount of material the box would hold is described as one cubic metre. The symbol used to denote cubic metres is m3.
The unit of volume measurement used for liquid adhesives and finishing materials is the litre. There are 1000 litres in 1 m3.
The basic formula for finding the volume of box shapes and cylinders is area of base multiplied by the perpendicular height.
Volume = Area of Base x Perpendicular Height
To apply this basic formula to the volume of a piece of timber you would calculate the area of the section (width by thickness) and multiply by the length.
Example 1
How many cubic metres are there in 120 metres of 250 x 50 rough sawn radiata pine. Note that all measurements must be converted to metres in the calculation so the answer will be in cubic metres.
Volume of timber = Length x Width x Thickness
= 120 x 0·250 x 0·050
= 1·5 m3
Example 2
The top of the table illustrated on the right is faced and edged with plastic laminate using contact adhesive. The table top measures 900 x 900 x 25.
How many litres of contact adhesive would be required for a batch of 80 tables? One litre of adhesive covers approximately 4m2. Allow 10% for wastage and discrepancies.
Before leaving this page, think of what you've just been reading, and test yourself with these questions.
[[ mm /f ][ Match the solid shape with the way to calculate its volume: ][ Cube ~ Square base area x height. ][ Cylinder ~ Circular base area x height. ][ Cone ~ Circular base area x height / 3. ][ Pyramid ~ Square base area x height / 3. ][ Cube => Square x height; Cylinder => Circle x height; Cone => Circle x height / 3; Pyramid => Square x height / 3. ]]
[[ mc /r /f ][ What is the total volume of a stack of 30 cabinet panels, each measuring 1200 mm x 900 mm x 25 mm? ][ 0.81m3 ][ * 27m3 ][ * 0.027m3 ][ * 81m3 ][ * 0.081m3 ][ 1.2 x 0.9 x 0.025 x 30 = 0.81m3 ]]
Without being too technical, the terms mass and weight mean much the same thing. When you work in the Furnishing Industry you will need to be able to perform basic calculations that involve the following units of measurement.
Units of mass (weight) measurement are the gram (g) kilogram (kg) and the tonne (t). There are 1000 grams in a kilogram and 1000 kilograms in a tonne.
You will generally perform basic calculations using these units of measurement when you are working out quantities of materials that are packaged and purchased by weight.
[[ sh /n ][ Standard Unit Packaging ]]Hardware stores and building material supply companies sell a large range of materials packaged in small quantities that are handy for your small furniture projects. However, in a furniture factory, materials are generally purchased in bulk at the lowest possible price.
When ordering bulk quantities you need to know how the materials are packaged by the manufacturer because, as a general rule, the larger the quantity or volume per unit in the package the cheaper the price.
In Example 2 in the previous section we worked out that 40 litres of contact adhesive would be required for the job. The brand of contact adhesive your employer likes to use for this type of job can be purchased in 1 litre and 5 litre cans. The 1 litre cans are packaged 12 to a carton and the 5 litre cans are packaged 4 to a carton.
Obviously, it would be cheaper to buy a 5 litre can than five 1 litre cans. Also, for bulk purchases the unit price (per can) would be cheaper by the carton. How many cartons of 5 litre cans would be required for the job?
You have been given the task of calculating material requirements for a batch of 45 wall units. Each wall unit is assembled using 38 longthread screws 60mm x 10g. These screws can be purchased in boxes of 200. How many boxes of screws will you need to order?
Your employer buys sheets of Single Sided MDF in standard packs. This product is available in two densities. The lighter one has an average mass of 735kg per m3 and the heavier one has an average mass of 810kg per m3.
You have worked out that 5 standard packs of the 810kg per m3 product will be required for a job you are costing. Sheet size is 25mm x 2400 x 1200 and each standard pack contains 20 sheets.
You also need to work out the total weight of the consignment so freight charges can be calculated at the current rate per tonne and included in the costings for the job. How many tonnes of Single Sided MDF will there be in the consignment?
Cubic metres per sheet = 0·025 x 2·400 x 1·200 (sheet size in metres)= 0·072 m3
Total cubic metres = 0·072 x 100 (5 packs x 20 sheets per pack = 100 sheets)
= 7·2 m3
Consignment weight = Total cubic metres x Mass per cubic metre
= 7·2 x 0·81 (810kg = 0·81 tonnes)
= 5·832 tonnes
Before leaving this page, think of what you've just been reading, and test yourself with these questions.
[[ mc /r /f ][ You need to order 38 screws for each of 45 wall units. If these screws are only sold in boxes of 200, how many boxes should you order? ][ 9 boxes. ][ * 8.55 boxes. ][ * 38 boxes. ][ * 45 boxes. ][ * 10 boxes. ][ 38 x 45 / 200 = 8.55 : You need to order 9 boxes. ]]
All measurements taken from a scale drawing bear the same ratio to full size. For example, if the drawing scale is 1:10 and you take a measurement of 12mm off the drawing, the full size measurement is 120mm.
If you are not using a scale rule you need to calculate 12 x 10 = 120 to find the full size measurement. In other words, 1:10 is the same ratio as 12:120. This is sometimes expressed as 1:10 :: 12:120 or:
The same principal can be applied to measuring ingredients that have to be mixed in certain proportions.
The constituents or ingredients of some adhesives and finishing materials are mixed in given proportions. This means that the parts must always be in the same ratio, irrespective of the quantity to be mixed.
You can check that the parts are in the same ratio by cross multiplying the equation that represents the ratios. If the ratios are the same you will get the same answer each time you cross multiply.
For example, cross multiplying the equation above we find that 10 x 12 = 120 and 1 x 120 = 120, therefore the ratios are the same.
If one of the values is missing (X) we can find it as follows:
Example 1
A certain brand of clear polyurethane is to be used to finish your furniture project. The manufacturer recommends that mineral turpentine be added for spraying, in the proportions of 1 part mineral turpentine to 12 parts polyurethane or 1:12.
You have estimated that you will need 3 litres of polyurethane for the job. How much mineral turpentine will you need to add for spraying?
Let X equal the volume of mineral turpentine to be added to 3 litres of polyurethane.
In the "Area" section we saw how rectilinear shapes can be divided into triangles to help us calculate the area of the overall shape. We can also use this principle of triangulation to scale the size of shapes up or down. In other words, to make them larger or smaller.
The illustration on the right shows a small pentagonal (five sided) shape divided into three shaded triangles.
From point A the sides of the triangles are extended to three times their length by measuring A1 on each line and marking it off two more times.
When the points marked 3 are joined, the shape formed is the same as the shaded shape but scaled up 3:1. The scale is represented by the number of times A1 is marked off. For example, if we needed to scale the shape 5:1 we would simply mark off A1 five times on each of the lines.
Scaling down simply works in reverse. If we were scaling down the larger figure 1:3 we would measure the sides of the large triangles and divide the measurements by three. The scaled down shape would be drawn by joining the points marked 1.
Before leaving this page, think of what you've just been reading, and test yourself with these questions.
[[ mc /r /f ][ A special 2-part adhesive needs to be mixed in the ratio A:B = 1:5 to ensure that it sets properly. If you have 200 ml of Part B, how much of Part A will you need for correct mixing? ][ 40 ml. ][ * 1000 ml. ][ * 5 ml. ][ * 50 ml. ][ * 200 ml. ][ x/200 = 1/5 ; x = 200*1/5 = 40 ml. ]]
Earlier in this chapter we looked at the measurement techniques and basic calculations you will use when estimating material quantities for furniture projects so we won’t need to cover them again in this section.
However, you should also consider the following when estimating quantities and listing materials for costing:
Recording material quantities using the right unit of measurement will save you a lot of time and extra calculations.
For example, quantities of dressed timber would be recorded as total linear metres for each size because the supplier’s prices are stated as a price per linear metre, also some sheet materials are priced per sheet or each (ea), while others may be priced per square metre (m2).
Make sure you understand any purchasing and costing policies that could apply to your work. For example, bulk supplies of finishing materials might be purchased in 20 litre drums but your employer’s costing policy might require individual jobs to be costed on a price per litre basis.
In this situation, if the price per litre was not supplied, you would need to divide the drum price by 20 to get the price per litre then estimate the number of litres required for your furniture project.
For each type of material, costing is simply a matter of multiplying the quantity (total units required) by the unit rate or price per unit.
The material cost for the furniture project will be the sum of the costs of all the different materials used.
The table below is an example of how you could record material quantities as you calculate them. Make sure you check that the unit rates (prices) are current before you enter them in the table to complete your costing calculations.
The material list and unit rates used here are indicative only and are not intended to represent a complete costing of a furniture project or current prices.