Seed rate and plant population calculations
How plant population affects yield, how to turn a target population into a seed rate using seed weight, germination and establishment, and spacing sums.
On this page
Every crop has a range of plant numbers per square metre within which it yields best. Too few plants leave light, water and nutrients unused; too many compete with each other, lodge, form small heads or fruits, and waste seed. Getting the plant population right, and converting it into a seed rate that will actually produce that population in the field, is one of the most practical calculations in agronomy.
These calculations appear in nearly every crop production exam, and they are worth mastering because the same few formulas cover every crop.
Population and yield
Two classic response shapes:
- Asymptotic: yield rises with population and then levels off, because plants compensate for each other's absence or presence. Total dry matter, and the grain yield of crops that compensate well (such as tillering cereals, which form more or fewer tillers), often behave like this.
- Parabolic: yield rises to a maximum and then falls, typical of crops where crowding reduces the harvested organ, such as maize (barren plants, smaller ears), sunflower, and many vegetables and root crops sold by size.
The optimum population depends on:
- Variety: compact, short, erect-leaved or hybrid varieties often tolerate higher densities.
- Water and fertility: well-watered, fertile fields support more plants; dryland crops are sown thinner so each plant has enough soil water.
- Sowing date: late-sown crops have less time to grow and compensate, so populations are often raised.
- The product: seed crops, fodder crops and crops sold by size or grade have their own optima.
Because seed costs money, the economic optimum is usually a little below the population that maximises yield.
Arrangement matters too
Beyond the number of plants, their arrangement affects competition. Rectangularity (the ratio of distance between rows to distance within the row) close to 1, approaching a square arrangement, generally reduces competition between neighbours; wide rows with crowded plants within the row increase it. Row spacing is often set by machinery and weeding, though.
From spacing to population
For crops sown in rows at fixed distances:
Maize population from spacing
Maize sown at 75 cm between rows and 20 cm between plants, one plant per hill:
- Area per plant = 0.75 × 0.20 = 0.15 m2.
- Plants per hectare = 10,000 ÷ 0.15 = 66,667, or 6.7 plants per m2.
At 60 × 25 cm: 10,000 ÷ 0.15 = the same 66,667 plants, with a more nearly square arrangement (rectangularity 2.4 instead of 3.75).
From population to seed rate
The seed rate must allow for seed size, germination and the seeds that germinate but fail to establish in the field:
The factor 100 converts units: plants per m2 × 10,000 m2 per ha × TGW ⁄ 1,000 g per seed ⁄ 1,000 g per kg = plants per m2 × TGW ⁄ 100.
- Thousand-grain weight (TGW), or thousand-seed weight, varies widely between varieties and seed lots, from a few grams for small-seeded crops to over 1,000 g for large legumes; check the actual seed lot.
- Germination comes from the seed label or a germination test.
- Field establishment is the proportion of germinating seeds that emerge and survive; it depends on seedbed, sowing depth, moisture, temperature, pests and seed vigour. Values from about 70 to 95 per cent are typical in good conditions, lower in poor ones.
Seed rate for wheat
Target: 250 plants per m2. Thousand-grain weight: 40 g. Germination: 90 per cent. Expected field establishment: 85 per cent.
Seed rate = 250 × 40 ⁄ (0.90 × 0.85 × 100) = 10,000 ⁄ 76.5 ≈ 131 kg/ha.
If the farmer instead uses a larger-seeded lot with a TGW of 50 g, the same population needs 250 × 50 ⁄ 76.5 ≈ 163 kg/ha: about 25 per cent more seed by weight for the same number of plants. Seed rates given as fixed kilograms per hectare, ignoring seed size, often give the wrong population.
Seed rate for maize
Target: 66,667 plants per hectare (6.67 per m2), one seed per hill. TGW: 300 g. Germination: 90 per cent. Establishment: 95 per cent with a precision planter.
Seed rate = 6.67 × 300 ⁄ (0.90 × 0.95 × 100) = 2,000 ⁄ 85.5 ≈ 23.4 kg/ha.
Hybrid maize seed is often sold by seed count (for example in bags of tens of thousands of seeds) rather than weight; then the number of seeds needed is 66,667 ÷ (0.90 × 0.95) ≈ 78,000 seeds per hectare.
Other useful conversions
- Seeds per metre of row = plants per m2 × row spacing (m) ÷ (germination × establishment). For wheat at 250 plants per m2, rows 0.20 m apart, germination 0.90 and establishment 0.85: 250 × 0.20 ÷ 0.765 ≈ 65 seeds per metre, which is how seed drills are calibrated.
- Transplanted crops: plants per hectare from spacing, then seedlings needed allowing for nursery losses (see the article on rice systems for a worked example).
- Pure live seed = purity × germination, used when seed lots contain impurities (see the article on seed certification).
Key points
- Yield rises with population to an optimum; biomass often levels off (asymptotic), while grain yield of many crops falls when crowded (parabolic).
- The optimum depends on variety, water, fertility, sowing date and product; the economic optimum is slightly below the yield maximum.
- Plants per hectare = 10,000 ÷ (row spacing × plant spacing in m) × plants per hill.
- Seed rate (kg/ha) = plants per m2 × TGW (g) ÷ (germination × establishment × 100).
- Account for seed size: the same population needs more kilograms of a larger-seeded lot.
- Seeds per metre of row = plants per m2 × row spacing ÷ (germination × establishment).
What the exams ask
- School-leaving and entrance papers: the effect of plant density on yield, and computing plants per hectare from spacing.
- Degree and research-fellowship entrances: seed rate from population, TGW, germination and establishment; asymptotic and parabolic yield–density relationships; rectangularity.
- Professional and agricultural engineering examinations: seed drill calibration, seeds per metre of row, and adjusting seed rates for seed lots and conditions.
Described in general terms: the kind of examination, not a past paper. Laisha never reproduces exam questions.
Questions people ask
Why do recommendations still give seed rates in kilograms per hectare?
Because it is simple and traditional. But since seed size varies between varieties and lots, calculating from a target plant population and the actual thousand-grain weight gives a more accurate stand.
Should I sow more seed to be safe?
A modest allowance for poor establishment is sensible, especially in rough seedbeds or late sowing. Sowing far more than needed wastes seed and can lower yield through competition, lodging and disease.
Why do tillering cereals tolerate a wide range of seed rates?
Because each plant can form more tillers when plants are sparse and fewer when they are dense, compensating for differences in population. Maize and sunflower, which do not tiller, have much narrower optimum ranges.
Sources
- Holliday, R. "Plant population and crop yield." Field Crop Abstracts 13, 159–167 and 247–254 (1960).
- Willey, R. W. and Heath, S. B. "The quantitative relationships between plant population and crop yield." Advances in Agronomy 21, 281–321 (1969).
- Reddy, S. R. Principles of Agronomy. Kalyani Publishers, latest edition. Chapter on plant population.
- Grains Research and Development Corporation (GRDC). GrowNotes for wheat and other crops: plant population and seed rate calculations. GRDC, various years.
- Duvick, D. N. "The contribution of breeding to yield advances in maize." Advances in Agronomy 86, 83–145 (2005).
More in agronomy and crop production
Discussion
Questions, corrections and notes from readers on this article. Every comment is checked before it appears: keep it on the topic, and do not share phone numbers, links or contact details.