Geometry Tool
Square Calculator
Calculate the area, perimeter, diagonal, and side length of a square. Enter any single known property to instantly solve for all other measurements.
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Interactive Square Calculator Workspace
Solved Square Dimensions
Side Length8.0000
Area64.0000
Perimeter32.0000
Diagonal11.3137
Step-by-Step Breakdown
We start with a side length of 8. Area = s² = 64.0000. Perimeter = 4 × s = 32.0000. Diagonal = s × √2 = 11.3137.
Mathematical Formula & Variables
Equation Model
Area = s², Perimeter = 4 × s, Diagonal = s × √2Calculates all geometric properties of an equilateral quadrilateral (square) from a single input side, area, perimeter, or diagonal.
Variable Definitions
| Symbol | Description |
|---|---|
| s (Side Length) | The length of any one of the four identical sides. |
| A (Area) | The two-dimensional space enclosed inside the square boundaries. |
| P (Perimeter) | The total outer boundary length (4 × side). |
| d (Diagonal) | The line segment joining opposite corners (side × √2). |
How to Use the Square Calculator
- Choose your input parameter (Side Length, Area, Perimeter, or Diagonal) from the option picker.
- Enter the known numeric value into the field.
- Review the updated values of all other dimensions in the results dashboard.
- Study the worked calculations to see the direct mathematical derivations.
Practical Example Calculation
Scenario Context: A homeowner wants to tile a square courtyard. They only know that the diagonal distance between corners is 14 meters.
Step 1: Identify given value: Diagonal (d) = 14 m.
Step 2: Calculate Side (s): s = d ÷ √2 = 14 ÷ 1.4142 ≈ 9.90 meters.
Step 3: Calculate Area (A): A = s² = (9.899)² ≈ 98.00 square meters (or A = d² ÷ 2 = 196 ÷ 2 = 98 m²).
Step 4: Calculate Perimeter (P): P = 4 × s = 4 × 9.899 = 39.60 meters.
The courtyard sides measure 9.90 m, with a total area of 98.00 m² and a perimeter of 39.60 m.
Frequently Asked Questions
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