# agri.seed-rate

How much seed to drill, in kg/ha, to end up with a target number of
established plants per square metre:

    seed rate (kg/ha) = target plants/m² x thousand-grain weight (g) / expected establishment (%)

`seedRate(260, 48, 7000)` is 178.3 kg/ha and 371.4 seeds/m²: 260 plants at
70% establishment needs 371.4 seeds/m², and 1000 seeds weigh 48 g.

The formula follows from the units: seeds/m² = plants / establishment; one
seed weighs TGW / 1000 g; and 1 g/m² is 10 kg/ha. It is the calculation behind
AHDB's seed rate conversion tool (seeds/m² against TGW, read off as kg/ha) and
the one UK agronomy guidance quotes.

## Establishment

`establishmentBasisPoints` is the share of seeds sown that become plants:
germination and field losses (slugs, seedbed, sowing date) together. If you
have a germination figure and a separate field-loss estimate, multiply them:
90% germination and 85% emergence is 76.5%, `7650`. AHDB's benchmarks are
around 70% for well-timed winter wheat, falling as drilling gets later.

## Exactness

The thousand-grain weight is taken to the nearest 0.01 g (half away from zero,
`math.round-float`), so the rate is exactly plants x centigrams / basis points
and is rounded once, half up, to 0.1 kg/ha. A float calculation gets 1.15 g at
100 plants and 100% as 1.1499999999999999 and rounds it to 1.1; this gives 1.2.

It does not choose the target population, adjust for sowing date or soil, or
round to what a drill can be set to.

## Limits

Plants 1 to 100,000 per m² (grass and small seeds are sown in thousands);
TGW more than 0 and at most 1000 g, and at least 0.01 g after rounding;
establishment 1 to 10,000 basis points.

## Sources

- AHDB, "Seed rate calculator – conversion tool",
  https://ahdb.org.uk/seed-rate-conversion-tool (seeds/m² to kg/ha by TGW).
- AHDB, "Establishment in wheat: germination and emergence (GS0–GS2)",
  https://ahdb.org.uk/knowledge-library/establishment-in-wheat-germination-and-emergence-gs0-gs2
  (the 70% establishment benchmark).
- Foundation for Arable Research, "Seed rate calculation",
  https://www.far.org.nz/resources/seed-rate-calculation: sowing rate =
  target plants x TGW x 100 / (% germination x % emergence); its worked
  example (225 plants, TGW 40 g, 90% x 85%, about 118 kg/ha) is a vector.