The yard is a unit of length. The metric ton, or tonne, is a unit of weight. These units have a relationship to one another through the physical property of density: mass divided by volume equals density. To perform a calculation that uses a physical constant -- the density of the substance an object is composed of -- to convert yards, a unit of volume, to the substance's weight in metric tons, you must first determine the object's volume. In regular, three-dimensional solids, volume is the product of the object's length, width and height.
Multiply the object's length, in yards, by its width, in yards. If it measures 2-by-1.5 yards, then 2 x 1.5 = 3 square yards.
Multiply your product by the solid's height, measured in yards. If it stands 1.25 yards tall, then 3 x 1.25 = 3.75 cubic yards.
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Multiply your result by the material's density, measured in pounds per cubic yard. If, for instance, you are doing these calculations for an object made of concrete, which weighs 4,000 lbs. per cubic yard, then 3.75 x 4,000 = 15,000 lbs.
Divide by 2,204.6 to convert your answer to metric tons. Each metric ton equals 2,204.6 lbs. 15,000 / 2,204.6 = 6.8 metric tons.