Namba's World: Math Basics 101
January 18, 2008
Many installers and sales personnel have told me that they hate math, they did not do well in school with math and don’t quite understand it. My response to them is, you use math everyday and most of you are doing a great job of using math. When we do an estimate on a jobsite we are using math to calculate how much product we will need, we know how to convert to either square feet or square yards, we figure the numbers and then give our client the final estimate. So give yourself an A for what you’re doing on a daily basis with math!
In this article, we’ll discuss calculating the amount of material for a tile and mixed media installation.
We’ll begin with the glass tile installation in Photo 1. This layout consists of a four-inch-by-four-inch tile with a four-by-eight pattern of one-inch-by-one-inch tiles to create the pattern. To begin the calculations for this type of installation, you need to find the repeat of the pattern. This one happens to be a four-inch-by-twelve-inch repeat (Photo 2).
Let’s use a room that is ten feet by ten feet with the tile pictured as an example. You will take the length times the width to get this number, 10x10 equals 100. Now, make sure that you add your usage/waste factor. You will need to add anywhere from 5% to 15%, depending on the layout, the more intricate the layout, the more you will add for usage/waste. We’ll add 7% to our area which now equals 107 square feet. The next step is to determine the amount of square footage of the pattern repeat. Multiply the 4 inch x12 inch, which equals 48. Take 48 and divide it by 144; there are 144 square inches to a square foot. 48 divided by 144 equals 0.33. The pattern repeat is .33 square feet. Take the 107 square feet that we need to cover and divide by .33. 107 divided by .33 equals 324.24. It will take 324.24 pattern repeats to cover the floor. We know that it will require 324.24 of the four inch by four inch tiles but we also need to determine the square footage necessary.
To determine the square footage of the four inch by four inch tile, take four times four, which equals 16 square inches. Divide 16 by 144 which equals 0.11, the square footage number. Multiply the square footage of the four inch tile to the number of pattern repeats. 0.11 x 324.24, this equals 35.66 square feet of 4 inch tile needed
To determine the square footage of the one-inch tiles, take four times eight which equals 32 square inches. Divide 32 by 144 which equals 0.22 square feet. Multiply the square footage of the one inch tile to the number of pattern repeats. 0.22 x 324.24, this equals 71.33 square feet of 1 inch tile needed. 35.66 plus 71.33 equals 106.99 square feet.
Let’s put all this into a mathematical equation:
Size of the room 10’x10’ = 100’
Add 7% usage 100 x7% = 107 square feet
Square footage of pattern 4”x12” = 48 square inches
Convert to square footage 48 / 144 = 0.33 sq. feet
Divide total square footage needed
By pattern repeat square footage 107/ 0.33 = 324.24 pattern repeats
Calculate sq. footage of 4”x4” tile 4x4= 16 square inches
Convert to square footage by dividing 16/144= 0.11 square feet
Multiply 4 in. tile square footage into
number of pattern repeats 0.11x 324.24= 35.66 square feet of 4 inch tile
Calculate sq. footage of one inch tiles 4x8= 32 square inches
Convert to square footage by dividing 32/144= 0.22 square feet
Multiply 1 in. tile square footage into
Number of pattern repeats 0.22x 324.24= 71.33 square feet of 1 inch tile
Add the two totals 35.66 + 71.33 = 106.99 square feet
Now you could just subtract the square footage of the 4 inch tile that is required from the total footage to get the square footage for the one inch tile, but I didn’t want to take a short cut on the explanation.
Make sure that you know how many square feet come in a carton with each type of tile that you will be using, as you may only be able to purchase full cartons and you will need to make sure you have this covered in your costs.
Now let’s take a look at a mixed media installation (Photo 3). In this photo, we have tile with wood to create a basketweave pattern on a diagonal. This one gets just a bit more involved as each tile shares a wood border. Let’s take another ten by ten foot room and this time let’s add 15% usage/waste factor to equal 115 square feet needed for this installation. The tile is a true 13-inch tile and the wood is measured at 5 inches in width. In order to determine the amount of wood required, it will be necessary to split the width of the wood plank for the basketweave in half; remember each tile is sharing the design; this gives us a full pattern repeat for each tile so that we can calculate. The 13-inch tile and 2.5 inches of wood (half the width of the wood) around the entire tile equals 18 inches.
Take 18 x 18, which equals 324 square inches, and divide by 144; this equals 2.25 square feet per pattern. Divide the 2.25 square feet into 115, the total amount needed to cover the floor. This number equals 51.1 pattern repeats. We now know that it will require 51.1 or 51 pieces of tile to construct this design. Now to break down the pattern, the tile is 13x13 so let’s take 13x13 which equals 169 square inches and divide by 144, this equals 1.17 square feet per tile. Subtract the tile 1.17 square feet from the full pattern repeat 2.25 square feet, this equals 1.08 of wood at 2.5 inches around each tile. Take the square footage number of the tile and times it by the number of pattern repeats required 1.17 x 51, this equals 59.67 square feet. Multiply the square footage of wood 1.08 to the total number of pattern repeats 51.1 this equals 55.18 square feet of wood needed.
Here is a mathematical equation:
Size of room 10’x10’= 100 square feet
Add 15% usage/waste equals 100’x15% = 115 square feet
Tile plus 1/2 width of wood
For pattern repeat calculation 13 + 2.5 around entire tile = 18x18 pattern
Calculate square footage of pattern 18x18= 324
Convert to square footage by dividing 324/ 144 = 2.25 square feet per pattern
Divide total square footage needed by pattern repeat square footage 115/ 2.25 = 51.1 pattern repeats
Break down of tile and wood square
Footage, tile is 13”x13” 13x13= 169 square inches
Convert tile to square foot 169/144= 1.17 square feet
Deduct tile square footage from pattern square footage to get amount of square feet of wood required for each pattern repeat 2.25- 1.17 = 1.08 square feet wood
Multiply square footage of tile, 1.17 into number of pattern repeats 1.17 x 51= 59.6 square feet tile needed
Multiply square footage of wood to pattern repeats required 1.08 x 51.1= 55.18 square feet of 5 in. wood
Add the two totals 59.6 + 55.18 = 114.78
Remember, we just made it 51 tiles to round off, instead of 51.1; that’s why the slight difference in total.
The short cut, take the total square footage required 115, and subtract tile square footage 59.67, which equals 55.33 square feet; the amount of wood required for this installation.
Keep in mind that this calculation is using random length boards. If you are going to be using a specific length of one piece for each portion of the basketweave, it may require more wood to achieve this as you may need to cut to length.