Plant Population from Row and Seed Spacing

Plant population is not really an agronomic quantity at all. It is a geometric one: each plant sits at the centre of a rectangle whose sides are the row spacing and the in-row seed spacing, and the population is however many of those rectangles fit into the ground. That is the whole equation, and it is a reciprocal because you are asking how many small areas fit inside a large one.

The North American corn planter makes the arithmetic concrete. Thirty-inch rows with a seed dropped every 6.5 inches gives each plant $30 \times 6.5 = 195$ square inches. An acre is 43,560 ft², and each of those holds 144 in², so an acre is 6,272,640 in². Dividing gives $6{,}272{,}640 / 195 = 32{,}167$ plants per acre, which is the round "32,000" that every seed brochure quotes. In metric a sugar-beet spacing of 75 cm by 20 cm gives $0.75 \times 0.20 = 0.15$ m² per plant, so $1/0.15 = 6.67$ plants per square metre, or 66,667 per hectare.

The classic mistake is confusing the seed drop spacing with the plant spacing. A planter meters seed, not plants, and the gap between the two is germination and emergence — the same two terms that appear in the seeding-rate calculation. Set a planter to a 6.5-inch drop and you will not find plants 6.5 inches apart at the three-leaf stage; you will find them 7 inches apart on average with occasional gaps of 14 where a seed failed. The population this equation returns is the SEEDED population, and the established one is lower.

What the geometry does not tell you is whether a given population is well arranged. The same 80,000 plants per hectare can sit in 75 cm rows at 16.7 cm apart or in 38 cm rows at 33 cm apart, and the second arrangement is measurably better for most row crops: each plant's rectangle is closer to a square, so the canopy closes sooner, more light is intercepted early, less water evaporates from bare soil between the rows, and weeds get less of a window. Narrowing rows is one of the few agronomic changes that costs nothing per hectare once the machine is bought.