A yard of dirt refers to a cubic yard, which is 3 feet by 3 feet by 3 feet. This can be calculated as 27 cubic feet of dirt, which refers to volume. An English ton is a unit of mass that is defined as 2,000 pounds. The conversion from volume to mass requires the use of bulk density, which is mass per unit volume. The bulk density of a material is the average packed density of a solid material. A liquid density is much more accurate in that a liquid always takes the exact volumetric form of its container. Solid materials tend to have a certain amount of void volume.
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Determine the bulk density of topsoil (or another type of dirt) by using a reference such as the one listed in this article. Topsoil has a bulk density of 83 pounds per cubic foot.

Convert yards of dirt to cubic feet by multiplying the number of yards by 27 (one yard equals 27 cubic feet). For instance, four yards of dirt is equal to 108 cubic feet.

Convert cubic feet to pounds by multiplying by the bulk density of topsoil, and then converting from cubic feet to tons. This is 83 pounds per cubic foot by 108 cubic feet, for a mass of 8,964 pounds. There are 2,000 pounds per ton, so the conversion from yards to tons is 8,964 divided by 2,000, or 4.5 tons.
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