To determine soil needs for a square or oblong bed, first measure the length and the width of the bed-to-be and multiply these two measurements to obtain the square footage of the area to be gardened. Now multiply the square footage by the depth of the soil to be placed. The result is the number of cubic feet of soil needed to create the bed. Divide that number by 27, the number of cubic feet in a cubic yard, and the quotient will show in cubic yards the amount of soil needed to cover the area.
To determine the amount of soil needed for an L-shaped bed, simply divide the bed into two rectangular beds, calculate the cubic yards for each bed using the above formula, and add the two subtotals to find the total number of cubic yards needed.
To find the quantity of soil needed for a free-form or circular planting bed, take three pairs of measurements from the bed's varying length and width. Multiply eqach of the the three lengths and widths separately to obtain three calculations of square feet. Add up those three square footages and multiply by the depth of the bed, to obtain the number of cubic feet. Divide that sum by 83. The figure you obtain will represent -- roughly -- the cubic yards of soil needed for the bed.