Economic N-Rate & The Profit-Optimal MRTN
Optimizes nitrogen for corn
Generic NPK tools push the maximum-yield nitrogen rate. This one finds the Maximum Return To Nitrogen (MRTN) — the rate that earns the most profit at today's N price and grain price, with the profitable range and how much yield you give up to get there.
Your crop & today's prices
Stopping at the MRTN saves 37.4 kg N/ha versus chasing maximum yield, while giving up only 119 kg/ha of grain. The economic optimum (MRTN) of 163 kg N/ha sits below the agronomic, max-yield rate of 200 kg N/ha because the last increments of N cost more than the extra grain they buy at an N:grain ratio of 6.4. Spending to maximum yield would waste 37.4 kg N/ha for just 119 kg/ha more grain.
Next: apply about 353 kg urea/ha (7.1 × 50-kg bags) in 2–3 splits — a starter at sowing, the bulk at peak demand. Anywhere in 140–185 kg N/ha earns within a whisker of peak profit, so don't over-buy N to chase the last 119 kg/ha of grain.
Y(N) = 6,100 + 34·N − 0.085·N²; MRTN = (b − Pn/Pg) / 2c. Matched row: Corn · responsive (corn after corn, medium soil). Source: ISU CNRC — responsive corn region.
Runs entirely in your browser — your prices never leave the device.
Economic N rate — key facts
- MRTN
- N* = (b − Pn/Pg) / 2c
- Agronomic optimum
- N = b / 2c (max yield)
- Response model
- Y(N) = a + b·N − c·N²
- Price ratio
- Pn ÷ Pg (N price ÷ grain price)
- Profitable range
- return within ~$1/ac of MRTN
- Urea is
- 46% N → kg ÷ 0.46, bags ÷ 50
- Corn MRTN (typ.)
- ≈ 150–190 kg N/ha
- Source
- ISU Corn N Rate Calculator + ICAR STCR
Why the most-profit rate is below the most-yield rate
Crop yield rises with nitrogen, but with diminishing returns: the first kilograms of N add a lot of grain, the last kilograms add almost none. A quadratic response, Y(N) = a + b·N − c·N², captures that curve. The maximum-yield, or agronomic-optimum, rate is the top of the curve at N = b/2c. But the top of the yield curve is not the top of the profit curve.
Profit is grain value minus nitrogen cost. Setting the marginal value of grain equal to the marginal cost of N gives the Maximum Return To Nitrogen: N* = (b − Pn/Pg) / 2c. The term Pn/Pg is the N:grain price ratio. When N is cheap relative to grain the MRTN sits close to the agronomic maximum; when N is dear it drops well below. Because the profit curve is flat near its peak, a whole profitable range of rates earns almost the same return — which is why over-applying to chase the agronomic maximum quietly burns money.
This tool carries quadratic response functions for corn, wheat and rice across four soil-response regions, calibrated to the Iowa State Corn Nitrogen Rate Calculator (MRTN database) and ICAR STCR targeted-yield response data. It pairs the 4R Right-rate decision with split-timing guidance and a urea bag count. Combine it with the Site-Specific Nutrient and Micronutrient Diagnosis calculators for a complete soil-fertility plan.
N-response reference — MRTN vs agronomic optimum
Worked at an N price of 1.40/kg N and grain price 0.22/kg (N:grain ratio ≈ 6.4). Your prices change every row.
| Crop · response region | MRTN (kg N/ha) | Agronomic max (kg N/ha) | Gap saved | Yield at MRTN (kg/ha) |
|---|---|---|---|---|
| Corn · highly responsive (continuous corn, low OM) | 194.8 | 233.3 | 38.6 | 9,569 |
| Corn · responsive (corn after corn, medium soil) | 162.6 | 200 | 37.4 | 9,381 |
| Corn · moderate (corn after soybean) | 121.5 | 158 | 36.6 | 9,457 |
| Corn · low (high-OM / manured ground) | 81.3 | 116.7 | 35.4 | 9,313 |
| Wheat · highly responsive (low-N irrigated) | 125.9 | 166.7 | 40.8 | 4,137 |
| Wheat · responsive (typical irrigated) | 97.7 | 137.5 | 39.8 | 3,986 |
| Wheat · moderate (medium soil N) | 67.9 | 106.7 | 38.8 | 3,910 |
| Wheat · low (high residual N) | 39 | 76.5 | 37.4 | 3,878 |
| Rice · highly responsive (low-N lowland) | 145.6 | 187.5 | 41.9 | 4,939 |
| Rice · responsive (typical lowland) | 111.6 | 151.9 | 40.3 | 4,595 |
| Rice · moderate (medium soil N) | 78 | 117.3 | 39.3 | 4,389 |
| Rice · low (high residual N) | 48.4 | 86.3 | 37.9 | 4,405 |
Optimize profit, not yield
The MRTN earns the most money — the agronomic maximum rarely does.
Prices drive the rate
Drag the chart line to feel how the N:grain ratio slides the optimum.
Stop over-buying N
See the kilograms you can cut for almost no yield loss.
Convert straight to urea
Get the kilograms and 50-kg bag count for the field.
Frequently Asked Questions
What is the MRTN nitrogen rate?+
MRTN stands for Maximum Return To Nitrogen — the N rate that earns the most profit, not the most grain. It is found where the extra grain from one more kilogram of N is exactly worth the cost of that nitrogen. Mathematically, with a quadratic response Y(N) = a + b·N − c·N², the economic optimum is N* = (b − Pn/Pg) / 2c, where Pn is the N price and Pg the grain price. It is always at or below the maximum-yield (agronomic) rate.
How is the MRTN rate different from the maximum-yield rate?+
The maximum-yield, or agronomic-optimum, rate is N = b/2c — the top of the yield curve, where adding more N no longer raises yield. The MRTN sits to the left of it because the last increments of N raise yield only slightly, and that tiny extra grain is worth less than the nitrogen costs. The calculator shows both, and the gap between them is the nitrogen you can stop buying without losing meaningful yield.
Why does the economic optimum N rate change with prices?+
Because profit, not yield, is what you optimize. When nitrogen is cheap relative to grain (a low N:grain price ratio) it pays to push N close to the agronomic maximum. When N is expensive relative to grain (a high ratio) the optimum drops, sometimes sharply. The formula N* = (b − Pn/Pg) / 2c makes this explicit: raise the price ratio and the optimum N falls.
How much nitrogen does corn actually need for the most profit?+
For a responsive Corn-Belt field at a moderate N:grain ratio, the MRTN typically lands around 150–190 kg N/ha (roughly 130–170 lb/ac), versus an agronomic maximum near 200 kg N/ha. Enter your crop, response region and current prices to get your figure; the tool also converts it to urea — about 326 kg urea per hectare, or roughly 6.5 fifty-kilogram bags, for a 150 kg N/ha rate.
What is the N:grain price ratio and what is a typical value?+
It is the price of one kilogram of nitrogen divided by the price of one kilogram of grain (Pn/Pg). It is the single number that drives the economic optimum. Historically corn N:grain ratios run from about 5 (cheap N) to 20+ (expensive N). The calculator computes it for you and lets you drag a line on the chart to see how each value slides the MRTN point.
What is the profitable range and why does it matter?+
The profitable range is the band of N rates whose net return is within a hair of the maximum — Iowa State quotes the rates that stay within about a dollar of the MRTN return. Inside this band, profit is essentially flat, so you have flexibility for weather, soil variability and application precision. The tool shades this band green on the chart and reports its lower and upper bounds in kg N/ha.
Is 200 kg N/ha too much nitrogen for corn?+
It depends on prices and your soil's response. 200 kg N/ha is near the agronomic maximum for a responsive field, so it buys top yield — but if nitrogen is expensive, the MRTN may be 150–170 kg N/ha and the extra 30–50 kg is spent chasing a few hundred kilograms of grain that does not pay for itself. The calculator quantifies exactly how much grain you give up by stopping at the economic optimum.
Does the MRTN approach apply to wheat and rice too?+
Yes. The same economics — set the marginal value of grain equal to the marginal cost of N — apply to any crop with a curved N response. This tool carries quadratic response functions for corn, wheat and rice across four soil-response regions, calibrated to Corn-Belt MRTN and ICAR STCR data, so it works for irrigated wheat and lowland rice as well as maize.
What does the '4R' in 4R nitrogen management mean?+
4R stands for the Right source, Right rate, Right time and Right place of nutrient application. This calculator is the Right-rate engine: it sets the economically optimal amount. Pair it with split timing (a starter at sowing and the bulk at peak demand), an appropriate N source such as urea or UAN, and banded or incorporated placement to capture the full benefit.
How do I convert the MRTN to bags of urea?+
Urea is 46% nitrogen, so urea needed = N rate ÷ 0.46, and bags = urea kg ÷ 50. For a 150 kg N/ha MRTN that is 150 ÷ 0.46 ≈ 326 kg urea, or about 6.5 bags of 50 kg per hectare. The calculator does this automatically and shows the bag count beside the rate.
What if nitrogen does not pay at all this season?+
When the N:grain price ratio rises above the response slope b, the formula returns a negative optimum, which the tool clamps to zero — meaning added N cannot pay for itself on that field at those prices. In that case hold N or apply only a small starter and rely on the soil's indigenous supply, then revisit as prices move.
Are these results a substitute for a soil test?+
No. They are sound planning figures from published regional response functions, but a field varies. Use them to set a budget and a target rate, then refine with a soil test, a pre-sidedress nitrate test, or local extension guidance. The point of the MRTN is to anchor your decision on profit and current prices rather than a blanket maximum-yield recommendation.