Square Calculator

A square is one of the most straightforward shapes in geometry, but calculating its area, perimeter, diagonal, or side length by hand gets repetitive fast. This calculator handles all of it for you. Whether you're working on a home project, a math assignment, or just need a quick answer, you can plug in any measurement you already know and instantly get everything else. No formulas to memorize, no scratch paper required.

Enter Details

Side length

Result

Enter side length for area, perimeter, and diagonal.

Area = s², perimeter = 4s, diagonal = s√2. Use consistent units.

How to Use the Square Calculator

Using the calculator is pretty simple. Start by choosing what you want to find, then enter the value you already have. The calculator works in both directions, so you can solve for a side length if you know the area, or find the diagonal if you know the perimeter.

Just pick the right section for your goal, type in your number, and the result appears right away. All the sections below are organized by what you're solving for, so scroll to whichever one matches your situation.

Square Area Calculator

The area of a square tells you how much flat space is enclosed inside it. You'll need this number for things like figuring out how much flooring to buy, how much paint a wall needs, or just solving a geometry problem.

Enter either the side length or the area itself, and the calculator will handle the rest. The two sections below explain exactly how the math works behind the scenes.

Area Formula of a Square

The formula for the area of a square is straightforward:

Area = side × side, which is also written as A = s²

Since all four sides of a square are equal, you just multiply one side by itself. That's it. If a square has a side length of 5 inches, its area is 25 square inches. The unit of area is always the square of whatever unit you're working in, so inches become square inches, meters become square meters, and so on.

Finding Area from Side Length

To find the area, take your side length and square it. A side of 8 feet gives you an area of 64 square feet. A side of 12 meters gives you 144 square meters. The calculation scales up the same way every time.

Going the other direction, if you already know the area and need the side length, just take the square root of the area. The square root of 64 is 8, so a square with an area of 64 square feet has sides that are 8 feet long. The calculator does this automatically either way.

Square Perimeter Calculator

The perimeter is the total distance around the outside of the square. You'd use this to figure out how much fencing to buy for a square yard, how much trim to cut for a room, or how far someone would walk if they circled the shape once.

Enter any side length and get the perimeter, or work backwards from a known perimeter to find the side. The formulas are simple, but it's easy to make arithmetic errors when you're in the middle of a bigger project, so letting the calculator do it saves time.

Perimeter Formula

The perimeter of a square is found by adding all four sides together. Since every side is the same length, that simplifies to:

Perimeter = 4 × side, or P = 4s

A square with sides of 6 meters has a perimeter of 24 meters. A square with sides of 10.5 feet has a perimeter of 42 feet. Multiply the side length by 4 and you're done.

Finding Side Length from Perimeter

If you know the perimeter but need the side length, just divide the perimeter by 4. A perimeter of 36 inches means each side is 9 inches long. A perimeter of 100 feet means each side is 25 feet.

This comes up more often than you might think. Say someone tells you a square garden has a perimeter of 48 feet and you want to know the side length before buying seeds or pavers. Divide by 4, and you've got your answer: 12 feet per side.

Square Diagonal Calculator

The diagonal of a square is the straight line connecting two opposite corners. It's longer than any single side, and it cuts the square into two equal right triangles. Knowing the diagonal matters when you're checking if a frame is square during construction, cutting fabric on the bias, or working through a geometry problem involving the Pythagorean theorem.

Enter a side length to get the diagonal, or enter the diagonal to work backwards to the side length.

Diagonal Formula

Because the diagonal splits the square into two right triangles, the Pythagorean theorem applies directly. The two legs are each equal to the side length s, and the diagonal is the hypotenuse. That gives us:

Diagonal = s × √2, or d = s√2

The value of √2 is approximately 1.4142. So a square with sides of 10 inches has a diagonal of about 14.14 inches. The diagonal is always longer than the side but shorter than twice the side length.

Finding Side Length from Diagonal

To reverse the formula and find the side length when you know the diagonal, divide the diagonal by √2 (approximately 1.4142). You can also multiply the diagonal by approximately 0.7071, which is the same thing.

So if the diagonal is 20 centimeters, the side length is about 14.14 centimeters. If the diagonal is 7 feet, the side is roughly 4.95 feet. The calculator handles the rounding and gives you a precise result without needing to remember what √2 equals.

Square Side Length Calculator

Sometimes you're starting from a measurement that isn't the side length, and that's exactly what this section is for. Whether you have the area, perimeter, or diagonal, you can back-calculate the side length.

From area: Side = √Area
From perimeter: Side = Perimeter ÷ 4
From diagonal: Side = Diagonal ÷ √2

Each of those is a one-step calculation, but it's easy to mix them up under pressure. Just enter whichever measurement you have and the calculator returns the side length directly. From there, you can use the other sections to find anything else you need.

Square Formulas and Properties

A square has a few properties that make it unique among quadrilaterals. All four sides are equal. All four angles are exactly 90 degrees. The two diagonals are equal in length, they bisect each other at right angles, and they bisect each corner angle too. It's one of the most symmetrical shapes you'll encounter.

Because of that symmetry, knowing just one measurement, whether it's the side, the area, the perimeter, or the diagonal, is enough to calculate everything else. That's what makes square calculations so clean compared to working with rectangles or other shapes where length and width differ.

Property	Formula
Area	A = s²
Perimeter	P = 4s
Diagonal	d = s√2
Side from area	s = √A
Side from perimeter	s = P ÷ 4
Side from diagonal	s = d ÷ √2

Area, Perimeter, and Diagonal Relationship

All three measurements are tied directly to the side length, so they're all connected to each other too. If the side doubles, the area quadruples (because it's squared), the perimeter doubles, and the diagonal also doubles. That proportional relationship is useful to keep in mind when you're scaling something up or down.

For example, if you know a square has a perimeter of 20 feet, you can find the side (5 feet), then the area (25 square feet), then the diagonal (about 7.07 feet), all from that one starting number. Every square measurement flows from every other one, which is why this calculator can work in any direction you need it to.