Square Area Calculator

A square has four equal sides and four right angles, so a single length describes it fully. That is what lets this calculator start from whichever measurement you have. Square patios, tiles, garden plots and quilt blocks are typical uses.

Formula

A = s²

A

the area

s

the length of one side

Area from the side

Multiply the side by itself. A tile with 12-inch sides covers 144 square inches, which is exactly one square foot. Because the side is squared, area grows quickly: doubling the side gives four times the area, and tripling it gives nine times.

Area from the diagonal

Measuring corner to corner is handy when a side is obstructed. The diagonal squared equals twice the area, so divide it by two. A square with a 10 m diagonal has an area of 100 ÷ 2 = 50 m², and its sides are about 7.07 m. There is no need to find the side first.

• A = d² ÷ 2
• s = d ÷ √2

Area from the perimeter

If you know the distance around, as with a length of fencing, divide it by four to get the side, then square the result. A square pen using 36 ft of fence has sides of 9 ft and an area of 81 ft².

Of all rectangles with the same perimeter, the square encloses the most area. That 36 ft of fence encloses only 56 ft² if arranged as 14 by 4, so a square layout is the efficient choice unless the site dictates otherwise.

• A = (P ÷ 4)²

Converting square units

Square units do not convert the way plain lengths do. A yard is 3 ft, but a square yard is 3 × 3 = 9 ft². A meter is 100 cm, but a square meter is 10,000 cm². One square meter is about 10.76 ft². Forgetting to square the conversion factor is the most common source of ordering errors, so the calculator lists square meters, square feet and acres for you. To find the side of a square from a known area, take the square root: an area of 200 gives a side of about 14.14.

Frequently asked questions