Find the area and perimeter of a square.
Area is the side length squared; perimeter is four times one side.
Area: side²
Perimeter: 4 × side
A square has four equal sides and four right angles, so one measurement is enough to describe it. This calculator takes the side length and gives the area, side × side, and the perimeter, 4 × side.
Square shapes are common in floor tiles, chessboards, rangoli grids, square plots, photo frames and paving slabs. Knowing the area tells you how much material covers the shape; knowing the perimeter tells you how much edging or fencing goes around it. It also works in reverse on paper: a room of 144 square feet that is square must have 12-foot sides. The square is the special case of a rectangle with length equal to width, and it is where the word squared in x² comes from.
1. Measure one side of the square, s.
2. Area = s × s = s².
3. Perimeter = 4 × s.
4. If you know the area instead, take its square root to find the side: s = √A.
5. If you know the diagonal d, the side is d ÷ √2 and the area is d² ÷ 2.
6. Write area in square units and perimeter in length units.
The area of a square with side x is x × x, so mathematicians call x² the square of x. Picture a 5 × 5 grid: 25 unit squares fill it exactly. This geometric view explains identities such as (a + b)² = a² + 2ab + b², which you can see by dividing a square of side a + b into one a-by-a square, one b-by-b square and two a-by-b rectangles. Algebra and geometry describe the same shape.
Doubling the side doubles the perimeter but multiplies the area by four. Tripling the side multiplies the area by nine. In general, scaling lengths by a factor k scales area by k². This is why buying a 2-foot-square tile instead of a 1-foot one means you need only a quarter as many tiles for a floor. It also means a small error in measuring the side becomes roughly double that error, in percentage terms, in the area.
The diagonal of a square cuts it into two right isosceles triangles, so by Pythagoras d = s√2 ≈ 1.414s. That gives a quick check: a 10 m square plot should measure about 14.14 m corner to corner, and if it does not, the corners are not right angles. Among all rectangles with the same perimeter, the square has the largest area. For a fixed amount of fencing, a square pen encloses the most ground.
Pooja is laying a square rangoli base on her courtyard floor with sides of 2.4 metres and wants to buy a coloured border to go all around it.
Answer: Area 5.76; Perimeter 9.6
Multiplying the side by 2 instead of squaring it. A 6 m side gives 36 m², not 12 m².
Using the diagonal as the side, which doubles the area.
Assuming a four-sided shape with equal sides is a square when its angles are not right angles. That is a rhombus.
Converting square units with the linear factor, for example treating 1 ft² as 12 in² instead of 144 in².
Taking the square root of the perimeter to find the side, instead of dividing it by 4.
Counting square tiles or paving slabs needed for a floor or courtyard.
Working out the side of a square plot from its area in square feet or square yards.
Planning square rangoli, quilts, chessboards and garden beds.
Finding border or fencing length around square spaces.
Understanding squares and square roots in Class 6 to 8 mathematics.
How is this different from the Rectangle calculator?
It is the same maths, just with length and width set equal. This version only needs one side length, instead of two separate numbers.