The short answer is this: for potatoes, the ideal depth for an urban planter box is about 18 to 24 inches (45 to 60 cm). If you are working with limited space, a depth of 12 to 16 inches (30 to 40 cm) can work as a minimum, but it gives you less room for error and usually produces a smaller harvest. Potatoes form tubers along buried stems, so the more loose, usable soil depth you can provide, the better your results are likely to be.
A planter box that is 18 to 24 inches deep gives potato plants enough room for roots, moisture buffering, and hilling. Hilling means adding soil or compost around the stems as the plants grow, which encourages more stem area underground and therefore more places for tubers to form. In a shallower box, you can still hill, but you may run out of depth quickly. If your box is only 12 inches deep, choose early potato varieties, keep the soil very loose, and hill carefully. Expect a modest crop rather than a large one.
When measuring depth, use the internal usable soil depth, not the outside height of the box. Leave about 2 to 3 inches of headspace below the rim so you can water without washing soil over the edge and so you have room to hill. Drainage is essential. Urban planter boxes should have drainage holes, and they should not sit in a low spot where water collects. Potatoes rot easily in waterlogged soil, so good drainage matters as much as depth.
For a productive urban potato planter, choose a box that is also wide enough to space plants properly. A width of at least 18 to 24 inches is helpful, and seed potatoes are usually spaced about 8 to 12 inches apart. Use a loose, well-drained mix rather than heavy garden clay. A blend of quality potting mix, compost, and a little sand or perlite works well. Potatoes prefer slightly acidic soil, around pH 5.5 to 6.5, and they need at least six to eight hours of direct sun for strong growth.
Plant certified seed potatoes about 4 to 6 inches deep, with the eyes facing up. When shoots reach about 6 to 8 inches tall, add more soil or compost around the stems, leaving the top leaves exposed. Repeat this hilling process as the plants grow until the box is nearly full. Water consistently so the soil is moist but not soggy. Feed lightly with compost or a balanced organic fertilizer, and avoid excessive nitrogen, which can produce lots of leaves but fewer tubers.
For harvest, you can dig new potatoes after flowering, or wait until the foliage yellows and dies back for mature potatoes. In an urban setting, remember that a deep planter box filled with moist soil can be heavy. Place it on a stable surface, consider the weight on balconies or roofs, and make sure excess water can drain away safely. If your space is very limited, a 12- to 16-inch-deep box can still grow potatoes, but 18 to 24 inches is the more reliable ideal depth for a healthy, productive crop.