⬜ Square Calculator: find A, P, d
Calculate area, perimeter, and diagonal of a square
How to Use This Calculator
Choose What You Know
Select which value you know: Side Length, Area, Perimeter, or Diagonal.
Enter Value
Input the known value (side, area, perimeter, or diagonal).
Click Calculate
Press the "Calculate Square Properties" button to get all square measurements: area (A), perimeter (P), diagonal (d), and side length.
Formulas
Area (A) = s²
Perimeter (P) = 4s
Diagonal (d) = s√2
Reverse Formulas (to find side from other values):
- From Area: s = √A
- From Perimeter: s = P / 4
- From Diagonal: s = d / √2
Example: Find all properties from side = 10
Area = 10² = 100 square units
Perimeter = 4 × 10 = 40 units
Diagonal = 10 × √2 ≈ 14.14 units
Example 2: Find all properties from area = 144
Side = √144 = 12 units
Perimeter = 4 × 12 = 48 units
Diagonal = 12 × √2 ≈ 16.97 units
About Square Calculator
The Square Calculator helps you find all square properties - area (A), perimeter (P), and diagonal (d) - from any single known value. A square is a regular quadrilateral with all four sides equal and all angles equal to 90°.
When to Use This Calculator
- Geometry: Calculate square properties for geometric problems
- Construction: Find dimensions when you know area or perimeter
- Design: Calculate square dimensions for layouts and designs
- Real Estate: Determine square dimensions from area measurements
- Education: Learn and practice square mathematics
- Architecture: Calculate square room or structure dimensions
Why Use Our Calculator?
- ✅ Flexible Input: Calculate from side, area, perimeter, or diagonal
- ✅ Complete Properties: Get all square measurements at once
- ✅ Instant Results: Calculate all values immediately
- ✅ Step-by-Step Display: See calculation formulas with your values
- ✅ Works with Any Units: Meters, feet, inches, or any unit
- ✅ 100% Accurate: Precise geometric calculations
- ✅ Completely Free: No registration required
Understanding Squares
A square is a special type of rectangle with all properties:
- Equal Sides: All four sides have the same length
- Right Angles: All interior angles equal 90°
- Diagonals: Both diagonals are equal and bisect at 90°
- Symmetry: Has 4-fold rotational symmetry and reflection symmetry
- Special Formulas: Area = side², Perimeter = 4 × side, Diagonal = side × √2
- Regular Polygon: A square is a regular quadrilateral
Real-World Applications
Flooring: If you know a square room has area 100 m², the side length is √100 = 10 m. The perimeter (for baseboards) is 4 × 10 = 40 m.
Fencing: To fence a square yard with perimeter 80 feet, each side is 80/4 = 20 feet. The area is 20² = 400 square feet.
Diagonal Measurements: Sometimes you can only measure diagonally. If diagonal is 14.14 units, side = 14.14/√2 = 10 units, area = 100 square units.
Frequently Asked Questions
What is the relationship between area and perimeter of a square?
For a square: If area = A, then side = √A, and perimeter = 4√A. So P = 4√A. Conversely, if perimeter = P, then side = P/4, and area = (P/4)² = P²/16.
How do I find the side length from the diagonal?
If diagonal = d, then side = d / √2. This comes from the Pythagorean theorem: in a square, diagonal² = side² + side² = 2side², so diagonal = side√2.
Why is the diagonal √2 times the side?
The diagonal splits the square into two right triangles. By Pythagorean theorem: diagonal² = side² + side² = 2side², so diagonal = side√2 ≈ 1.414 × side.
Can I find area if I only know the perimeter?
Yes! If perimeter = P, then side = P/4, and area = (P/4)² = P²/16. For example, if P = 40, then side = 10 and area = 100.
What's the difference between area and perimeter?
Area (A) is the space inside the square (measured in square units). Perimeter (P) is the distance around the square (measured in linear units). For a square with side s: A = s², P = 4s.
Can I use this for rectangles?
No, this calculator is specifically for squares (all sides equal). For rectangles, you need both length and width. However, a square is a special rectangle where length = width.
Why are squares important in geometry?
Squares are fundamental shapes with perfect symmetry. They're the building blocks for understanding area, coordinate systems, and many geometric concepts. Squares also serve as reference shapes for units (e.g., square meter, square foot).