Square Calculator

A square is a convex quadrilateral having all sides of equal length and right angles to each other. It is also called a tetragon which is a regular polygon with four equal sides. The useful formulas to calculate the square area, perimeter, diagonal length, and side length are given below

• Area of a Square Formula:
  • Area A = s²
• The perimeter of a Square Formula:
  • Perimeter P = 4s
• Diagonals of a Square Formula:
  • p = q = √(2s²) = s√2
• Side of a Square Formula:
  • If square diagonal is given, then
    • Side length s = q / √2
  • If the square perimeter is given, then
    • Side length s = P / 4
  • If the square area is given, then
    • Side length s = √A

Square Calculations:

In this section, you can get the formulas to get the unknown measures of a square. Make use of these formulas to solve any kind of question-related to the geometric shape square.

• If the side length of a square is known, then
  • Diagonal length is q = s√2
  • The area is A = s²
  • Perimeter is P = 4s
• If the diagonal length of the square is known, then
  • Side length is s = q / √2
  • Perimeter is P = 2√2 q
  • Area is A = q² / 2
• If the square perimeter is given, then
  • Side length is s = P / 4
  • Diagonal length is q = 2√2 P
  • Area is A = P² / 16
• If the area of a square is given, then
  • Side length is s = √A
  • Perimeter is P = 4√A
  • Diagonal length is q = √(2A)

Where, A is the area of a square

P is the perimeter of a square

s is the side length of a square

q is the diagonal length of a square

In a square, not only sides but also diagonals are of equal length. Each interior angle is 90° and its diagonals bisect each other. Below given are few simple and easy instructions to find the square perimeter, area, diagonal length, and side length. Go through these steps and follow them while solving the questions.

Square Perimeter:

• Process 1:
  • Get the side length of a square from the question.
  • Multiply it with 4 to get the perimeter.
• Process 2:
  • Check out the diagonal length.
  • Multiply it with 2√2 to obtain perimeter.
• Process 3:
  • Make a note of the square area.
  • Find the square root of the area and multiply it with 4.

Square Area:

• Process 1:
  • Check the length of the side of a square from the question.
  • Square the side length to find the area.
• Process 2:
  • Note down the diagonal length from the question.
  • Square the diagonal length and divide it by 2.
• Process 3:
  • Get the perimeter of the square.
  • Find the square root to the area & multiply it with 4.

Square Diagonal Length:

• Process 1:
  • Check the area of a square.
  • Double the area and apply square root to it to check diagonal.
• Process 2:
  • Get the square perimeter.
  • Multiply the perimeter with 2√2 to get the diagonal length.
• Process 3:
  • Note down the side length of the square.
  • Multiply the √2 with the side length to find the diagonal of a square.

Square Side Length:

• Process 1:
  • Get the area of a square from the question.
  • Find the square root of the area to check the side length.
• Process 2:
  • Note down the perimeter of the square.
  • Divide the perimeter by 4 to check the side length.
• Process 3:
  • Check the diagonal length of a square.
  • Divide the diagonal by √2 to know the length of the side of a square.

Example 1: Square has a side of 52 m length. Find its area, diagonal length, and perimeter?

Solution:

Given that,

Side length of a square s = 52 m

Area of a square A = s²

= 52² = 52 * 52

= 2704

Square Perimeter P = 4s

= 4 * 52 = 208

Square diagonal length q = s√2

= √2 * 52

= 52√2 = 73.528

∴ Squre of 52 m side length has an area of 2704 m², perimeter of 208 m, diagonal length of 72.528 m.

Example 2: A square is having a diagonal length of 12 cm. What are the square side length, area, and perimeter?

Solution:

Given that,

Diagonal length of a square q = 12 cm

Side length of a square formula is s = q / √2

= 12 / √2

= 8.48

Area of a square formula is A = q² / 2

= 12² / 2

= (12 * 12) / 2

= 144 / 2

= 72

Perimeter of a square formula is P = 2√2 q

= 2√2 * 12

= 24√2 = 33.94

∴ Square of 12 cm diagonal has side length of 8.48 cm, area of 72 cm², perimeter of 72 cm.

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1. How do you work out the length of a square from the area?

Generally, the area of the square is given by the square of side length.

Area = side²

Then, Side length = √Area

2. What are the properties of a square?

The four sides of a square are equal.

All the interior angles are 90°.

The opposite sides are parallel to each other.

Two diagonals of the square are equal and bisect each other.

3. How do you use a square calculator?

Enter the unknown parameters in the specified input sections and press the calculate button to find the square area, perimeter, and diagonal length.

4. What is the diagonal formula of the square?

Diagonal divides the square into two triangles. The diagonal formula is √(2side²) i.e side√2.