Bulb Spacing Calculator

Counting bulbs for a bed is a circle packing problem with a horticultural constraint. In a square grid, plants sit at the corners of squares of side S, so the count is rows times positions per row. In a staggered layout, alternate rows shift sideways by half the spacing, letting rows sit closer: row separation drops to S times the square root of 3 divided by 2, about 0.866 times S. Hexagonal packing is the densest arrangement of equal circles in a plane, proved in general by Laszlo Fejes Toth in 1940, and it yields roughly 15 percent more bulbs in the same rectangle while removing the visual corridors that betray a grid. Spacing and depth conventions come from bulb morphology rather than geometry. The working rule is to space bulbs two to three times their diameter apart, center to center, and to set them two to three times their height deep. That gives crocus and grape hyacinth 3 to 4 inches apart and deep, tulips 4 to 6 inches apart and 6 to 8 deep, daffodils and hyacinth 6 to 8 inches in both dimensions, allium and lily 8 to 12 inches apart, and dahlias 18 to 24 inches. Spring-flowering bulbs go in during autumn once soil falls below roughly 60 degrees F, since most need 12 to 16 weeks below about 48 degrees F to initiate flowering; gladiolus and dahlia wait until after the last frost. The counts assume a rectangle planted edge to edge, overstating needs for irregular beds, and the cost bands of roughly 0.30 to 1.50 dollars per bulb vary by cultivar, bulb grade in centimeters of circumference, and quantity.

Bulb cultivation as an organized trade is a Low Countries story. Tulips reached western Europe from Ottoman gardens in the mid sixteenth century, with Carolus Clusius planting them at the Leiden botanical garden from 1593 and doing much to spread the species. Speculation in rare bulbs peaked in the Dutch Republic in the winter of 1636 to 1637 in the episode known as tulip mania, and although the bubble collapsed, the horticultural infrastructure it left behind, on the sandy reclaimed soils behind the dunes between Haarlem and Leiden, became the foundation of a permanent industry. Dutch growers established the grading conventions still used, sizing bulbs by circumference in centimeters, and Keukenhof, opened as a display garden in 1949, standardized the dense mass-planting style that drives modern spacing recommendations. The geometry side developed separately. Johannes Kepler conjectured the densest sphere packing in 1611 in his pamphlet on the six-cornered snowflake, and the two-dimensional hexagonal case was settled by Fejes Toth in 1940, long after gardeners had arrived at staggered rows by eye. Formal spacing guidance for ornamental and field plantings was consolidated by horticultural institutions in the nineteenth and twentieth centuries, notably the Royal Horticultural Society, founded in 1804, whose bulb planting advice remains a standard reference, alongside land-grant extension services in the United States and the Netherlands Flower Bulb Information Center, which has published planting instructions for the export trade since the mid twentieth century.