Economic N-Rate & The Profit-Optimal MRTN

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.