Square Area Calculator – Find Area, Perimeter and Diagonal
Calculate the area, perimeter, and diagonal of a square instantly. Enter the side length to get all measurements – perfect for construction, crafts, and math homework.
Measure one side
Since all sides of a square are equal, you only need to measure one. Enter the length in any unit.
Click Calculate
The calculator instantly computes the area, perimeter, and diagonal length.
Read your results
Get all three measurements at once. Area is in square units, perimeter and diagonal in linear units.
A square is a special quadrilateral with four equal sides and four right angles. This symmetry makes calculations straightforward – you only need one measurement to find everything else.
Area tells you how much space the square covers. It's calculated by squaring the side length (s²). If a square has sides of 5 cm, its area is 25 square centimeters.
Perimeter is the total distance around the square. Since all four sides are equal, perimeter = 4 × side. A 5 cm square has a perimeter of 20 cm.
Diagonal runs from one corner to the opposite corner. Using the Pythagorean theorem, diagonal = side × √2 (approximately side × 1.414). A 5 cm square has a diagonal of about 7.07 cm.
| Measurement | Formula | Example (s=5) |
|---|---|---|
| Area | A = s² | 5² = 25 sq units |
| Perimeter | P = 4s | 4 × 5 = 20 units |
| Diagonal | d = s√2 | 5 × 1.414 = 7.07 units |
| Side from Area | s = √A | √25 = 5 units |
| Side from Perimeter | s = P/4 | 20/4 = 5 units |
Four Equal Sides
All sides have the same length, making squares a special type of rhombus.
Four Right Angles
Each corner measures exactly 90 degrees, making squares a special type of rectangle.
Equal Diagonals
Both diagonals are the same length and bisect each other at 90 degrees.
Lines of Symmetry
Squares have four lines of symmetry: two through opposite sides and two through opposite corners.
Rotational Symmetry
A square looks the same after 90°, 180°, 270°, and 360° rotations.
| Field | Application | What to Calculate |
|---|---|---|
| Construction | Floor tiles, ceiling tiles | Area for material quantity, perimeter for edging |
| Gardening | Raised beds, lawn sections | Area for soil/mulch, perimeter for borders |
| Crafts | Quilting, scrapbooking | Cutting squares to exact sizes |
| Real Estate | Room measurements | Square footage for pricing |
| Manufacturing | Sheet metal, fabric cutting | Minimize waste by optimizing square cuts |
How do you calculate the area of a square?
Multiply the side length by itself: Area = s². If one side is 6 inches, the area is 36 square inches. This works because a square's length equals its width.
How do you find the diagonal of a square?
Use the formula diagonal = side × √2. The diagonal creates two right triangles inside the square, and by the Pythagorean theorem, d² = s² + s² = 2s², so d = s√2.
What's the difference between area and perimeter?
Area measures the space inside the square (square units). Perimeter measures the distance around the outside (linear units). A 4×4 square has area 16 sq units and perimeter 16 units – same number but different meanings.
Can I find the side length if I know the area?
Yes. Take the square root of the area: side = √area. If the area is 64 square meters, the side length is √64 = 8 meters.
Is a square a rectangle?
Yes, a square is a special type of rectangle where all sides are equal. All squares are rectangles, but not all rectangles are squares. A square is also a special type of rhombus with right angles.
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