Square Area Calculator

Formula

A = l²,   with l as the side length.

Area of a square: formula and worked example

A square is the regular quadrilateral: four equal sides, four right angles. Since both dimensions are the same length, the usual area formula just becomes the side raised to the second power, A = L². So a side of L = 4 m gives an area of 16 m². Two related quantities come up a lot. The perimeter is P = 4L, and the diagonal — which you get from Pythagoras applied to the two equal legs — works out to d = L√2 ≈ 1.4142·L. Notice that the unit is always squared (m², cm², km²), since you're multiplying two perpendicular lengths together.

Where the square shows up in practice

You run into squares everywhere once you start looking. Square tiles and floor planks. Plots of land filed as squares in cadastral registries. Judo and karate tatami, where the standard competition area is an 8 m × 8 m square. Even pixel grids in digital imaging count: a w·h block of pixels is technically a rectangle, but each pixel is itself a tiny square. When estimating paint or tiles, builders usually pad the figure by about 10% to cover cuts and waste.

One famous puzzle stayed open for millennia: squaring the circle. The challenge was to build a square with the same area as a given circle using only a straightedge and compass. Ferdinand von Lindemann put it to rest in 1882 when he proved that π is transcendental. Constructible numbers have to be algebraic, so a transcendental π means the construction simply can't be done.

FAQ

How do I find the side if I only know the area? Take the square root, L = √A. An area of 25 m² means the side is 5 m.

Is a square also a rectangle? Yes. It's a special case of rectangle, since all its angles are 90°, and a special case of rhombus, since all its sides are equal. It happens to fit both definitions at once.

Why is area measured in squared units? Because you're multiplying two lengths. Meters times meters gives square meters, which is the standard SI unit for area.