Plant Population per Acre: A Worked Guide

Plant population per acre is the number of plants that stand on one acre when rows are spaced evenly and plants are spaced evenly in each row. It comes from two measurements only, row spacing and in row spacing. Turn those two measurements into area per plant, then divide the area of one acre by area per plant.

Why two spacings decide the count

A plant in a row crop stands in a rectangle of ground. Row spacing is the distance between rows. In row spacing is the distance between plants in the same row. Multiply the two distances to get the ground area for one plant, then divide one acre by that area.

Halve row spacing alone and the population doubles. Double in row spacing alone and the population halves. Halve both and the population quadruples.

The Plant Population Calculator takes row spacing and in row spacing, and gives plants per acre and per hectare, total plants for your area, and seeds to sow from an entered emergence figure.

The formula in plain steps

Work in one unit system throughout. Use metres for a metric sum, or feet for an imperial sum, and convert each spacing to that unit first.

Metric: plants per sq m equals 1 divided by row spacing times in row spacing, both in metres. Per hectare equals plants per sq m times 10,000. Per acre equals plants per sq m times 4,047, the factor used on the calculator page. Imperial: area per plant in square feet equals row spacing in feet times in row spacing in feet, and plants per acre equals 43,560 divided by area per plant.

Worked example 1: rows 76 cm apart, plants every 15 cm

Rows are 76 cm apart, with plants every 15 cm, or 0.76 m by 0.15 m.

Area per plant is 0.76 times 0.15, which is 0.114 sq m. Plants per sq m is 1 divided by 0.114, which is 8.7719, shown as 8.77. Per hectare is 8.7719 times 10,000, which is 87,719, shown on the page as about 87,700. Per acre by the page formula is 8.7719 times 4,047, which is 35,500.

Worked example 2: 30 inch rows, 6 inch spacing

Rows are 30 in apart, and plants stand every 6 in in the row. In feet, row spacing is 2.5 ft and in row spacing is 0.5 ft.

Area per plant is 2.5 times 0.5, which is 1.25 sq ft. Plants per acre is 43,560 divided by 1.25, which is 34,848. Per hectare is 34,848 times 2.47105, which is 86,111. Per sq m is 34,848 divided by 4,047, which is 8.61.

A 50 acre field at this spacing holds 1,742,400 plants, because 34,848 times 50 is 1,742,400.

Warning: the two page examples are not the same spacing

The metric example uses 76 cm rows and 15 cm in row spacing, and the imperial example uses 30 in rows and 6 in in row spacing.

76 cm is 29.92 in, not 30 in, and 15 cm is 5.91 in, not 6 in. Both differences point the same way, so the metric example gives 35,500 plants per acre against 34,848 for the imperial example, a difference of 652 plants per acre.

Present them as two separate examples: 87,719 per hectare and 35,500 per acre for the metric spacing, and 86,111 per hectare and 34,848 per acre for the imperial spacing.

Plants per hectare and per acre at metric spacings

Density for the metric example and other common metric spacings:

Row spacing	In row spacing	Plants per sq m	Plants per hectare	Plants per acre
76 cm	15 cm	8.77	87,719	35,500
76 cm	20 cm	6.58	65,789	26,625
76 cm	25 cm	5.26	52,632	21,300
90 cm	20 cm	5.56	55,556	22,483
60 cm	15 cm	11.11	111,111	44,967
50 cm	10 cm	20.00	200,000	80,940

At 76 cm by 20 cm, 0.76 times 0.20 is 0.152 sq m. 1 divided by 0.152 is 6.5789, shown as 6.58 per sq m, 65,789 per hectare and 26,625 per acre.

Worked example 3: wider and narrower rows at 6 inch spacing

At 36 in rows, row spacing is 3 ft and in row spacing is 0.5 ft. Area per plant is 1.5 sq ft, so plants per acre is 43,560 divided by 1.5, which is 29,040, a fall of 5,808 from 34,848.

At 20 in rows, row spacing is 1.6667 ft, so area per plant is 0.8333 sq ft, and plants per acre is 43,560 divided by 0.8333, which is 52,272, a rise of 17,424 from 34,848.

The Plant Spacing Calculator and Plants per Square Foot Calculator use the same area method for a single spacing.

Plants per acre at imperial row widths

Row width changes with in row spacing fixed at 6 in:

Row spacing	In row spacing	Area per plant	Plants per acre
20 in	6 in	0.83 sq ft	52,272
30 in	6 in	1.25 sq ft	34,848
36 in	6 in	1.50 sq ft	29,040
30 in	8 in	1.67 sq ft	26,136
30 in	5 in	1.04 sq ft	41,818
30 in	6.5 in	1.35 sq ft	32,167

A one inch change in in row spacing, from 6 in to 5 in, raises the count by 6,970 plants per acre at 30 in rows.

The inches shortcut

Plants per acre equals 6,272,640 divided by row width in inches times in row spacing in inches. The constant 6,272,640 comes from 43,560 times 144, because one acre is 43,560 sq ft and one sq ft is 144 sq in.

At 30 in by 6 in, the product is 30 times 6, which is 180. 6,272,640 divided by 180 is 34,848 plants per acre. At 30 in by 6.5 in, the product is 30 times 6.5, which is 195. 6,272,640 divided by 195 is 32,167 plants per acre.

Check your stand in the field

A calculator figure assumes even spacing. A real field has gaps and doubles, so only a field count shows what actually stands. The check below comes from 4calculators.

Use a row length that covers 1/1000 acre. That length equals 43.56 divided by row width in feet. At 30 in rows it is 17.42 ft, or 17 ft 5 in. At 15 in rows the length is 34.85 ft, at 20 in rows 26.14 ft, and at 36 in rows 14.52 ft. Count the plants in that length of one row and multiply by 1,000 to get plants per acre.

Their worked count uses four rows of 17.42 ft at 30 in rows, with counts of 33, 35, 32 and 36 plants, a total of 136 plants over 174.2 sq ft. Plants per acre equals 136 times 43,560 divided by 174.2, which is 34,006, about 842 below the calculator figure of 34,848. The average count is 34 plants, and 34 times 1,000 is 34,000 plants per acre, close to the 34,006 from the area sum.

Seeds in brief

Seeds are not the same as plants. Seeds equal plants divided by emergence, where emergence is written as a decimal. At 90 percent emergence, emergence is 0.90, so 34,848 plants needs 38,720 seeds per acre, because 34,848 divided by 0.90 is 38,720. Do not treat a plant count as a seed count.

What the calculator assumes, and what it does not give

The calculator assumes even spacing. Gaps and doubles change the real number. Optimum populations depend on crop, variety and conditions. Edge rows and headlands are included.

The calculator gives population per acre, per hectare and per sq m, total plants for an area, and seeds to sow from an entered emergence figure only. It gives no seed weight, bag count, plant cost, seed cost, yield, fertiliser rate, triangular layout, or replant decision.

Common mistakes to avoid

First, do not mix units inside one sum. Pick metres or feet at the start.

Second, do not treat 76 cm by 15 cm as 30 in by 6 in. 76 cm is 29.92 in, 15 cm is 5.91 in, and the populations are 35,500 and 34,848 per acre.

Third, do not use one spacing when the method needs two: one spacing leaves one side of the rectangle unknown.

Fourth, do not treat the calculator figure as a field count. Check the field with the 1/1000 acre method above.

Fifth, do not round too early. Work with 8.7719 through the steps, and round only at the end.

How to use your figure when you plan a field

Write down both spacings beside the population figure, every time, with the unit beside each spacing.

Check the planter setting against the table before planting, and check the stand against the field method after emergence. The Vegetable Plant Spacing Guide gives spacing guidance for vegetables. The Acres per Hour Explained guide explains field work rate, a work rate, not a plant count.

Frequently Asked Questions

Q: How do I calculate plant population per acre?

A: Divide 43,560 by area per plant in square feet. At 30 in rows and 6 in spacing, area per plant is 1.25 sq ft, so 43,560 divided by 1.25 is 34,848 plants per acre.

Q: What is plant population per acre?

A: It is the number of plants on one acre at even row spacing and even in row spacing.

Q: Is 76 cm by 15 cm the same as 30 in by 6 in?

A: No. 76 cm is 29.92 in and 15 cm is 5.91 in. The metric spacing gives 35,500 plants per acre, while the imperial spacing gives 34,848.

Q: How do I check plants per acre in the field?

A: Use a row length that covers 1/1000 acre, 43.56 divided by row width in feet. At 30 in rows that is 17.42 ft, or 17 ft 5 in. Count the plants in that length and multiply by 1,000.

Q: How many seeds do I need for a target plant population?

A: Seeds equal plants divided by emergence as a decimal. At 90 percent emergence, 34,848 plants needs 38,720 seeds per acre.

Q: What does the Plant Population Calculator give?

A: It gives population per acre, per hectare and per sq m, total plants for an area, and seeds to sow from an entered emergence figure. It gives no seed weight, bag count, plant cost, seed cost, yield, fertiliser rate, triangular layout, or replant decision.