Fertiliser calculations: nutrient content and doses
Turning a nutrient recommendation into kilograms of fertiliser: grades, oxide conversions, straight and complex products, per-plant doses and fertigation.
On this page
- Reading a fertiliser grade
- The basic calculation
- Straight fertilisers
- Complex fertilisers: work in the right order
- Cost per kilogram of nutrient
- Per-plant doses in orchards and plantations
- Fertigation: parts per million
- Area and unit conversions
- Key points
- What the exams ask
- Questions people ask
- Sources
- Related on Laisha
- Discussion
A soil test or a recommendation says how much nutrient a crop needs, for example 120 kg of nitrogen per hectare. A farmer buys fertiliser, in bags of products that contain only part nutrient. Turning one into the other, choosing the right mix of products, and working out the cost of each kilogram of nutrient are everyday calculations in agronomy, and some of the most common numerical questions in agriculture exams.
The arithmetic is simple, but a few conventions trip people up: the oxide form of phosphorus and potassium, the order in which to work out a mixture, and units in fertigation. This article works through them.
Reading a fertiliser grade
A fertiliser's grade (or analysis) gives its nutrient content as percentages by weight, by convention in the order N–P2O5–K2O. A bag labelled 10–26–26 contains 10 per cent nitrogen, 26 per cent "phosphate" expressed as P2O5, and 26 per cent "potash" expressed as K2O. Secondary and micronutrients, such as sulphur or zinc, are listed separately.
Phosphorus and potassium are expressed as oxides for historical reasons. To convert:
The factors come from molecular weights: P2O5 is 141.94 g/mol, of which phosphorus is 2 × 30.97 = 61.94, so P is 61.94 ⁄ 141.94 = 0.436 of it. Recommendations in some countries and many research papers use elemental P and K, so check which a figure means before converting.
The basic calculation
So 120 kg N from urea (46 per cent N) needs 120 ⁄ 0.46 = 261 kg of urea per hectare.
The reverse gives the nutrient supplied: 100 kg of DAP (18–46–0) supplies 18 kg N and 46 kg P2O5.
Straight fertilisers
A recommendation met with straight fertilisers
A crop needs 120 kg N, 60 kg P2O5 and 40 kg K2O per hectare. The farmer uses urea (46 per cent N), single superphosphate (16 per cent P2O5) and muriate of potash (60 per cent K2O).
- Urea: 120 ⁄ 0.46 = 260.9 kg.
- Single superphosphate: 60 ⁄ 0.16 = 375.0 kg, which also supplies about 375 × 0.12 = 45 kg of sulphur.
- Muriate of potash: 40 ⁄ 0.60 = 66.7 kg.
Total product: about 703 kg per hectare. If nitrogen is applied in splits (for example half at sowing and half at a later stage), only the urea is divided; phosphate and potash usually go on at sowing.
Complex fertilisers: work in the right order
When one product supplies more than one nutrient, calculate first the product that supplies the nutrient with only one source, then account for what it adds of the others.
Using DAP with urea and potash
Same recommendation, 120–60–40, using DAP (18–46–0), urea and muriate of potash.
- Phosphorus first, because DAP is the only phosphate source: DAP = 60 ⁄ 0.46 = 130.4 kg.
- Nitrogen supplied by that DAP: 130.4 × 0.18 = 23.5 kg N.
- Nitrogen still needed: 120 − 23.5 = 96.5 kg N, from urea: 96.5 ⁄ 0.46 = 209.8 kg urea.
- Potash: 40 ⁄ 0.60 = 66.7 kg muriate of potash.
Total product: about 407 kg per hectare, much less bulk than with single superphosphate, but with no sulphur. Had the farmer started with nitrogen and ignored DAP's nitrogen, the crop would have received 23.5 kg N more than recommended.
The same logic applies to NPK complexes: satisfy the nutrient that limits the choice, then top up the others with straight fertilisers.
Cost per kilogram of nutrient
Comparing fertilisers by bag price is misleading; compare the price per kilogram of nutrient.
Which nitrogen source is cheaper?
A 50 kg bag of urea (46 per cent N) costs 30 currency units; a 50 kg bag of ammonium sulphate (21 per cent N, 24 per cent S) costs 22.
- Urea: N per bag = 50 × 0.46 = 23 kg, so N costs 30 ⁄ 23 = 1.30 per kg.
- Ammonium sulphate: N per bag = 50 × 0.21 = 10.5 kg, so N costs 22 ⁄ 10.5 = 2.10 per kg.
Urea is cheaper nitrogen. But if the crop also needs sulphur, the ammonium sulphate's 12 kg of S per bag has value too, and on alkaline soils with high volatilisation risk, the effective cost of urea nitrogen may be higher than it looks. The cheapest nutrient is the one that ends up in the crop.
Per-plant doses in orchards and plantations
Tree crops are usually fertilised per plant.
Fertilising an orchard
A recommendation for mature trees is 500 g N per tree per year, in two splits, using urea. The orchard has 400 trees per hectare.
- Urea per tree per year: 500 ⁄ 0.46 = 1,087 g, so about 544 g per split.
- Urea per hectare per year: 1.087 kg × 400 = 435 kg.
Spread it over the root zone, under and slightly beyond the canopy, rather than against the trunk, and water it in.
Fertigation: parts per million
In drip and greenhouse systems, nutrients are dissolved in irrigation water and expressed as concentration. 1 ppm = 1 mg per litre (for water-based solutions).
Making a 100 ppm nitrogen solution
To supply irrigation water containing 100 ppm N using urea (46 per cent N):
- Urea needed per litre = 100 mg N ⁄ 0.46 = 217 mg.
- For a 1,000-litre tank: 217 mg × 1,000 = 217 g of urea.
If a 1 : 100 injector is used, so that 1 litre of stock solution is diluted into 100 litres of irrigation water, the stock must be 100 times stronger: 21.7 kg of urea in 1,000 litres of stock. Check the fertiliser's solubility, and never mix calcium-containing fertilisers with phosphates or sulphates in the same concentrated stock, as they precipitate.
Area and unit conversions
- 1 hectare = 10,000 m2 = about 2.47 acres; 1 acre ≈ 0.405 ha. A rate of 100 kg/ha ≈ 89 lb/acre.
- For a small plot, scale by area: 261 kg urea per hectare is 26.1 g per m2, or 2.61 kg for a 100 m2 plot.
- Recommendations based on soil tests often come as nutrient per hectare to a given depth; use bulk density to convert mg/kg in soil to kg/ha (see the article on bulk density).
Key points
- Fertiliser grades are N–P2O5–K2O percentages by weight.
- P = P2O5 × 0.436; K = K2O × 0.830.
- Fertiliser needed = nutrient needed ÷ nutrient fraction.
- With multi-nutrient products, calculate the single-source nutrient first, then subtract what that product supplies of the others.
- Compare fertilisers by cost per kilogram of nutrient, not per bag.
- In fertigation, 1 ppm = 1 mg/L; a 1 : 100 injector needs a stock 100 times stronger.
What the exams ask
- School-leaving and entrance papers: reading a grade, and calculating the amount of urea, superphosphate or potash for a given nutrient dose.
- Degree and research-fellowship entrances: oxide–element conversions, combining complex and straight fertilisers, and cost per kilogram of nutrient.
- Professional and extension examinations: fertiliser schedules for field crops and orchards, splits, fertigation concentrations, and converting soil test results into recommendations.
Described in general terms: the kind of examination, not a past paper. Laisha never reproduces exam questions.
Questions people ask
Why are phosphorus and potassium given as P2O5 and K2O?
It is a nineteenth-century convention from when analyses were reported as oxides. It survives on most labels and in many recommendations. The oxides do not exist as such in the fertiliser; they are just a way of expressing content.
Is more expensive fertiliser always better?
No. Products differ in nutrient content, other nutrients they bring (such as sulphur or calcium), solubility, acidifying effect and losses under particular conditions. Compare cost per kilogram of nutrient actually used by the crop.
Can I mix fertilisers myself?
Many straight fertilisers can be mixed shortly before spreading, but some combinations become sticky or lose nitrogen (for example urea with superphosphate can become damp). Check compatibility guidance and mix only what will be spread soon.
Sources
- Havlin, J. L., Tisdale, S. L., Nelson, W. L. and Beaton, J. D. Soil Fertility and Fertilizers, 8th edition. Pearson, 2014.
- FAO. Fertilizer Use by Crop and Plant Nutrition for Food Security. FAO Fertilizer and Plant Nutrition Bulletins.
- International Fertilizer Association. Fertilizers and Their Use, 4th edition. IFA and FAO, 2000.
- Kafkafi, U. and Tarchitzky, J. Fertigation: A Tool for Efficient Fertilizer and Water Management. IFA and IPI, 2011.
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Discussion
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