Fertilizer Calculator
A 10-10-10 bag is a tenth nitrogen, so a kilogram of nitrogen takes ten kilograms of product.
The formula
product = nutrient wanted * 100 / percent on the label
The three numbers are percentages
A bag marked 10-10-10 is ten per cent nitrogen, ten per cent phosphate and ten per cent potash by weight. To deliver one kilogram of nitrogen you therefore need ten kilograms of product. The rest is carrier, filler and the other two nutrients.
Phosphate is not phosphorus
The second and third numbers are P₂O₅ and K₂O, not the elements. Elemental phosphorus is 43.6 % of phosphate and elemental potassium 83 % of potash. Soil test reports often give elements while bags give oxides, and comparing the two directly overstates the phosphorus you are applying by more than a factor of two.
Nitrogen is the one to be careful with
Phosphate and potash largely stay where they are put. Nitrogen leaches, and what leaves the root zone ends up in groundwater and watercourses. Standard practice is to split a season's nitrogen into several small applications rather than one large one, which the plant uses better and the water table sees less of.
Rules of thumb, and the field
Every figure here describes an average season on an average site. Soil type, aspect, drainage, variety and weather each move the answer by more than the arithmetic does, and a grower who has kept records for a few years on one piece of ground knows it better than any formula. Use these to plan an order or size an implement, then trust what the ground has actually done before.