Square Calculator
Calculate area, perimeter, and diagonal of any square instantly
Calculation Results
Enter a Square measurement to calculate all properties.
Side Length: units
Area: square units
Perimeter: units
Diagonal: units
Square Diagram
The Square: A Fundamental Geometric Shape
A square is a basic and highly symmetrical geometric shape. It is a type of quadrilateral with four equal sides and four right angles. Every angle in a square is exactly 90 degrees.
Key Properties of a Square
- Side (s) – All four sides are equal in length.
- Perimeter (P) – Total distance around the square (P = 4s).
- Area (A) – The space enclosed within the square (A = s²).
- Diagonals – Two equal-length diagonals that bisect each other at 90° (d = s√2).
- Angles – Each interior angle is 90°, and all angles are congruent.
- Symmetry – A square has 4 lines of symmetry and rotational symmetry of 90°.
Mathematical Equations of a Square
- Perimeter
P = 4s - Area
A = s² - Diagonal
d = s√2
Why Are Squares Important?
- Architecture & Design – Common in buildings, tiles, and layout planning.
- Mathematics – Integral in algebra, geometry, and coordinate systems.
- Engineering – Useful in load distribution and framing structures.
- Everyday Life – Found in objects like books, screens, signs, and tiles.
Facts About Squares
- The word "square" comes from Latin "quadratus" meaning "four-sided."
- A square is both a rectangle and a rhombus.
- All squares are parallelograms, but not all parallelograms are squares!
Squares are simple yet powerful shapes found everywhere—from floor tiles to art frames. Understanding squares lays the groundwork for mastering geometry and real-world design.
Square Formulas
- Side (s): s = √A = d/√2 = P/4
- Area (A): A = s² = d²/2 = (P/4)²
- Perimeter (P): P = 4s = 4√A = 2√2·d
- Diagonal (d): d = s√2 = √(2A) = P/(2√2)
Note: √ denotes the square root.
Side (s)
Diagonal (d)
Area (A)
Perimeter (P)
How to Use the Square Calculator
This Square Calculator helps you quickly compute the properties of a square like Side, Area, Perimeter, Diagonal based on the value you provide. Follow these steps:
1 Select the Input Type
Choose what you already know:
- Side (s)
- Area (A)
- Perimeter (P)
- Diagonal (d)
Example: If you know the area, select "Area".
2 Enter the Known Value
Input a positive numeric value.
- Decimals are accepted (e.g., 6.25).
Example: If the side is 4, enter 4.
3 Click "Calculate"
Click the Calculate button to get results. The tool will compute:
- Side (s)
- Area (A)
- Perimeter (P)
- Diagonal (d)
Example Output:
If Side = 4, then:
- Area = 16
- Perimeter = 16
- Diagonal ≈ 5.66
Example Use Cases
- Estimating the area of a square field or floor tile.
- Calculating material needed for square glass panels.
- Measuring diagonals in TV or monitor sizes.
Example Calculations
-
Example 1: Side = 6 units:
- Area = 36 units²
- Perimeter = 24 units
- Diagonal ≈ 8.49 units
-
Example 2: Area = 49 units²:
- Side = 7 units
- Perimeter = 28 units
- Diagonal ≈ 9.9 units
-
Example 3: Diagonal = 10 units:
- Side ≈ 7.07 units
- Area ≈ 50 units²
- Perimeter ≈ 28.28 units
Frequently Asked Questions
Area is calculated using:
A = s²
Where:
- s = side length
A square has all sides equal and all angles 90°, while a rectangle has opposite sides equal but not necessarily all four sides.
Use the formula:
s = √A
Example: If A = 64, then s = √64 = 8
- Architecture: Measuring floors, walls, and tiles
- Engineering: Designing components and layouts
- Design: UI elements, prints, and packaging
- Art: Creating balanced compositions