The following pictures show $n$ unit squares packed inside the smallest known square (of side length $s$). For the $n ≤ 100$ not pictured, the trivial packing (with no tilted squares) is the best known packing. Where a polynomial root is known for $s$ of degree $3$ or higher, a 🔒 icon is shown; click this to see the polynomial root form of $s$.
See also older records and/or alternative packings. For more information on each packing, view its SVG's source code. Zoom: