Square Calculator

Calculate the area, perimeter, and diagonal of a square from its side length instantly. Free online square calculator with formulas shown.

Square Properties

Area

25

square units

Perimeter

20

units

Diagonal7.0711
Side5

Side Length

Formulas Used

  • Area = side² = 5² = 25
  • Perimeter = 4 × side = 4 × 5 = 20
  • Diagonal = 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

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.

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.

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.

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).

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.

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.