Perimeter of a Square Calculator

Calculate square perimeter from side length, diagonal, area, or perimeter

Calculate Square Perimeter

Length of one side of the square

Square Calculation Results

0.000
Side Length (cm)
0.000
Perimeter (cm)
0.000
Area (cm²)
0.000
Diagonal (cm)

Calculation Details

Perimeter Formula: P = 4a = 4 × 0.000 = 0.000 cm

Area Formula: A = a² = 0.000² = 0.000 cm²

Diagonal Formula: d = a√2 = 0.000 × √2 = 0.000 cm

Square Properties

Example Calculation

Picture Frame Example

Scenario: Making a frame for a square painting

Side length: 4 inches (as in competitor example)

Need to find: How much pine board is needed

Solution: Calculate the perimeter of the square

Step-by-Step Solution

P = 4 × a

P = 4 × 4 inches

P = 16 inches

This matches the competitor's example exactly!

Square Properties

4

Equal Sides

All four sides have the same length

90°

Right Angles

All interior angles are 90 degrees

√2

Diagonal Ratio

Diagonal = side × √2

Formula Reference

Perimeter

P = 4a

Sum of all four sides

Area

A = a²

Side length squared

Diagonal

d = a√2

Using Pythagorean theorem

From Perimeter

a = P/4

Find side from perimeter

Understanding Square Perimeter

What is Perimeter?

The perimeter of a square is the total distance around its outer edge. Since all four sides of a square are equal in length, we can calculate the perimeter by multiplying the side length by 4.

Why Squares are Special

  • Among all rectangles with the same perimeter, the square has the largest area
  • The relationship 16 × area = perimeter² holds only for squares
  • Perfect symmetry in all directions
  • Fundamental shape in mathematics and architecture

Formula Derivation

P = a + a + a + a = 4a

  • P: Perimeter of the square
  • a: Length of one side
  • 4: Number of equal sides

Related Formulas

From diagonal: a = d/√2, then P = 4a

From area: a = √A, then P = 4a

Area-perimeter relation: 16A = P²

Step-by-Step Calculation

1

Measure Side

Find the length of one side

2

Apply Formula

Multiply by 4: P = 4a

3

Calculate

Perform the multiplication

4

Apply Units

Include correct units