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
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
Equal Sides
All four sides have the same length
Right Angles
All interior angles are 90 degrees
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
Measure Side
Find the length of one side
Apply Formula
Multiply by 4: P = 4a
Calculate
Perform the multiplication
Apply Units
Include correct units