How to Calculate Tonnage in a Grain Bin

The tonnage of a grain bin depends on what is in it.

A familiar sight in farming areas, grain bins are designed to store, and sometimes to dry, harvested cereal crops. The tonnage of a grain bin is influenced by the density of the stored grain and by the height and width of the bin. Large grain bins may exceed 50 feet in diameter and hold hundreds of tons of grain.

The tonnage is approximate because the water content of grain may vary according to harvesting and weather conditions.

Things You'll Need

• Calculator
• Tape measure

Instructions

1. Measure the internal diameter of the grain bin. Measure the bin at ground level if it is on legs and measure at the top only if this is not possible. The diameter is a line from one side of the bin to the other, passing through the central point. The manufacturers' documentation may give details of bin dimensions.

2. Find the radius of the bin by dividing the diameter by two. For example, if the diameter is 50 feet, the radius is 25 feet (50/2 = 25).

3. Square the radius and then multiply it by pi, the mathematical constant approximated as 3.1415. Using the radius from the previous step, the calculation is 25 x 25 x 3.1415. The result, 1963.4375 square feet, is the area of the bin's base.

4. Calculate the volume of the bin by multiplying the base area by the depth of the grain within it. For example, given a depth of 20 feet and a base area of 1963.4375 square feet, the volume is 39,268.75 cubic feet.

5. Convert volume to tonnage by multiplying the bin volume by the weight of a cubic foot of the crop held in the bin. For example, wheat weights approximately 48.18 lb. per cubic foot. Using the volume determined in the previous step, the total weight of wheat in the bin would be 1,891,968.375 lb. -- 39,268.75 x 48.18 lb.

6. Convert pounds into tons by dividing the result from Step 6 by 2,000, the number of pounds in a ton. The result is the actual tonnage of the grain bin. For example, a bin holding 1,891,968.375 lb. contains 946 tons (1,891,968.375 / 2,000 = 945.98).

Tips & Warnings

• Agricultural merchants can offer advice about tonnage, and some manufacturers, in their marketing literature, state approximate tonnages for different crops.

• Never stand in a filled grain bin to take measurements. If you fall into the grain, you may sink and be suffocated.

References

• University of Kentucky, College of Agriculture; Biosystems and Agricultural Engineering; Storage
• "Webster's New World College Dictionary 4th Edition"; Michael Agnes, ed.; 2007
• Western Kentucky University, Department of Mathematics; The Area of a Circle; Tom Richmond Ph.D
• University of Missouri: Diameter Measurement
• Math.com: Volume Formulas
• University of Missouri Extension, Department of Agronomy: Tables for Weights and Measurement: Crops

Resources

• Penn State Department of Agricultural and Biological Engineering; Bulk Storage; John T. Tyson and