Plant population is the first number to fix on any field, because almost everything else follows from it. Seed rate is derived from it. Fertiliser recommendations assume it. Yield per acre is meaningless without it. Get it wrong and every later calculation is wrong by the same proportion, which is why two fields given identical treatment can return very different harvests.
The formula
Plant population is the planted area divided by the ground each plant is given, multiplied by how many plants you leave at each station.
Plants per acre = 4,047 divided by (row spacing in metres multiplied by within-row spacing in metres), multiplied by plants per station.
The 4,047 is the number of square metres in an acre. For a hectare, use 10,000 instead and the same sum works. Spacing must be in metres for this to come out right, so 75 cm becomes 0.75 and 30 cm becomes 0.30.
A worked example
Maize planted at 75 cm between rows and 30 cm within the row, thinned to one plant per station:
4,047 divided by (0.75 multiplied by 0.30) is 4,047 divided by 0.225, which is 17,987. Round that to about 18,000 plants per acre.
The same spacing per hectare: 10,000 divided by 0.225 is 44,444 plants.
If you left two plants at each station instead of one, the population doubles to about 36,000 per acre, on ground and fertiliser calculated for 18,000. That is the single most common way a maize field is quietly overcrowded.
Common spacings and what they give
These are the populations the arithmetic produces at one plant per station. They are what the spacing implies, not a recommendation for your soil.
| Spacing | Plants per acre | Plants per hectare |
|---|---|---|
| 75 cm by 30 cm | about 18,000 | about 44,400 |
| 75 cm by 25 cm | about 21,600 | about 53,300 |
| 90 cm by 30 cm | about 15,000 | about 37,000 |
| 60 cm by 30 cm | about 22,500 | about 55,600 |
| 50 cm by 20 cm | about 40,500 | about 100,000 |
| 1 m by 1 m | about 4,050 | 10,000 |
Spacing by crop, with the reasoning behind each: maize spacing, bean spacing and seed rate, tomato spacing and pineapple spacing and plant population.
Measuring the spacing you actually have
The calculation is only as good as the measurement, and the within-row spacing is where it usually goes wrong. Row spacing gets measured because the rows are visible and permanent. Within-row spacing gets paced, and a pace drifts.
Check it after planting rather than before. Lay a tape along ten metres of an established row and count the plants. Ten metres at 30 cm should hold about 34 plants. If it holds 28, your real spacing is nearer 36 cm and your real population is about 15,000 rather than 18,000, which is a sixth of the crop missing before anything else has gone wrong.
Do this in three places in the field, not one. Planting discipline tends to fall off as the day goes on and as the planter gets further from the path.
Gaps, and why the planted population is not the standing one
Population calculated from spacing is the population you intended. The one that matters is the one standing at harvest. Between the two sit germination failure, damping off, termites, birds taking seed, and thinning.
Count the standing crop two to three weeks after emergence and use that figure, not the planned one, when you work out yield per plant or decide a top dressing. If the gap is large, the question for the next season is the seed rather than the spacing: see how to test seed germination and understanding seed germination rates.
Turning population into a seed order
Once you know the population you want standing, the seed order follows from the germination rate and the seed size. That calculation is set out in how to calculate seed rate per acre.
Frequently Asked Questions
How many maize plants should an acre hold in Uganda? At the commonly used 75 cm by 30 cm spacing with one plant per station, the arithmetic gives about 18,000 plants per acre, or roughly 44,400 per hectare. Whether that is the right target for your field depends on soil, moisture and variety, which is what the maize spacing guide works through. Treat 18,000 as what the spacing implies, not as a recommendation on its own.
Does plant population change the fertiliser I need? Yes, and this is the part most often missed. A fertiliser recommendation is given per acre or per hectare on an assumed population. If you plant at double that population, the same fertiliser is spread across twice as many plants, so each one gets half. Fix the population first, then work out the rate using how to calculate fertiliser requirements.
Why do I get a different answer per acre and per hectare? Because an acre is 4,047 square metres and a hectare is 10,000, so a hectare holds about 2.47 acres. If a figure looks roughly two and a half times too big or too small, a unit has been mixed somewhere in the sum. The conversions are in acre to hectare conversion for farmers.
Should I count a station with two plants as one or two? As two. The formula counts plants, not planting holes. Multiply the stations per acre by the plants you leave standing at each one. If you intended one and thinning never happened, your real population is double what you planned for.
What is the quickest way to check population in an existing field? Measure ten metres along a row, count the plants, and measure the distance between that row and the next. Plants per acre is then the plants in ten metres divided by ten, divided by the row spacing in metres, multiplied by 4,047. It takes a tape and five minutes, and it uses the field you have rather than the field you planned.