# Tiling with Squares of Different Sizes, How Many Tiles are Needed?

Tiling with squares of two different sizes is called a Pythagorean tiling and is one of the most common two-tile patterns for indoor and outdoor resurfacing projects. In a Pythagorean tiling, both sizes of tile are used in equal quantities.

If you know the side lengths of each square, the spacing between tiles, and the overall dimensions of the area to be covered, you can quickly and accurately estimate the total number of tiles needed. You can use the calculator on the left, or follow the mathematical explanation below.

**Step 1: ** First compute the total amount of space that one large tile and one small take up in the pattern. If the side length of the larger tile is *A* inches, the side length of the smaller tile *B* inches, and the spacing between adjacent tiles *S* inches, then the total amount of space they take up is

(A + S)² + (B + S)² square inches

or equivalently

[A² + B² + 2(A+B)S + 2S²] square inches.

**Step 2:** Compute the area of the space you are going to tile, in square inches. To do this, simply multiply the square footage by 144. For a rectangular floor space with a length of *L* feet and a width of *W* feet, the area is

144LW square inches.

**Step 3:** Divide the number you obtained in Step 2 by the number you obtained in Step 1. This is the *exact* number of large square/small square pairs you would need to cover the area, including any tiles that need to be cut, without any overage.

Realistically, this figure underestimates the actual number of tiles you need, since some material will have to go to waste. For a better estimate, add 5%-7% to your answer.

Alternatively, you can add the two tile side lengths to both the width and length in Step 2. For example, suppose the area to be tiled has a width of 20' and a length of 25', and suppose the side length of the smaller tile is 3" while the side length of the larger tile is 5". Then the adjusted values of L and W are

L = 25' + 3" + 5" = **25'8"**

W = 20' + 3" + 5" = **20'8"**

This method is employed by the calculator above.

**Example:** You are tiling a floor space that is 12' wide and 24' long. You are using two different sizes of square tile, the larger being 4.5" wide and the smaller being 2.5" wide. The spacing between tiles is 1/8" (0.125").

First, figure the amount of space each tile pair needs according to Step 1. This is:

(4.5 + 0.125)² + (2.5 + 0.125)² = 28.28 in²

Next, the area of the floor space in square inches is 144*12*24 = 41472 in².

Now divide the first number into the second to compute the exact number of square tile pairs needed: 41472/28.28 = 1467.

Finally, add about 6% more to this figure: 1467 + 0.06*1467 = 1555. This means you need 1555 smaller square tiles **and** 1555 larger square tiles, for a total of 3110 tiles.

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