Plant count comes from bed area divided by the area each plant occupies, and the layout pattern changes that by about 15 percent. Staggered rows fit more plants into the same bed than a square grid does.
Staggered rows or square grid
In a square grid each plant occupies spacing squared. In a staggered, triangular layout each plant occupies spacing squared times 0.866 — about 15 percent less, so 15 percent more plants fit.
Staggered is what you want for ground cover and mass plantings, because it closes gaps faster and reads as a continuous sweep rather than rows. Square grid is easier to lay out and better for anything formal.
Use mature spread, not nursery spacing
The most common planting mistake is spacing for how the plants look today. A one-gallon shrub tagged at four feet of mature spread goes four feet from its neighbor even though it is eighteen inches wide in the pot.
A bed planted at mature spacing looks sparse for one season and correct for the next twenty. A bed planted tight looks perfect for one season and then needs thinning every year.
Ground cover is the exception
For ground cover the goal is closure speed, so spacing is deliberately tighter than mature spread. Twelve inches is common for fast spreaders, eighteen for slower ones.
The trade-off is plant count, and it rises fast — halving the spacing quadruples the number of plants.
Leave room at the edges
The count above fills the whole area. Keep the outer row a half-spacing in from the bed edge so plants have room to reach their full width without flopping onto the lawn or the walk.
Planting in odd numbers and drifts
Even spacing across a whole bed is how a nursery plants and rarely how a good garden looks. Grouping in odd numbers — threes, fives, sevens — and in drifts rather than rows reads as more natural.
The spacing arithmetic still applies within each group. Work out the count for the area a drift will occupy rather than for the bed as a whole.
The exception is a formal hedge or an edging, where even spacing in a straight line is exactly the point and the calculator's grid is what you want.
Spacing decides airflow and disease
Plants crowded tighter than their mature spread stay damp between the leaves for longer after rain and dew, and that is the condition most foliar diseases need.
It also produces plants that grow tall and thin as they compete for light, and that flower less.
The temptation is always to plant close because a new bed looks sparse. The honest answer is to plant at mature spacing and fill the gaps with annuals for the first two seasons.