Approximately 0.024 lbs per cubic inch. A common pressure-treated 2x6 that is 12 feet long (2x6x144 inches) will weigh 38 to 40 pounds.
Example: a 4" x 12" x 10' pressure treated beam
(note that 10' = 120 inches)
4 x 12 x 120 = 5760 * 0.024 = approx 138 lbs for the beam
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Per cent moisture content has a dramatic impact on wood weight and especially so in the case of PT lumber, which is artificially infused with water during manufacturing and typically takes some weeks and months to dry to equilibrium. I came across the above in trying to research how much moisture my current PT decking has, and the above formula gives 10.0 lbs for the 1" x 5.5" x 76" boards I have (I've got about a dozen). However, their actual weights (measured just this morning) vary between 8.6 lbs and 13.2 lbs (i.e. an 86% to 132% variation from the above formula). Is it even possible (reasonable?) to specify weight for PT lumber without also identifying its per cent moisture content?
So the above would be an average weight.
A 6x6x8 cedar post typically weighs around 80-100 pounds, depending on the density of the wood and any moisture content. The weight can vary slightly based on the specific characteristics of the wood and how it was treated or processed.
Round bales you are asking about are probably the large 5'wide x6' bales that require a forklift or other special means to handle. They typically weigh 1200 pounds if baled from fescue, brogham or other very "stemmy" grass. If the bale is a legume hay like alfalfa or a broad leaf like clover it will be closer to 1600-2,200 lbs. These round bales are often referred to as one-ton (2000 lbs). The baling pressure can be adjusted, and the baling speed can affect the result. Higher compression results in more material in the same space. Faster forward speed results in faster bale formation, less loss of fines or leaves resulting in a slightly lighter bale but more nutritionally viable hay. Because the round shape is somewhat more weather resistant than rectangular, there are some small round balers on the market. These small rounds are usually 20 inches around and 30-40 inches long and weigh around 75-130 pounds very similar to their small square cousins. Large square bales 6x6x8 are usually the heaviest of all at 2,200 to 3,000 pounds. The advantage of square bales is obviously their stackability. The advantage of round bales is that they have a natural water-shedding ability. The advantage of small bales is the ability to be handled by a single person. A mechanized farm benefits from the reduced "manpower" of being able to move large quantities of hay in the larger format.