Lime Requirement Calculator

Introduction to lime requirement and soil buffering

Soil pH controls which nutrients a crop can actually reach. The pH scale is logarithmic, so each whole unit the soil drops represents a tenfold increase in hydrogen ion activity. Most agronomic crops perform best somewhere between pH 6.0 and 6.8, where phosphorus stays soluble, molybdenum remains available, and exchangeable aluminium is precipitated out of the root zone. Below about pH 5.2 aluminium and manganese toxicity start to prune root systems, nodulation in legumes falters, and applied fertiliser is quietly wasted. A lime requirement calculation is the bridge between a soil test report and a tonnage on a spreader.

The important thing a soil test tells you is that soil acidity has two separate parts. Active acidity is the hydrogen ion concentration in the soil solution, and that is what a routine 1:1 water pH reading measures. Reserve acidity is the much larger pool of hydrogen and aluminium held on clay surfaces, organic matter and hydroxide coatings. Reserve acidity is what gives a soil its buffering capacity, and it is typically ten to a thousand times larger than the active pool. A liming material has to neutralise both. That is why two fields reading exactly pH 5.4 in water can need wildly different tonnages, and why a recommendation built on water pH alone can be badly wrong in either direction.

A buffer pH test solves this. The laboratory adds a solution strongly buffered near pH 8 to the soil, lets it equilibrate, and measures how far the soil drags the buffer down. The depression is proportional to the total acidity that must be neutralised. This calculator implements the two buffer equations published by the University of Delaware Cooperative Extension - the Adams-Evans equation calibrated on twenty Delaware soil types, and the Mehlich equation used by Penn State and Virginia Tech - and keeps a texture-based rule of thumb for fields where no buffer test has been run.

How to use this lime requirement calculator

1. Enter the field area in acres for the field or management zone you are budgeting.
2. Choose a lime requirement method. Use Adams-Evans or Mehlich if your soil test report carries a buffer pH; use the texture estimate only when it does not.
3. Enter the current water pH from the soil test, then the target pH for the crop you intend to grow.
4. Enter the buffer pH exactly as reported. Adams-Evans values normally fall between 7.0 and 8.0; Mehlich values fall between about 4.5 and 6.6. If you picked the texture method, choose the soil texture instead.
5. Set the sampling and incorporation depth. The published equations are anchored to a 6.67 inch furrow slice, and the depth factor scales the tonnage for shallower or deeper mixing.
6. Enter your product's ECCE percentage - the effective calcium carbonate equivalent from the supplier's analysis. Leave it at 100 to see the pure carbonate requirement.
7. Optionally add a delivered price per ton to get a material cost, then calculate. Re-run with a different target pH or a different product to compare.

The Adams-Evans buffer pH lime formula

The Adams-Evans method converts water pH into an acid saturation figure - the fraction of the soil's exchange capacity occupied by acidity - at both the current pH and the target pH, then charges the lime bill for the difference. The buffer pH depression sets the absolute size of the acid pool.

Here LR_AE is pounds of liming material per acre, pH_b is the Adams-Evans buffer pH, ECCE is the effective calcium carbonate equivalent as a decimal, and d is the depth correction factor relative to a 6.67 inch furrow slice (0.90 for a 6 inch sample, 1.18 for an 8 inch sample). Divide by 2000 for tons per acre. The two acid saturation terms come from the same quadratic, evaluated at the water pH and at the target pH:

That square root is real only for pH values at or above about 4.40, which is why the calculator refuses Adams-Evans inputs below that point and tells you to use a direct exchangeable-acidity measurement instead. The Mehlich route is algebraically simpler. It converts the buffer reading straight into an exchangeable acidity AC in milliequivalents per 100 cubic centimetres, then prorates it across the pH gap:

LR_M is tons per acre of a 90 percent ECCE material, so the calculator multiplies by 0.90 to put it back on a pure carbonate basis before applying your own product's ECCE. Where no buffer test exists at all, the texture rule of thumb multiplies the pH gap by a per-acre coefficient:

where F is the texture factor in tons of pure limestone per acre per pH unit. Whichever route produced the pure-carbonate figure, converting it into a tonnage of real product is one more division:

Buffer pH methods and texture factors compared

The three routes are not interchangeable. Buffer methods measure the acid reserve directly; the texture factors merely assume a typical reserve for a broad soil class, and their error on any individual field is easily a factor of two. This comparison table sets out what each route needs and where it is calibrated.

The texture coefficients themselves are the ones long quoted by extension bulletins for a 6.67 inch furrow slice. Denser and more organic soils carry a larger factor because their exchange sites hold more reserve acidity.

Worked example: 40 acres of pH 5.4 sandy loam

A grower samples a 40 acre field to 8 inches ahead of grain corn. The laboratory reports a water pH of 5.40 and an Adams-Evans buffer pH of 7.65. The target pH for corn is 6.00. The depth factor for an 8 inch sample is 1.18, and the delivered product is ordinary agricultural limestone at 67 percent ECCE.

First the two acid saturation values. At the water pH of 5.40, the quadratic gives H₁ = 0.558; at the target pH of 6.00 it gives H₂ = 0.382. In other words the field is 55.8 percent acid saturated and needs to come down to 38.2 percent. Now the main equation: 8000 multiplied by (8.00 − 7.65) is 2800; dividing by H₁ gives 5018; multiplying by the acid saturation difference of 0.176 gives 882 pounds per acre of pure carbonate; dividing by an ECCE of 0.67 gives 1316; and multiplying by the depth factor of 1.18 gives 1553 pounds per acre, or 0.78 tons per acre of agricultural limestone.

Across 40 acres that is 31.1 tons of product, or 20.8 tons on a pure calcium carbonate basis. The published University of Delaware Adams-Evans lookup table for a target pH of 6.0 gives 0.75 tons per acre for exactly this water pH and buffer pH combination, so the equation and the table agree to within the rounding of the table. At a delivered price of 42 dollars per ton the material bill is about 1305 dollars, before spreading.

Now change one thing. Suppose the same field had returned a buffer pH of 7.30 instead of 7.65 - still an unremarkable reading. The (8.00 − buffer pH) term more than doubles to 0.70, and the recommendation doubles with it to 1.55 tons per acre, or 62 tons for the field. Nothing about the water pH changed. That single number is the difference between a 1300 dollar and a 2600 dollar lime bill, and it is the reason a buffer test is worth its small laboratory fee.

Liming materials, ECCE and fineness

The tonnage the equation returns is a quantity of neutralising power, not a quantity of rock. Two things separate the two. The first is chemical purity, expressed as calcium carbonate equivalent (CCE): pure calcite is 100 percent by definition, dolomite is about 109 percent because magnesium carbonate is lighter per unit of carbonate, burned lime is near 179 percent and hydrated lime near 136 percent. The second is fineness. Coarse particles that will not pass a 60 mesh screen contribute almost nothing within the first cropping season, so state regulations credit each size fraction differently. Multiplying CCE by the fineness credit gives the effective calcium carbonate equivalent, ECCE, and that is the number to type into the calculator.

Ordinary quarry aglime typically lands between 55 and 80 percent ECCE, which is why the Delaware lookup tables assume 67 percent. Pelletized lime is finely ground stone bound into granules, so its ECCE is high, but the pellet has to disperse before any of it reacts. Dolomitic stone supplies magnesium alongside calcium, valuable where a soil test shows magnesium below about 100 pounds per acre and pointless where it does not; it also dissolves more slowly than calcite. Hydrated and burned lime react fastest and are the easiest materials with which to overshoot a target pH.

Reaction speed matters as much as tonnage. Even a well-ground material takes several months to move the field pH, because carbonate has to dissolve in soil water and then diffuse to the acidity held on soil surfaces. Incorporation with tillage puts the particles in contact with far more soil than a surface pass does, and in a no-till system the pH change tends to stay in the top two inches for years. Applying lime the season before it is needed, rather than in the spring the crop goes in, is usually the difference between a recommendation that works and one that appears to have failed.

Limitations and assumptions of this lime estimate

This tool makes several assumptions that will not hold on every field, and they should be understood before a tonnage is ordered.

• The buffer equations are regional. Adams-Evans was calibrated on twenty Delaware soil types with kaolinitic clay and low cation exchange capacity. Applied to a high-CEC Midwestern mollisol it will under-recommend. Use the buffer your own laboratory ran, and prefer the lookup tables your laboratory publishes when they exist.
• A uniform plough layer is assumed. The depth factor scales the soil mass linearly, which assumes the lime is mixed evenly through that depth and that bulk density is close to the standard 2 million pounds per acre furrow slice. Surface application without incorporation violates both assumptions.
• No lime credit is applied. Material spread within the previous eighteen months has not finished reacting. Extension guidance is to credit 75 percent of a rate applied within 6 months, 50 percent within 12 months and 25 percent within 18 months, and to subtract that credit from the figure this calculator gives.
• Spatial variability is ignored. A composite sample averages a field that may contain a full pH unit of range. Grid or zone sampling with variable-rate spreading routinely beats a single whole-field rate, which is exactly what the game below is about.
• Over-liming is not automatically prevented. Pushing a low-buffer sandy soil above about pH 7 ties up iron, manganese, zinc and boron and can trigger visible interveinal chlorosis. The calculator flags high targets but cannot know your soil's micronutrient status.
• Cost output is material only. Spreading, hauling beyond the quoted delivery and any custom application fee are not included.
• Limitations of the texture route in particular. The texture factors carry no laboratory calibration at all. Treat them as an order-of-magnitude budgeting tool and confirm with a buffer test before committing to a purchase.

Soil pH also drifts back. Ammonium-based nitrogen fertiliser acidifies as it nitrifies - roughly 1.8 pounds of pure calcium carbonate are consumed per pound of ammonium nitrogen fully nitrified - and legume nitrogen fixation and rainfall leaching add to the drift. Re-testing every two to three years and re-running the calculation is a normal part of the cycle rather than a sign that the first application failed.

Frequently asked questions about agricultural lime

Sources and further reading

Sources: the Adams-Evans and Mehlich lime requirement equations, the 6.67 inch furrow-slice depth factors, the 67 percent ECCE assumption for agricultural-grade limestone and the lime credit schedule used in the limitations section are taken from the University of Delaware Cooperative Extension publications listed below. Texture coefficients are extension rules of thumb, not laboratory calibrations.

• Shober, Gartley & Sims, A Comparison of Methods to Determine Lime Requirement, University of Delaware Cooperative Extension - the source of the Adams-Evans, Mehlich and SMP/Sikora equations used here.
• Shober, Gartley & Sims, Calculating the Lime Recommendation Using the Adams-Evans Buffer Method - the lookup tables and worked example this calculator is checked against.
• University of Georgia Agricultural and Environmental Services Laboratories, Buffered pH, Lime Requirement, Exchangeable Hydrogen - the Adams-Evans buffer procedure and the exchangeable hydrogen relationship.
• Sawyer, Soil pH and Liming, Iowa State University - calcium carbonate equivalent, fineness and the ECCE concept.
• Michigan State University Extension, Lime for Michigan Soils (E-471) - liming material comparison and application timing.