328 unit squares in a square
Container side ≈ 18.614377
0.106% smaller container side than the value listed in Francisco Couzo’s catalogue on 19 October 2026.
Packing problems
Fitting shapes into as little space as possible. A hobby and a testbed for mixed discrete–continuous optimization. Each packing below improves on the best value listed in its linked public catalogue on 19 October 2026.
Squares: minimize the container side. Circles: maximize the radius in a unit square.
Unit squares in a square
503 unit squares in a square
Container side ≈ 22.944668
0.0562% smaller container side than the value listed in Francisco Couzo’s catalogue on 19 October 2026.
757 unit squares in a square
Container side ≈ 27.976914
0.0465% smaller container side than the value listed in Francisco Couzo’s catalogue on 19 October 2026.
Circles in a unit square
577 circles in a unit square
Radius ≈ 0.021930216
0.0564% larger radius than the value listed on Packomania on 19 October 2026.
503 circles in a unit square
Radius ≈ 0.023424480
0.0496% larger radius than the value listed on Packomania on 19 October 2026.
531 circles in a unit square
Radius ≈ 0.022869085
0.0352% larger radius than the value listed on Packomania on 19 October 2026.
All 108 arrangements 100 square packings · 8 circle packings
| Arrangement | Side / radius | Original comparison |
|---|---|---|
| 328 squares | 18.614377 | 0.106% smaller container side19 October 2026 |
| 330 squares | 18.692672 | 0.000136% smaller container side19 October 2026 |
| 339 squares | 18.907351 | 0.0209% smaller container side19 October 2026 |
| 344 squares | 18.992728 | 0.00525% smaller container side19 October 2026 |
| 365 squares | 19.614377 | 0.0354% smaller container side19 October 2026 |
| 377 squares | 19.925472 | 0.00125% smaller container side19 October 2026 |
| 378 squares | 19.942019 | 0.00244% smaller container side19 October 2026 |
| 379 squares | 19.950890 | 0.0106% smaller container side19 October 2026 |
| 380 squares | 19.961350 | 0.00126% smaller container side19 October 2026 |
| 381 squares | 19.974740 | 3.00e-06% smaller container side19 October 2026 |
| 404 squares | 20.614377 | 0.0337% smaller container side19 October 2026 |
| 412 squares | 20.822995 | 0.000320% smaller container side19 October 2026 |
| 417 squares | 20.934672 | 0.0374% smaller container side19 October 2026 |
| 418 squares | 20.939184 | 0.0174% smaller container side19 October 2026 |
| 419 squares | 20.957805 | 0.00911% smaller container side19 October 2026 |
| 420 squares | 20.966588 | 0.0361% smaller container side19 October 2026 |
| 421 squares | 20.976371 | 0.0246% smaller container side19 October 2026 |
| 422 squares | 20.983575 | 0.000152% smaller container side19 October 2026 |
| 453 squares | 21.822995 | 8.86e-05% smaller container side19 October 2026 |
| 459 squares | 21.937228 | 0.0234% smaller container side19 October 2026 |
| 460 squares | 21.950988 | 0.0299% smaller container side19 October 2026 |
| 461 squares | 21.966193 | 0.0233% smaller container side19 October 2026 |
| 462 squares | 21.966193 | 0.0396% smaller container side19 October 2026 |
| 463 squares | 21.973676 | 0.0452% smaller container side19 October 2026 |
| 464 squares | 21.986269 | 0.00675% smaller container side19 October 2026 |
| 496 squares | 22.822876 | 0.000609% smaller container side19 October 2026 |
| 502 squares | 22.934446 | 0.0339% smaller container side19 October 2026 |
| 503 squares | 22.944668 | 0.0562% smaller container side19 October 2026 |
| 504 squares | 22.962119 | 0.0368% smaller container side19 October 2026 |
| 505 squares | 22.964254 | 0.0319% smaller container side19 October 2026 |
| 506 squares | 22.972145 | 0.00417% smaller container side19 October 2026 |
| 508 squares | 22.983309 | 0.0194% smaller container side19 October 2026 |
| 548 squares | 23.944668 | 0.0487% smaller container side19 October 2026 |
| 550 squares | 23.961059 | 0.00190% smaller container side19 October 2026 |
| 551 squares | 23.965802 | 0.00458% smaller container side19 October 2026 |
| 552 squares | 23.966629 | 0.00114% smaller container side19 October 2026 |
| 553 squares | 23.979787 | 0.00392% smaller container side19 October 2026 |
| 554 squares | 23.986315 | 0.0300% smaller container side19 October 2026 |
| 595 squares | 24.944668 | 0.0204% smaller container side19 October 2026 |
| 597 squares | 24.958142 | 0.0135% smaller container side19 October 2026 |
| 598 squares | 24.958221 | 0.0131% smaller container side19 October 2026 |
| 599 squares | 24.962833 | 0.0163% smaller container side19 October 2026 |
| 600 squares | 24.979787 | 0.00377% smaller container side19 October 2026 |
| 601 squares | 24.986315 | 0.00668% smaller container side19 October 2026 |
| 602 squares | 24.990356 | 0.0129% smaller container side19 October 2026 |
| 603 squares | 24.990356 | 0.0156% smaller container side19 October 2026 |
| 647 squares | 25.949898 | 0.0129% smaller container side19 October 2026 |
| 648 squares | 25.961053 | 0.0225% smaller container side19 October 2026 |
| 649 squares | 25.974939 | 0.00783% smaller container side19 October 2026 |
| 650 squares | 25.974939 | 0.0282% smaller container side19 October 2026 |
| 651 squares | 25.982879 | 0.00351% smaller container side19 October 2026 |
| 652 squares | 25.990356 | 0.0150% smaller container side19 October 2026 |
| 654 squares | 25.994867 | 0.00393% smaller container side19 October 2026 |
| 700 squares | 26.963730 | 0.0332% smaller container side19 October 2026 |
| 701 squares | 26.971171 | 0.0162% smaller container side19 October 2026 |
| 702 squares | 26.976693 | 0.00297% smaller container side19 October 2026 |
| 703 squares | 26.981389 | 0.0225% smaller container side19 October 2026 |
| 704 squares | 26.987140 | 0.0264% smaller container side19 October 2026 |
| 705 squares | 26.990473 | 0.0140% smaller container side19 October 2026 |
| 706 squares | 26.997919 | 0.00231% smaller container side19 October 2026 |
| 755 squares | 27.951463 | 0.000147% smaller container side19 October 2026 |
| 756 squares | 27.976914 | 0.0203% smaller container side19 October 2026 |
| 757 squares | 27.976914 | 0.0465% smaller container side19 October 2026 |
| 758 squares | 27.984284 | 0.0340% smaller container side19 October 2026 |
| 759 squares | 27.988569 | 0.0187% smaller container side19 October 2026 |
| 760 squares | 27.992923 | 0.00750% smaller container side19 October 2026 |
| 810 squares | 28.951463 | 2.19e-07% smaller container side19 October 2026 |
| 811 squares | 28.974849 | 0.0225% smaller container side19 October 2026 |
| 812 squares | 28.976914 | 0.0153% smaller container side19 October 2026 |
| 813 squares | 28.981594 | 0.0288% smaller container side19 October 2026 |
| 814 squares | 28.981594 | 0.0421% smaller container side19 October 2026 |
| 815 squares | 28.992923 | 0.00724% smaller container side19 October 2026 |
| 816 squares | 28.995945 | 0.00784% smaller container side19 October 2026 |
| 817 squares | 28.997492 | 0.00256% smaller container side19 October 2026 |
| 868 squares | 29.974562 | 0.00943% smaller container side19 October 2026 |
| 869 squares | 29.974937 | 0.0214% smaller container side19 October 2026 |
| 870 squares | 29.981594 | 0.0128% smaller container side19 October 2026 |
| 871 squares | 29.981594 | 0.0174% smaller container side19 October 2026 |
| 872 squares | 29.992623 | 0.00800% smaller container side19 October 2026 |
| 873 squares | 29.992623 | 0.0125% smaller container side19 October 2026 |
| 874 squares | 29.992883 | 0.0116% smaller container side19 October 2026 |
| 875 squares | 29.996974 | 0.00603% smaller container side19 October 2026 |
| 927 squares | 30.969979 | 0.0177% smaller container side19 October 2026 |
| 928 squares | 30.974937 | 0.00174% smaller container side19 October 2026 |
| 929 squares | 30.975406 | 0.00913% smaller container side19 October 2026 |
| 930 squares | 30.977403 | 0.0133% smaller container side19 October 2026 |
| 932 squares | 30.992623 | 0.00409% smaller container side19 October 2026 |
| 933 squares | 30.992883 | 0.00437% smaller container side19 October 2026 |
| 934 squares | 30.994174 | 0.00364% smaller container side19 October 2026 |
| 935 squares | 30.994174 | 0.00375% smaller container side19 October 2026 |
| 989 squares | 31.974937 | 0.00169% smaller container side19 October 2026 |
| 990 squares | 31.975406 | 0.00786% smaller container side19 October 2026 |
| 991 squares | 31.977403 | 0.0128% smaller container side19 October 2026 |
| 992 squares | 31.977815 | 0.0218% smaller container side19 October 2026 |
| 993 squares | 31.983896 | 0.00296% smaller container side19 October 2026 |
| 994 squares | 31.992883 | 0.00238% smaller container side19 October 2026 |
| 995 squares | 31.994174 | 0.00191% smaller container side19 October 2026 |
| 996 squares | 31.994174 | 0.00191% smaller container side19 October 2026 |
| 997 squares | 31.996876 | 0.00445% smaller container side19 October 2026 |
| 998 squares | 31.996876 | 0.00445% smaller container side19 October 2026 |
| 223 circles | 0.034791767 | 0.00868% larger radius19 October 2026 |
| 411 circles | 0.025913825 | 0.0306% larger radius19 October 2026 |
| 423 circles | 0.025428531 | 0.00709% larger radius19 October 2026 |
| 463 circles | 0.024353409 | 0.0141% larger radius19 October 2026 |
| 503 circles | 0.023424480 | 0.0496% larger radius19 October 2026 |
| 531 circles | 0.022869085 | 0.0352% larger radius19 October 2026 |
| 547 circles | 0.022462383 | 0.00136% larger radius19 October 2026 |
| 577 circles | 0.021930216 | 0.0564% larger radius19 October 2026 |