13.3 Area Math and Mixing Concentrates
Key Takeaways
- Acres = square feet ÷ 43,560; a 1,320 ft by 660 ft Terrell County peanut block is exactly 20 acres.
- Rectangle area is length × width; circle area is πr² using 3.14 unless the problem states another value.
- Amount of product = (tank gallons × labeled rate per acre) ÷ GPA, or acres-per-tank × rate per acre.
- Measure emulsifiable concentrates and other true liquids by volume; measure wettable powders and most dry flowables by weight, not by a liquid cup.
- If calibration GPA is wrong, mixing arithmetic can be perfect and the field rate still illegal—the label rate remains the law.
13.3 Area Math and Mixing Concentrates
Appendix C of the National Core Manual and Georgia General Standard 6 meet in this section: you cannot mix a legal tank until you know acres per load, and you cannot know acres per load until you know GPA from section 13.2 and field area. Rule 40-21-5 asks contractors to record acreage or size and rate. Wrong area math becomes a wrong record and a wrong dose.
Acres from square feet
Acres = square feet ÷ 43,560
Memorize 43,560. It is the number of square feet in one acre. Exam items bury it in a peanut field, a circular ornamental bed, or a rectangular turf lawn.
| Shape | Square-foot formula | Then convert |
|---|---|---|
| Rectangle or square | length × width | ÷ 43,560 |
| Circle | 3.14 × radius × radius | ÷ 43,560 |
| Triangle | (base × height) ÷ 2 | ÷ 43,560 |
Rectangles
Use the same units for both sides. If a question gives yards, convert: 3 feet = 1 yard. If it gives miles: 5,280 feet = 1 mile; a one-mile square is 640 acres (5,280 × 5,280 ÷ 43,560 = 640).
Worked rectangle — Terrell County peanuts
A rectangular block is 1,320 feet long (1/4 mile) and 660 feet wide (1/8 mile).
Area = 1,320 × 660 = 871,200 sq ft
Acres = 871,200 ÷ 43,560 = 20.0 acres
If your boom is calibrated at 16.5 GPA (the Dooly County catch test from 13.2), mixture needed for the whole block = 20 × 16.5 = 330 gallons. A 300-gallon tank cannot cover it in one fill at that GPA; plan two loads (for example 10 acres × 16.5 = 165 gallons of mixture per 10-acre pass, plus rinsate planning from Chapter 12).
Worked rectangle — cotton on a different shape, same acres
A Crisp County cotton cut is 2,640 ft by 330 ft: 2,640 × 330 = 871,200 sq ft = 20.0 acres again. Mixing math does not care about the shape once square footage is right. It does care if you measure the wrong field—fence-row-to-fence-row versus planted acres—so walk the treated area, not the tax map, when the two differ.
Circles
Area = πr². Use π = 3.14 unless the problem states otherwise. Radius is half the diameter.
Worked circle — ornamental bed, Category 24 site
A circular landscape bed is 40 feet across (diameter 40, r = 20 ft).
Area = 3.14 × 20 × 20 = 3.14 × 400 = 1,256 sq ft
Acres = 1,256 ÷ 43,560 = 0.0288 acres (about 0.029 acre)
A backpack delivering 1 gallon per 1,000 sq ft needs 1.256 gallons of mixture for that bed. That is a spot/bed rate, not boom GPA, but the area law is the same. Treating the bed as a 40-by-40 square (1,600 sq ft) would mix about 27 percent extra spray.
Worked circle — mix-load pad buffer
A circular pad with a 30-foot radius: 3.14 × 30² = 3.14 × 900 = 2,826 sq ft = 2,826 ÷ 43,560 = 0.065 acre. If you ever treat a circular livestock loafing area (Category 22) or a circular ornamental, do not treat it as a square of side equal to the diameter.
Mixing concentrates: the tank formula
Once GPA is measured and acres are known:
Amount of product = (tank gallons × labeled rate per acre) ÷ GPA
Equivalent two-step:
- Acres per tank = tank gallons ÷ GPA
- Product = acres per tank × rate per acre
Rate units stay with the product: pints per acre stay pints; pounds per acre stay pounds. Do not convert EC pints into WP pounds with 128. The 128 fl oz = 1 gal conversion is for liquid volume (water, EC, flowable liquids), not for the mass of a dry powder.
Leave air space in the tank for agitation. Adding 300 gallons of water plus 5 gallons of EC into a 300-gallon tank overflows. Add most of the water first, start agitation, add product as the label’s mixing order requires, then top to the intended finished gallons.
Worked EC mix — cotton insecticide, 300-gallon tank
Calibrated GPA = 15. Label rate 2 pints of EC per acre. Tank 300 gallons.
Acres per fill = 300 ÷ 15 = 20 acres
Product = 20 × 2 = 40 pints
40 pints ÷ 8 pints per gallon = 5 gallons of EC in 300 gallons of finished spray.
Formula check: (300 × 2) ÷ 15 = 600 ÷ 15 = 40 pints. Same answer, one step.
If the operator still thought the boom was 15 GPA but a catch test later showed 12 GPA at the new speed, acres per 300-gallon fill would really be 300 ÷ 12 = 25 acres, and 40 pints would apply 40 ÷ 25 = 1.6 pints/acre, below the labeled 2 pints. That is a calibration error, not a mixing-arithmetic error, and it is still a label violation. Conversely, if actual GPA is 20 while you mixed for 15, 300 gallons cover only 15 acres and 40 pints become 2.67 pints/acre—an over-application.
128-ounce check on a small EC rate. Label 8 fl oz EC per acre, 100-gallon tank, 20 GPA: acres = 100 ÷ 20 = 5; product = 5 × 8 = 40 fl oz = 40 ÷ 128 = 0.31 gallon. You can work entirely in ounces because 128 oz = 1 gal.
Worked WP mix — peanut fungicide, weigh don’t scoop
Label: 2 pounds WP per acre. Tank 200 gallons. Calibrated 20 GPA.
Acres per fill = 200 ÷ 20 = 10 acres
WP to add = 10 × 2 = 20 pounds
| Formulation | How to measure | Why |
|---|---|---|
| EC, solutions, many liquid flowables | Volume (fl oz, pints, gallons) | Density is consistent enough for a liquid measure; 128 fl oz = 1 gal |
| WP, many DF/WDG dry products | Weight (pounds or ounces on a scale) | Bulk density changes with settling, humidity, and fluff; a pint cup of powder is not a pint of EC |
Put WP into a slurry in a little water before the tank is full, with agitation on, after the tank is at least half filled with water in most label orders. EC usually goes in with agitation after water—and after WPs if you tank-mix (compatibility order is Chapter 7; here the exam point is how you measure).
Percent solutions (backpacks and ornamentals)
A 1 percent spray by volume is 1 gallon of product per 100 gallons of mixture, or 1.28 fl oz of product per gallon of mixture (128 × 0.01 = 1.28). For 50 gallons of a 0.5 percent mix: product = 50 × 0.005 = 0.25 gallon = 32 fl oz. A “2 tablespoons per gallon” homeowner line is not how commercial labels write professional rates—use the labeled professional rate and the tank formula above.
Label rate is law; calibration error is the trap
Georgia commercial applicators live under the label and under Rule 40-21-3 competency, not under “what the tank looked like last year.” If the label says 1.5 pints/acre, delivering 2.0 pints/acre because nozzles were worn (output up) or because you used the wrong GPA in the mixing formula is not a rounding issue—it is misuse.
Exam traps to expect:
- Using row spacing as nozzle spacing when nozzles are 20 inches apart on a 36-inch cotton row
- Forgetting 128 oz = 1 gal and treating catch ounces as gallons
- Mixing WP by volume from a liquid cup
- Computing acres with 43,560 omitted (reporting 871,200 “acres”)
- Changing speed for cotton after a peanut calibration and not recalculating product
- Treating band acres as broadcast acres so the strip is double-dosed
Finish every word problem with three checks: (1) catch-test GPA from 13.2, (2) acres from 43,560, (3) product = (tank × rate) ÷ GPA in matching units. That chain is National Core Appendix C, and it is how you keep a Georgia Category 21 or 24 application inside the label.
A Terrell County peanut field measures 1,320 feet by 660 feet. How many acres is the field?
A 300-gallon tank will be sprayed at a calibrated 15 GPA. The cotton insecticide label rate is 2 pints of EC per acre. How much EC product should be added to a full 300-gallon batch?
A peanut fungicide wettable powder is labeled at 2 pounds per acre. You are mixing a 200-gallon tank at 20 GPA. How must you measure the 20 pounds of WP the formula requires?