Square Calculator
A = s² | P = 4s | d = s√2
A square calculator computes area (s²), perimeter (4s), diagonal (s√2), and other properties of a square with side length s. Squares are special rectangles with all sides equal and all angles 90°.
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Tip: The square is the rectangle with maximum area for a given perimeter. A square with perimeter 40 has area 100. A rectangle 5×15 with the same perimeter has area 75 — 25% less efficient.
- 1Area = s² (side length squared)
- 2Perimeter = 4s
- 3Diagonal = s√2 ≈ 1.414s
- 4Inscribed circle radius = s/2; Circumscribed circle radius = s√2/2
Side = 5=Area = 25, Perimeter = 20, Diagonal = 7.071
Area = 64=Side = 8, Perimeter = 32s = √64 = 8
| Property | Formula | s = 10 |
|---|---|---|
| Area | s² | 100 |
| Perimeter | 4s | 40 |
| Diagonal | s√2 | 14.142 |
| Inscribed circle (r) | s/2 | 5 |
| Circumscribed circle (R) | s√2/2 | 7.071 |
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Fun Fact
The square is the most efficient shape for packing — a grid of squares covers 100% of a plane without gaps. Hexagons also cover 100% but with a shorter total perimeter per unit area, which is why honeycombs use hexagons (less wax needed).
References
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