How the problems work
Each set has a code, and a class link carries the code and every setting, so the whole class gets the same numbers. Products go by their grade (25-5-15 fertilizer) or are a plain material such as urea (46-0-0).
Common slips get a hint: the percent multiplied instead of divided, P2O5 given for P, the DAP's nitrogen left out of a blend, a part bag not rounded up.
A blend from the Delaware nutrient handler review, worked the same way
A field needs 60 lb N, 50 lb P2O5 and 65 lb K2O per acre from DAP (18-46-0), urea (46-0-0) and potash (0-0-60). DAP is the only P source, so start with it.
- DAP: 50 ÷ 0.46 ≈ 108.6957, so 108.70 lb per acre, which also brings 108.6957 × 0.18 ≈ 19.5652 lb N.
- Urea: (60 − 19.5652) ÷ 0.46 ≈ 87.90 lb per acre.
- Potash: 65 ÷ 0.60 ≈ 108.33 lb per acre.
Formulas and where they come from
| What | Formula | Source |
|---|---|---|
| Nutrient in a bag | weight × % ÷ 100 | STMA (2017); Delaware (2013) |
| Product for a rate | nutrient wanted ÷ (% ÷ 100); per acre = per 1,000 sq ft × 43.56 | STMA (2017); IPNI (2011); Virginia DCR (2022) |
| Oxides | P = P2O5 × 0.44; K = K2O × 0.83; P2O5 = P × 2.29; K2O = K × 1.21 | IPNI (2011); CTAHR; exact factors from CIAAW atomic weights |
| Blend | P source first, then the N it supplies comes off the N target | Delaware (2013); Virginia DCR (2022) |
| Cost | price ÷ lb of N in the package | STMA (2017); IPNI (2011) |
| Liquid | gallons = lb ÷ lb per gallon | IPNI (2011); WSU FS035E; Virginia DCR (2022) |
| Spreader | lb caught ÷ (swath × run) × 1,000 or × 43,560 | Delaware (2013) |
| Slow-release N | water-insoluble N ÷ total N × 100 | UGA L376 (2000); Seminole County (2021) |
| Per hectare | 1 lb per acre = 1.12 kg per ha (1.1209 from NIST units) | Teagasc (2025); Yara UK; NIST SP 811 (2008) |
Sources checked October 25, 2026. Some Irish and UK bags print elemental N-P-K (Teagasc's 18-6-12 brings 23 kg P per 389 kg); every grade on this page is N-P2O5-K2O, as on US labels.
Questions
How do you calculate how much fertilizer to apply?
Divide the nutrient rate you want by the percent in the product, written as a decimal. For 0.75 lb of N per 1,000 sq ft from 25-5-15: 0.75 ÷ 0.25 = 3 lb of product per 1,000 sq ft, and 3 × 43.56 = 130.68 lb per acre (STMA worksheet).
What do the three numbers on a fertilizer bag mean?
They are the percent N, P2O5 and K2O by weight, always in that order. A 50 lb bag of 26-8-16 holds 50 × 0.26 = 13 lb N, 4 lb P2O5 and 8 lb K2O.
How do you convert P2O5 to P and K2O to K?
Multiply P2O5 by 0.44 for P and K2O by 0.83 for K; go back with × 2.29 and × 1.21 (IPNI). So 200 lb of 10-20-10 has 40 lb P2O5, or 17.6 lb P. The exact 0.4364 and 0.8302 are under Conventions; 0.8301 and CTAHR's K × 1.20 are accepted too.
How do you find the cost per pound of nitrogen?
Divide the price by the pounds of N in the package. A 50 lb bag of 34-0-0 at $22.10 holds 17 lb N, so N costs $1.30 a pound. Compare products this way, not by the bag price.
How do you calibrate a fertilizer spreader?
Run the spreader over a measured strip, catch and weigh what comes out, then divide by the strip's area. Delaware's example: 5 lb of 25-5-3 on 7 ft × 100 ft is 0.15 lb K2O on 700 sq ft, or 9.33 lb K2O per acre.
How many gallons of liquid fertilizer do I need?
Find the pounds of product, then divide by its weight per gallon. For 150 lb N from UAN 28-0-0 at 10.7 lb per gallon: 150 ÷ 0.28 = 536 lb, and 536 ÷ 10.7 = about 50 gallons (IPNI).
How do you work out the percent of slow-release nitrogen?
Divide the water-insoluble (slow-release) N on the label by the total N and multiply by 100. A bag with 16% total N and 4% water-insoluble N is 25% slow release (University of Georgia).
Sources: STMA, Doak, Calculations Worksheet, 2017 (PDF); University of Delaware, Commercial Nutrient Handler Calculation Review with answers (PDF); IPNI, Math Anxiety: Fertilizer Calculations, 2011 (PDF); University of Hawaii CTAHR, Calculating NPK (PDF); Virginia DCR, Commercial Fertilizer Calculations (PDF); WSU Extension FS035E (PDF); University of Georgia Leaflet 376 (PDF); Seminole County, percentage of slow release nitrogen (PDF); Teagasc, Weights and Measures, 2025 (PDF); CIAAW standard atomic weights; Yara UK, units and conversion; NIST SP 811, 2008 (PDF).