Side Length
Your Results
Results are also pinned to the bottom of your screen.Square Properties
Area
25
square units
Perimeter
20
units
Formulas Used
Area = side² = 5² = 25Perimeter = 4 × side = 4 × 5 = 20Diagonal = side × √2 = 5 × 1.4142 = 7.0711
Quick Answer
To calculate square properties from one side s: Area = s^2. Perimeter = 4s. Diagonal = s x sqrt(2) = 1.4142 x s. For a square with side 5: Area = 25 square units, Perimeter = 20 units, Diagonal = 7.07 units. Because all four sides are equal, a single side measurement fully determines the square.
Key Facts
- Formula: Area = side^2
- Formula: Perimeter = 4 x side
- Formula: Diagonal = side x sqrt(2) = 1.4142 x side
- A square with side 5 has area 25, perimeter 20, and diagonal 7.07
- The diagonal splits a square into two 45-45-90 right triangles
- A square is a rectangle (and a rhombus) with four equal sides and four 90-degree angles
- To get side from area, take the square root: s = sqrt(Area)
Frequently Asked Questions
How do I calculate the area of a square?
Square the side length: Area = s^2. A square with side 5 has area 25 square units. If you know the diagonal instead, Area = diagonal^2 / 2.
How do I find the diagonal of a square?
Multiply the side by the square root of 2 (about 1.4142). This comes from the Pythagorean theorem across the square: diagonal = sqrt(s^2 + s^2) = s x sqrt(2). A side-5 square has diagonal 7.07.
What is the perimeter of a square?
Add all four equal sides: Perimeter = 4 x side. A side-5 square has perimeter 20 units. To fence a square yard, the perimeter tells you the total fencing length.
How do I find the side length from the area?
Take the square root of the area: s = sqrt(Area). For an area of 49, the side is 7. For the diagonal d, the side is d / sqrt(2).
Why is the diagonal of a square always side x sqrt(2)?
The diagonal forms a right triangle with two sides. By the Pythagorean theorem, diagonal^2 = s^2 + s^2 = 2s^2, so diagonal = s x sqrt(2). This ratio holds for every square regardless of size.
How many squares fit in a larger square?
By area, divide: (large side / small side)^2. Four squares of side 2.5 fit in a square of side 5. Physically tiling only works cleanly when the side ratio is a whole number.