Perimeter of Square
The perimeter of a square is defined as the total length that its boundary covers. The perimeter of any closed geometrical object is calculated by finding the distance around that object. For a square, the perimeter can be calculated by finding the sum of all the sides. Let us have a look at the article in order to understand the concept in a better way.
1.  What is the Perimeter of Square Formula? 
2.  Derivation of Perimeter of Square Formula 
3.  How to Calculate Perimeter of a Square 
4.  FAQs on Perimeter of Square 
What is the Perimeter of Square Formula?
A perimeter of any shape is either a path that encompasses/surrounds/outlines a shape (in two dimensions) or its length (onedimensional). The perimeter of a square can be calculated by adding the length of all its sides. The formula to calculate the perimeter of a square can be given as,
Perimeter of square, (P) = 4 × Side
Example: Calculate the perimeter of a square with each side measuring 7 units.
Solution: Given: Side length of square = 7 units
We know, using the perimeter of a square formula,
Perimeter of square = 4 × Side
⇒ 4 × 7 = 28 units
Derivation of Perimeter of Square Formula
The perimeter of the square is defined as the total length of the boundary of a square. In order to calculate the perimeter of the square, we will find the sum of all of its sides. Since, all the sides of a square are equal, for a square, with each side measuring "s" units, perimeter will thus be given as,
Perimeter of square = s + s + s + s
⇒ Perimeter of square = 4s, where "s" is the side length of the square.
How to Calculate Perimeter of a Square?
The perimeter of the square can be calculated following different methods depending upon the known parameters. This section will cover the method using,
 Side length
 Diagonal
 Area
Perimeter of Square Using Side Length
We generally find the perimeter for this case by multiplication of side length with 4.To find the perimeter of a square using the side length, we can follow the steps given below,
 Step 1: Note down the measurement of the side.
 Step 2: Multiply the noted length with 4.
 Step 3: Express the obtained result with the unit.
Perimeter of Square Using Diagonal
The perimeter of the square can also be calculated if the length of its diagonal is known to us. To find the perimeter of a square using the diagonal, we can follow the steps given below,
 Step 1: Note down the measurement of the diagonal of the square.
 Step 2: Calculate the side length using the diagonal,
Side = diagonal/√2 = √2 × diagonal/ 2  Step 3: Multiply this obtained value of side length, (√2 × diagonal/ 2) by 4 and express the answer in units,
Perimeter = (√2 × diagonal/2) × 4 = 2√2 × diagonal units.
Perimeter of Square Using Area of Square
We can find the perimeter of the square given the area. To find the perimeter of a square using the area, we can follow the steps given below,
 Step 1: Note down the area of square.
 Step 2: Calculate the side length using the area,
Side = √area  Step 3: Multiply this obtained value of side length, (√area) by 4 and express the answer in units,
Perimeter = (√area) × 4 = 4√area units.
Let us have a look at a few solved examples to understand the perimeter of the square better.
Solved Examples on Perimeter of Square

Example 1: If the perimeter of a square is 64 units, find its side.
Solution:
To Find: Side length of square
Given: Perimeter of square = 64 units
Using the perimeter of a square formula,
Perimeter of square = 4 × side units
Substituting values, we get,
64 = 4 × side
⇒ Side = 64/4 = 16 unitsAnswer: The side length of the given square measures 16 units.

Example 2: The area of a square is given as 225 square units. Using the perimeter of a square formula, calculate its perimeter.
Solution:
To find: Perimeter of given square
Given: Area of square = 225 square units
We know, area of a square = (side)^{2} square units
⇒ 225 = (side)^{2}
⇒ side = √225 = 15 unitsNow, using perimeter of a square formula,
Perimeter of square, P = 4 × side units
⇒ P = 4 × 15 = 60 unitsAnswer: The perimeter of the given square = 60 units.
FAQs on Perimeter of Square
What is the Formula of Perimeter of Square?
The perimeter of a square is defined as the length that its boundary covers. The formula to calculate the perimeter of a square is given as: P = 4 × side.
How to Find Perimeter of Square?
The perimeter of a square can be calculated by finding the total sum of all its sides. Since, the measure of all the sides of a square is equal, to calculate the perimeter of a square we can simply multiply 4 with its side length.
How to Find the Side Length of a Square When the Perimeter is Given?
The perimeter of a square is given as, P = 4 × side. On rearranging the above formula to calculate the side length of the square when the perimeter is given, we get, side = P/4. Therefore, the side length of a square can be calculated by dividing the given perimeter by 4.
How to Find Perimeter of Square When Area is Given?
The area of a square can be calculated using the formula, area = side × side. On rearranging this formula to calculate the side length of the square using the area, we get, side = √area. Since the perimeter of a square is given as: 4 × side, we can calculate the perimeter of a square when the area is given using the formula: 4√area.
What is the Unit of Perimeter of Square?
The perimeter of a square is the total distance around its boundary, or the lengths of its sides added together. Perimeter (P) is measured in units such as inches(in), yards(yd), millimeters(mm), centimeters(cm), and meters(m).
How to Find Perimeter of Square When Diagonal is Given?
The diagonal of a square is given as, √2 × side. Rearranging this formula to calculate the side of the square, we get, side = diagonal/√2 = (√2 × diagonal)/2 . Thus, the perimeter of the square can be calculated using the formula, P = 2√2 × diagonal.