Nine square feet make one square yard. Not three — nine. This is the squaring trap in its purest form: three feet make a yard, and squaring three gives nine.
About the units
The square foot and the square yard are both derived from imperial lengths, and their relationship follows automatically from the three feet in a yard. In exact metric terms, a square foot is 0.09290304 m² and a square yard is 0.83612736 m², and dividing the second by the first gives exactly nine. The pair exists as a practical matter because the two trades that use them work at different scales: buildings are measured in feet, while soft floor coverings have historically been manufactured and sold by the yard.
The exact factor
The factor is exactly 9, and both directions are exact. The error this page exists to prevent is dividing by three: a room of 180 square feet is 20 square yards, not 60. Ordering three times the carpet needed is an expensive mistake and a common one, because the linear relationship is so familiar that it gets applied without thinking. The same trap appears one level up, where 43,560 square feet make an acre rather than any number related to 5,280.
Where you meet this conversion
Carpet, vinyl and artificial turf in the United States, where the material is priced per square yard and the room is measured in feet. Concrete is the other case: slab area in square feet, thickness in inches, and volume ordered in cubic yards, which involves both a nine and a twenty-seven. Wallpaper, tarpaulins and awnings follow the same split. Anyone estimating materials for an American job needs the nine at hand, and the safe habit is to convert the whole calculation into one unit before doing anything else.