Population Yield Response & Find the Yield Your Stand Will Give
Models maize
Both too thin and too thick a stand cost yield — enter your actual plant population, the optimum for the crop and the maximum yield to get the yield percent of potential, estimated yield and how far you sit off the optimum.
Check your stand vs optimum
Next: your stand is 20% off the optimum, costing yield; adjust seed rate so the next crop lands nearer 75,000 plants/ha to recover the missing tonnage.
Yield falls off quadratically either side of the optimum — too few plants waste land, too many cause competition and lodging; the peak is broad, so being a little off matters less than being far off.
Population yield response — key facts
- Deviation
- |actual − optimum| ÷ optimum
- Yield %
- 100 × (1 − deviation²)
- Estimated yield
- max yield × yield% ÷ 100
- Response shape
- dome — peaks at optimum
- Penalty
- symmetric above & below
- Maize optimum
- ≈ 75,000–90,000 plants/ha
- Why it matters
- too thin or thick both lose
- Privacy
- Runs in your browser; nothing uploaded
There is a best stand — and a cost to missing it either way
Yield does not rise forever as you add plants. The response to plant population is a dome: too few plants leave light and water unused, while too many force the crop to compete with itself, lodge and set smaller heads or cobs. Yield peaks at an optimum population, and moving off it in either direction costs yield. This tool applies a standard quadratic penalty to how far your stand sits from that optimum, so you can see the share of potential yield your population will actually capture.
It returns the yield percent of potential, the estimated yield and the deviation off the optimum from your population, the crop's optimum and the maximum yield. Use it to judge whether a thin or thick stand is worth re-sowing, to set a seed rate that lands the stand near the optimum, and to put a yield figure on a stand count. Pair it with the Field Establishment, Seed Replacement Rate and Triangular Planting Density tools to plan the whole stand.
Value your stand
Turn a stand count into a yield percent of potential.
Decide on re-sowing
See whether an off-optimum stand is worth fixing.
Aim the seed rate
Land the established stand near the yield peak.
Works any crop
Maize, wheat, soybean, cotton and more.
Frequently Asked Questions
How is the yield response to plant population calculated?+
The tool measures how far your actual population sits off the optimum as a fraction, then applies a quadratic penalty: yield percent = 100 × (1 − deviation²). The estimated yield is that percent of the maximum yield you enter, and the deviation percent shows the gap. So a stand close to the optimum keeps almost all the yield, while a large deviation either way costs a lot.
Why does too thick a stand lose yield as well as too thin?+
A response curve to plant population is a dome, not a straight line. Too thin and there are not enough plants to fill the field's light and water; too thick and plants compete with each other for the same resources, lodge, and set smaller heads or cobs. Yield peaks at an optimum in the middle, which is why deviating in either direction costs you.
What is the optimum plant population?+
The optimum is the stand that gives the highest yield for a crop, variety and environment — the top of the response dome. It is published per crop, for example roughly 75,000–90,000 plants per hectare for many maize hybrids, lower for water-limited fields. Enter the figure for your crop and conditions as the target the tool measures your stand against.
Is a thin stand or a thick stand worse?+
It depends how far off you are; the penalty is symmetric in the deviation, so being 20% below the optimum costs the same yield percent as being 20% above. In practice a thin stand is often easier to spot and sometimes compensates by branching, while an over-thick stand wastes seed and risks lodging. The tool quantifies either so you can judge it for your crop.
How do I use the result to set seed rate?+
If the calculator shows your planned population sits well off the optimum, change the seed rate to move it back. Account for establishment loss: required seeds = target population ÷ establishment fraction. The goal is to land the established stand near the optimum, where the yield percent is highest, rather than over- or under-sowing.
What is the maximum yield I should enter?+
Enter the yield the crop would give at its optimum population in your field — the realistic ceiling for your variety, soil and season, in your own units. The tool scales it by the yield percent to estimate what your off-optimum stand will actually deliver. Using a field-realistic maximum keeps the estimated yield meaningful.
Does this work for any crop?+
Yes — maize, wheat, soybean, cotton, sunflower and most field crops show a dome-shaped yield response to plant population. Only the optimum population and maximum yield change by crop and conditions. Enter your crop's figures and the response calculation holds.
Are the figures exact?+
They are a clean planning estimate from a standard response shape, not a field trial. Real curves vary with the variety, spacing pattern, water and nitrogen, so treat the yield percent as a guide rather than a guarantee. Use it to decide whether your stand is close enough to the optimum to leave alone or worth re-sowing.