Square Perimeter Calculator

This square perimeter calculator allows you to find the perimeter of a square, which is the sum of all four equal sides. You can perform the calculation regardless of what data you have available. Whether you input the length of one side, area, diagonal or even the perimeter itself, all other values will be filled in automatically and the perimeter will be shown as the main result. Just enter the values, select the unit and check out the results.

What is the perimeter of a square?

A square is a quadrilateral with four equal sides and four right angles of 90 degrees each. Chessboard patterns, sticky notes, and tiles are examples of this shape.

The perimeter is the total length of the border, or the distance you would travel if you walked around the outside edge. Since all sides are equal in length, you only need to measure one side.

Formula for calculating the perimeter of a square:

Add up all four sides of equal length, which is the same as multiplying the length of one side by 4.

In this formula, P is the perimeter and a is the length of one side. Let's say that you have a square with a side of 10 centimeters. In this case, the perimeter would be 4 times 10 or 40 centimeters.

Conversely, if the perimeter is known, it can be divided by 4 to find the length of one side.

For a square with a perimeter of 40 centimeters, the length of one side is found by dividing 40 by 4 to get 10 centimeters. If you enter any value, the calculator will instantly fill in the other value.

Calculate the perimeter from area or diagonal:

Since a square has only one independent measure, knowing any single datum value determines all other data. If the area is known, first find the square root of the area to get the side length and then multiply that by four.

A square with an area of 25 square meters has a side length of 5 meters and a perimeter of 20 meters.

If the diagonal is known, then the side length can be found by dividing the diagonal by the square root of 2. This is because the diagonal divides a square into two right triangles.

A square with a diagonal of 10 centimeters has sides about 7.07 centimeters long and a perimeter of about 28.28 centimeters. Enter the diagonal to find the remaining values.

Here's how to use this calculator:

Enter the known values into their respective fields and select the unit. As soon as you enter a value in one of the fields, the tool will calculate the whole square and show the perimeter as its main result. You do not have to specify which measurement you started with.

When you select the "Fence" option, you can estimate the required dimensions for fence posts and panels for the square. When you select the "Circle" option, you can compare a circle with the same perimeter as the square. The graph display allows you to see how the perimeter and area change when you make the square larger or smaller.

Here is a list of all measurements for a square.

If one value is determined then all other values are fixed. The following table shows the relationships used in the calculation tool where "a" represents side length and "d" represents diagonal.

Example calculation:

The following table shows the perimeter of some squares. Notice that the perimeter is directly proportional to the length of a side. This is because we are adding up the individual sides rather than multiplying them together.

The last line is a common example. For a square oil painting with sides of 3.5 feet, you would need 14 feet of molding before you account for the corners. This is four times the length of one side.

Given a perimeter, a square can enclose the greatest area.

Of all quadrilaterals with the same perimeter, a square has the largest area; symbolically speaking, there is a simple relationship between the area and the perimeter of a square, while no other shape achieves this.

If you stretch a square into an elongated rectangle while keeping the perimeter constant, its area will decrease continuously until it approaches zero. If we extend our consideration to shapes with more than four sides, then the circle becomes the optimal solution. A circle with the same circumference as a square has an area that is about 27 percent larger. You can display the corresponding values for the square by activating the "Circle" option.

The diagonal of a square

A diagonal line runs from one corner to the opposite corner and divides the square into two equal right triangles. Its length is approximately 1.414 times the side length, since it multiplies the side length by the square root of 2. So it's always longer than a side but shorter than the sum of two sides.

Since the diagonal and side length are in a fixed ratio to each other, one can be calculated if one is known. In addition, perimeter and area can also be determined. For this reason, the diagonal is one of four measurements that can be entered as starting data into this tool.

Use of a square's perimeter

The circumference answers everyday questions such as: How long are all the sides put together? It tells you how much material is needed for a frame around a square picture or photograph, how much material is required to trim square windows or tiles and how much bias tape or ribbon is needed for the edge of a square cushion or patchwork block.

In the outdoors, perimeter is used to describe the length of a fence that surrounds a square garden, pasture or field and also the length of edging around a square patio or raised bed. The inside of a baseball diamond is a known square with ninety feet between bases. So the distance traveled when going around all four bases once is 360 feet. When the length of the square frame is important, only its perimeter is needed.

Tips for accurate results:

Make sure all measurements are in the same unit before proceeding to check your answer. Also verify that it is indeed a square by checking if all four sides are equal and all four angles are right angles. If the sides are not equal, then you are either dealing with a rectangle or some other quadrilateral shape which will require different formulas. When purchasing materials such as fencing or bordering, buy slightly more than what your calculations indicate to allow for corners, overlaps, and wastage.