Measuring the area of a set of stairs

How much would  you need to spend on buying a carpet for your stairs?

It sounds like a fairly straight forward question, and many people would just get a carpet fitter to call round to give them a quote. In this example, you won’t. Just get a tape measure and measure one of your steps, then I’ll show you how to calculate the area needed.

Let us tackle this problem using some maths and some Excel. First using maths:-

If you look at your stairs, they are essentially a series of rectangles (also called oblongs). There are two rectangles per step. The vertical one is called the rise and the horizontal one is called the run.  Add the rise and run together will give you the length.

The area of a rectangle is calculated by multiplying the length by the width (or you could say depth times breadth, it is the same thing).  If we call length L, and width W the formula would be Area = L * W. So what ever our measured length is, and whatever our measured width is, we can work out the area.

To calculate the area of each step, measure the rise and the run and then multiply this by width of the stair. A typical rise would be around 20cm, and a typical run would be about 25cm (adding these together gives 45cm). The width of the stair will depend on circumstances. One at home would generally be between 90 and 120cm.

It doesn’t matter if you prefer centimetres, millimetres or feet and inches. You’ll find it easier to use just one unit and stick to it. I call this the one unit rule.

A typical step could be 45cm * 90cm. So if Area = L * W, if you substitute the letters for the numbers, you have Area = 45*90.

This works out at 4050 cm2 . We say this as “four thousand and fifty centimetres squared”. You could say “square centimetres”, it means the same thing.

You then count the number of stairs that you have, for sake of argument settle on 12, we know to multiply the area of one step by 12 times. So we calculate Area of Whole Carpet = Area of step * 12

This will give 48,600 cm2 This is a lot of centimetres squared. You couldn’t go in to your local carpet shop and ask for a square centimetre of carpet. That would be bonkers. They sell carpets in metres squared (AKA square meters) and the symbol is m2.

You have to convert 48,600 cm2 in to m2. To do this you divide it by 10,000. You can use a calculator if you want to, or write the number to one decimal place, and move the decimal point 4 places to the left (four places as there are four zeros in 10000).  48,600 can be written as 48,600.0  Moving the decimal point four places to the left will give you 4.86.

You will need to buy 4.86 m2 of carpet. To calculate the cost of the stair carpet, multiply the cost per metre squared by the area. Let us say the cost is £10.00 it means the carpet will be £48.60.

In practice your carpet shop will probably want to add an amount of carpet for wastage in cutting. I’m guessing you’d want to buy about 6m2. If you are going for a complex pattern that needs to be carefully laid, then call in an expert for advice.

Some carpet shops will sell their wares “by the linear metre”. This is because their carpets come at a standard width and if you need 5m you get 5m by the standard width. You also get a lot of wastage.

To create a spreadsheet to calculate this yourself in Excel enter the following

Cell Reference Enter Contents Format
A1  Leave Blank
A2 Length of RISE Text
A3 Length of RUN Text
A4 Total Length Text
A5 Width Text
A6 Area of Step Text
A7 Number of Steps Text
A8 Total carpet Text
A9 Convert to m2 Text
A10 Price Per m2 Text
A11 Total Text
B1 In cm Text
B2 20 Number
B3 25 Number
B4 =sum(b2:b3) Number
B5 90 Number
B6 =sum(b4*b5) Number
B7 12 Number
B8 =sum(b6*b7) Number
B9 =sum(B8/10000) Number
B10 17.99 Number
B11 =sum(b9*b10) Number

You’ll end up with a spreadsheet looking something like this:-

In cm
RUN 25
Length 45
Width 90
# STEPS 12
Price  £        17.99
Total  £        87.43


Play with changing the values, for example width and price to see what happens to the values

Please download an example spreadsheet from the Examples section

If you want to see a video of this being  demonstrated in Excel, please visit my YouTube channel here