Find square area, perimeter, and diagonal from side length
Result
Square Results
Step-by-Step Derivation
Square Formula
A = s², P = 4s, d = s√2
A square has four equal sides and four right angles. Its area is side squared, its perimeter is four times the side, and its diagonal follows from a right triangle.
⚠Side length must be nonnegative. A side length of 0 gives zero area and zero perimeter.
How Square Measurements Work
Because all sides of a square are equal, one side length determines every major measurement of the shape.
Equal Sides
All four sides have length s.
Area
Area is side times side.
Perimeter
Perimeter is four equal sides.
Diagonal
The diagonal is s√2 by Pythagorean theorem.
💡 Example: For side 6, area=36, perimeter=24, diagonal≈8.485.
Applications of Square Area and Perimeter
TilesGrid LayoutsLand PlotsGeometry Homework
Frequently Asked Questions
What is a square area and perimeter calculator?▼
It calculates area, perimeter, and diagonal from one square side length.
What are the square formulas?▼
Area A=s², perimeter P=4s, and diagonal d=s√2.
How do I use this calculator?▼
Enter the side length and click Calculate.
Can the side length be negative?▼
No. Side length is a distance and cannot be negative.
Where are square formulas used?▼
They are used in tiles, grids, land plots, design, and geometry homework.
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