Square
Find the area, perimeter, diagonal, inradius and circumradius of a square from its side, diagonal, perimeter or area.
What is known:
Side a
x
Units:
Lengths are positive numbers (whole or decimal), angles are in degrees.
The square calculator finds all elements of a square from one known value: the side, the diagonal, the perimeter, the area, the inradius or the circumradius. The solution is shown step by step, and the results can be given in the units you need.
Square formulas
| Value | Formula |
|---|---|
| Area | S = a² = d²/2 |
| Perimeter | P = 4a |
| Diagonal | d = a√2 |
| Inradius | r = a/2 |
| Circumradius | R = d/2 = a√2/2 |
| Side from area | a = √S |
Example 1. The side of a square is 5 cm.
S = 5² = 25 cm², P = 4 · 5 = 20 cm, d = 5√2 ≈ 7.07 cm.
Example 2. The diagonal of a square is 10 cm.
a = 10/√2 ≈ 7.07 cm, S = d²/2 = 100/2 = 50 cm².
Properties of a square
- All sides are equal, all angles are right angles.
- The diagonals are equal, perpendicular, bisect each other and bisect the angles.
- A square is a rectangle, a rhombus and a regular quadrilateral at the same time.
- Among all rectangles with a given perimeter, the square has the largest area.
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