What this calculator does
Find out how much fertilizer to buy and spread so your lawn or garden gets the right amount of each nutrient. Advice is almost always given as an amount of nutrient, such as one pound of nitrogen per 1,000 square feet. But the product you buy is only partly made of that nutrient. The three numbers on the bag are called the grade, or N-P-K. They give the percentage by weight of nitrogen, phosphate and potash. A 20-5-10 product is 20% nitrogen, so supplying one pound of nitrogen takes five pounds of product.
This calculator does that math for you. Enter the grade, pick which nutrient your advice is about, and enter the target rate and the area. You get the amount of product to spread, in total and per unit of area, and the number of bags. You also see how much of each of the three nutrients you end up applying along the way.
Where it's used
Why this math matters outside the classroom:
- Lawn feeding. To put 1 lb of nitrogen on 1,000 ft² with a 25-10-10 product, a homeowner spreads 1 ÷ 0.25 = 4 lb of fertilizer.
- Bag coverage. A 5,000 ft² lawn at 4 lb of product per 1,000 ft² needs 20 lb, which tells the buyer whether one bag is enough.
- Vegetable gardens. Gardeners use the middle number on the label to work out how much product supplies a target amount of phosphate.
- Sports turf. Groundskeepers turn a nitrogen target per 1,000 ft² into pounds of product for a whole playing field before loading the spreader.
- Finding the whole. Students solve for the whole from a part and a percent: 0.5 lb of nitrogen from a 10% product needs 5 lb.
Grade level and standards: Grades 6–7; Common Core State Standards for Mathematics 6.RP.A.3.c. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
How to use it
- Choose US units (pounds per 1,000 square feet) or metric units (grams per square meter).
- Enter the three numbers of the grade printed on the bag.
- Pick the nutrient your advice is based on, and enter the target rate of that nutrient.
- Enter the area and the bag size. Then read the product to spread and the nutrients applied.
What the inputs mean
- N on the label
- The grade lists nitrogen, then phosphate, then potash, as percentages of the product's weight. A 0 for a nutrient means the product has none of it.
- P₂O₅ on the label
- By long-standing label custom, the middle number is given as phosphate (P₂O₅), not as pure phosphorus. Soil test advice normally uses the same custom.
- K₂O on the label
- The last number is given as potash (K₂O), not as pure potassium.
- Nutrient the rate refers to
- Most lawn advice is given as an amount of nitrogen. Garden and soil test advice sometimes targets phosphate or potash instead.
- Target rate of that nutrient
- A soil test report or the product's own directions is the best source. The right amount depends on the plants, the soil and the time of year.
Formula and method
product rate = target nutrient rate ÷ (label percent ÷ 100) product (lb) = product rate (lb per 1,000 ft²) × area (ft²) ÷ 1,000 product (kg) = product rate (g/m²) × area (m²) ÷ 1,000 nutrient applied = product × label percent ÷ 100 (for each of N, P₂O₅, K₂O) bags = product ÷ bag size, rounded up
N is nitrogen, P₂O₅ is phosphate and K₂O is potash. The label percent is the share of the product's weight that's the nutrient. So dividing the nutrient rate by that share gives the weight of product that delivers it. US rates are per thousand square feet, so the area is divided by 1,000. Metric rates are in grams per square meter, so the total in grams is divided by 1,000 to give kilograms.
When you spread enough product to meet the target for one nutrient, you also apply the other two. How much depends on their label percentages. The calculator lists all three, which helps when a soil test says one of them isn't needed.
Some sources use pure (elemental) amounts. To compare, phosphorus is about 43.6% of the weight of P₂O₅, and potassium is about 83% of the weight of K₂O.
Worked example
A 5,000 ft² lawn should get 1 lb of nitrogen per 1,000 ft², using a 20-5-10 product sold in 20 lb bags.
- Product rate: 1 ÷ 0.20 = 5 lb of product per 1,000 ft².
- Total product: 5 × (5,000 ÷ 1,000) = 25 lb.
- Bags: 25 ÷ 20 = 1.25, which rounds up to 2 bags.
- Nutrients applied: N 25 × 0.20 = 5 lb, P₂O₅ 25 × 0.05 = 1.25 lb, K₂O 25 × 0.10 = 2.5 lb.
Result: Spread 25 lb of the 20-5-10 product (11.34 kg). That takes 2 bags of 20 lb and supplies 5 lb of nitrogen in total.
Understanding the result
Set your spreader to deliver the product rate, not the nutrient rate. Spreader settings on the bag are usually for the product, so check that they agree with the figure here.
The full amount may be more than the product's directions allow at one time. If so, split it into several lighter feedings spread out over the season.
Assumptions and limitations
- The grade on the label is the guaranteed analysis (the promised content) by weight of a dry product.
- The target rate and the label use the same terms: N, P₂O₅ and K₂O.
- The product is spread evenly over the whole area entered.
- The calculator converts a rate you give it. It doesn't decide how much fertilizer your plants or soil need. A soil test or local advice does that.
- Liquid products sold by volume need their density to convert to weight, which isn't included here.
- Slow-release portions, secondary nutrients and micronutrients on the label aren't considered.
Frequently asked questions
What do the three numbers on a fertilizer bag mean?
They're the percentages by weight of nitrogen (N), phosphate (P₂O₅) and potash (K₂O), always in that order. A 50 lb bag of 10-10-10 holds 5 lb of each. The rest of the weight is other compounds and filler that carry the nutrients.
How much fertilizer gives 1 lb of nitrogen per 1,000 square feet?
Divide 100 by the first number of the grade. For a 20-5-10 product that's 5 lb of product per 1,000 ft². For a 10-10-10 product it's 10 lb, and for a 32-0-4 product it's about 3.1 lb.
Why does the calculator show all three nutrients?
Spreading a product to meet one nutrient target also applies the other two. Seeing the totals helps you avoid adding phosphate or potash where a soil test shows the soil already has plenty.
Can I use this for a vegetable garden?
Yes. Enter the bed area and the rate from your soil test or seed-packet advice, in pounds per 1,000 ft² or grams per square meter. Small beds need only a little product, so the metric option can be easier to measure.
How this calculator is checked
Method: Guaranteed-analysis arithmetic: product = nutrient rate ÷ label fraction × area; nutrients applied = product × label fraction; exact pound–kilogram factor. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
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