Whether you're buying carpet or paint, grass seed or fertilizer, roof shingles or paving stones, you need to know how to calculate the amount required. Buy too much, and you waste money. Buy too little, and you run out before the job is done. Being able to calculate area can save time and money but requires understanding what "square" means.

To "square" means to calculate the value of a number multiplied by itself. A simple example is three squared, or three times three. Mathematically the problem looks like this: 3² = 3 × 3 = 9. The exponent 2, written as superscript 2 (N²), says to multiply a number (N) by itself, like so: N² = N × N. Squared numbers always have the exponent or superscript of 2.

For large numbers, online calculator programs can be used. (See Resources)

To calculate area, multiply the length of the area by the width of the area. So, if carpet is needed for a 12-foot-long by 10-foot-wide room, simply multiply 12 × 10 to get 120 square feet, generally written as 120 ft². In the case of a 10-foot square room, since the length equals the width, the calculation becomes 10 × 10 = 10² = 100 ft².

To help visualize area, use a piece of graph paper. Outline a rectangle four squares long by three squares wide. Count how many squares are contained within the outline. There are 4 × 3, or 12, squares contained within the outlined space. Area always has squared units, no matter what units (feet, meters, inches, etc.) have been measured.

Remember that 12 linear inches equals 1 foot. On the graph paper, outline a space 12 squares long and 12 squares wide. Within that outlined square are 12² or 12 × 12 = 144 smaller squares. So, 1 square foot contains 144 square inches.

To convert square inches to square feet requires dividing the area in square inches by 144 because 144 in² equals 1 ft². So, if an area is 1440 in², but the paint container gives its coverage in terms of square feet, divide the 1440 in² by 144 (because 144 in² equals 1 ft²) and find that the area 1440 in² equals 10 ft². If a gallon of paint covers up to 400 square feet, then buying a pint of paint for this wall makes more economic sense.

If deciding whether to multiply or divide seems challenging, remember that there are 144 square inches in each square foot. The calculation from square inches to square feet should end up with a smaller number (division) while the calculation from square feet to square inches should end with a larger number (multiplication).

Converting square feet to square yards requires the same process. Returning to the graph paper, outline a three-by-three square (because 3 feet equals 1 yard). Counting the number of enclosed squares yields nine squares. Therefore, the conversion from square feet to square yards requires dividing by 9 while converting from square yards to square feet requires multiplying by 9.

Since meters and feet come from different measurement systems, a conversion factor is necessary. Calculating based on 2.54 centimeters equaling 1 inch isn't complicated – just laborious – while looking up the conversion factor shows that 1 square meter (m²) equals 10.764 square feet (ft²). To change from square meters to square feet, multiply the number of square meters by 10.764 ft² per m². To convert from square feet to square meters, divide by 10.764.