What the three numbers on the bag actually guarantee
Every fertiliser sold in the United States carries a guaranteed analysis: three numbers, in a fixed order, that are percentages by weight of nitrogen (N), available phosphate (P2O5) and soluble potash (K2O). The format and the wording are set by state fertiliser laws written to the model bill maintained by the Association of American Plant Food Control Officials, which is why a bag in Iowa reads the same as a bag in Georgia. Urea is 46-0-0, so 46% of its weight is nitrogen. DAP is 18-46-0. Muriate of potash is 0-0-60.
The conversion from nutrient to product is one division: pounds of nutrient divided by the decimal analysis. Need 100 lb of N and holding urea at 46%? 100 ÷ 0.46 = 217.4 lb of urea. That single line is the entire calculation, repeated once per nutrient.
The complication that trips people up is that the second and third numbers are oxides, not elements. P2O5 is 43.64% elemental phosphorus by weight and K2O is 83.01% elemental potassium. No fertiliser bag contains any P2O5 molecules — the oxide convention is a nineteenth-century analytical legacy that stuck because everyone's records, recommendations and prices are built on it. Since soil test recommendations in North America are also written in oxide terms, the two match and you never need to convert. You only need the factors when reading a plant tissue analysis, a European fertiliser label, or a scientific paper, all of which usually work in elemental P and K.
Why the order of the calculation matters
If every product supplied exactly one nutrient, you would do three independent divisions and stop. Most phosphate sources supply two. Diammonium phosphate is 18-46-0: it carries 18% nitrogen alongside its phosphate, and monoammonium phosphate is 11-52-0. That nitrogen is real, it is available to the crop, and it must be credited against the nitrogen recommendation or you will over-apply.
So the order is fixed:
One. Meet the phosphate requirement first, because the phosphate source is the constrained one — you cannot get the P without accepting whatever N comes with it.
Two. Work out the nitrogen that came along for the ride. Pounds of phosphate product times its %N.
Three. Subtract that from the nitrogen recommendation, and buy straight nitrogen for the remainder only.
Four. Meet the potash requirement independently, since muriate and sulphate of potash carry no nitrogen or phosphate.
Skip step two and a typical 150-60-60 recommendation gets 23 lb per acre more nitrogen than the soil test asked for. On 500 acres that is over five tons of urea equivalent bought and applied for no reason, and on nitrate-sensitive ground it is an environmental issue as well as a financial one.
There is a case where the credit swamps the recommendation entirely: a high phosphate rate against a low nitrogen recommendation. A 60 lb P2O5 rate from DAP brings 23.5 lb of N with it, so if your recommendation is 15 lb of N you are already over it before you buy any urea. The calculator schedules no nitrogen product and tells you so. If the excess matters — on a legume, or where nitrogen is regulated — switch to triple superphosphate (0-45-0), which carries none.
Worked example: 150-60-60 on 80 acres
Your soil test calls for 150 lb N, 60 lb P2O5 and 60 lb K2O per acre. You have DAP at $750/ton, urea at $550/ton and muriate of potash at $520/ton, and 80 planted acres.
- DAP for the phosphate. 60 ÷ 0.46 = 130.43 lb/acre.
- Nitrogen credit from the DAP. 130.43 × 0.18 = 23.48 lb N/acre.
- Nitrogen still owed. 150 − 23.48 = 126.52 lb N/acre.
- Urea for the balance. 126.52 ÷ 0.46 = 275.05 lb/acre.
- Potash. 60 ÷ 0.60 = 100.00 lb/acre.
- Total product. 130.43 + 275.05 + 100.00 = 505.48 lb/acre.
- Tons for the field. 505.48 × 80 ÷ 2,000 = 20.22 short tons — 5.22 tons of DAP, 11.00 of urea and 4.00 of potash.
- Cost per acre. DAP: 130.43 × 750 ÷ 2,000 = $48.91. Urea: 275.05 × 550 ÷ 2,000 = $75.64. Potash: 100 × 520 ÷ 2,000 = $26.00. Total $150.55 per acre.
- Whole-field cost. $150.55 × 80 = $12,044.
Check the nutrients you have actually bought: N = 23.48 (DAP) + 126.52 (urea) = 150.0, P2O5 = 60.0, K2O = 60.0. Exactly the recommendation, with no rounding drift, because every step was a division rather than a lookup.
Reading the result: cost per pound of nutrient
Two numbers matter once the order sheet is done. The first is total pounds per acre, because that is the physical load the spreader handles. At 505 lb/acre a 10-ton tender covers about 40 acres per fill, and the spread pattern of a blend at that rate depends on the products having similar particle size and density — segregation in the hopper is a real cause of streaked fields.
The second is cost per pound of nutrient, which is how you compare sources properly. Urea at $550/ton delivers nitrogen at 550 ÷ 2,000 ÷ 0.46 = $0.598 per pound of N. UAN 32% at $400/ton delivers it at 400 ÷ 2,000 ÷ 0.32 = $0.625 per pound. The cheaper ton is not the cheaper nitrogen. Run that division on every quote before you buy; the reference table below does it for the common products.
The phosphate comparison is subtler because DAP and MAP both carry nitrogen. To value DAP fairly, price the nitrogen it carries at your urea nitrogen cost, subtract that from the DAP price, and divide the remainder by the phosphate. It is the same logic as the blend order, applied to money instead of pounds.
Where results carry agronomic or regulatory consequence, remember what this calculator does not know: it does not know your soil test values, your yield goal, your manure credits, your legume credits or your state's nutrient management rules. It converts a recommendation into product. Getting the recommendation itself right is a job for a soil test and a certified crop adviser. Once you have the acres and the products settled, the same acreage figure drives your field area, your seed order and the cost side of your break-even price.
Common fertiliser grades and what a ton delivers
| Product | Grade (N-P₂O₅-K₂O) | lb nutrient per ton | lb product per 100 lb nutrient |
|---|---|---|---|
| Anhydrous ammonia | 82-0-0 | 1,640 lb N | 122 lb |
| Urea | 46-0-0 | 920 lb N | 217 lb |
| Ammonium nitrate | 34-0-0 | 680 lb N | 294 lb |
| UAN solution | 32-0-0 | 640 lb N | 313 lb |
| Ammonium sulphate | 21-0-0-24S | 420 lb N | 476 lb |
| MAP | 11-52-0 | 1,040 lb P₂O₅ + 220 lb N | 192 lb |
| DAP | 18-46-0 | 920 lb P₂O₅ + 360 lb N | 217 lb |
| Triple superphosphate | 0-45-0 | 900 lb P₂O₅ | 222 lb |
| Muriate of potash | 0-0-60 | 1,200 lb K₂O | 167 lb |
| Sulphate of potash | 0-0-50-18S | 1,000 lb K₂O | 200 lb |
Nutrient per ton is 2,000 × the analysis; product per 100 lb of nutrient is 100 ÷ the decimal analysis, rounded. Sulphur guarantees are shown where they are part of the standard grade.
Mistakes that cost money or yield
- Forgetting the nitrogen in DAP or MAP. The most common error in the whole exercise. Credit it, or you buy nitrogen twice.
- Confusing P₂O₅ with elemental P. If a recommendation is written in elemental terms, multiply P by 2.29 and K by 1.20 before using it against a fertiliser label. Mixing the conventions understates phosphate by more than half.
- Applying to deeded acres instead of treated acres. The tons figure scales directly with area, so an acreage error is a tonnage error of the same percentage.
- Comparing products on price per ton. Compare price per pound of nutrient. A cheaper ton of a lower analysis is often the more expensive nitrogen.
- Ignoring nutrient credits. Manure, a previous legume crop and irrigation water all supply nutrients. Subtract those credits from the recommendation before you enter it here, not after.
- Spreading a blend of mismatched particle sizes. Physical segregation in the spreader produces streaks that look like an application-rate problem but are a blending problem.
- Surface-applying urea and expecting all of it to reach the crop. Urea left on a warm, moist surface loses nitrogen as ammonia. Incorporate it, irrigate it in, or use a urease inhibitor — the calculator assumes the nutrient you buy is the nutrient the crop gets.
Blends, liquids and the 4R framework
Retailers usually sell a custom dry blend rather than three separate products, and they build it exactly as this calculator does: phosphate first, nitrogen to fill, potash last, with micronutrients and sulphur added as separate ingredients. Asking your dealer for the blend sheet lets you check their arithmetic against yours. A blend quoted as, say, 92 lb of nitrogen in a 505 lb blend simply reflects the same divisions expressed as an overall grade.
Liquid programmes work identically once you convert weight to volume. UAN 32% weighs about 11.06 lb per gallon, so a gallon carries roughly 3.54 lb of N; 10-34-0 ammonium polyphosphate weighs about 11.65 lb per gallon. Divide your pounds per acre by the pounds per gallon to get gallons per acre, then treat it like any other liquid application through your tank mix arithmetic.
Finally, rate is only one of the four decisions that make up the nutrient stewardship framework used across North American agronomy — right source, right rate, right time, right place. This calculator answers source and rate. Timing and placement decide how much of what you bought the crop actually captures, and on nitrogen in particular they can matter as much as the rate itself. Split applications, banded starter and side-dressing are all ways of improving capture without changing a single number on this page.