How much does a square foot of snow weigh?

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According to a news story on NBC Today Show, which aired Feb 13, 2015, one cubic square of dry snow weighs about 7 pounds. One cubic foot of "wet" snow weighs about 20 pounds. Ice adds more to the weight of both wet or dry snow. The extreme heaviness of snow, therefore, can cause multiple problems, for example, it can make roofs collapse or contribute to heart attacks from over-exertion when people are shoveling snow.
A square foot of snow does not have a weight: the depth of the snow is needed to give the weight because weight relates to the volume of snow. Even if you know the depth of the snow, say a foot, giving a cubic foot of snow, there is a wide range of possible weights because snow can vary in density depending on whether it is lightly or densely packed.

The range of density of snow compared to the density of water can vary from 100:1 (for snow that is 100 times less dense or heavy than the equivalent volume of water) to 3:1.
A more common density might be around 12:1.

Water has a mass of 1kg/L so for a cubic metre (1000L) of snow, the mass could be anything in the range of 10kg to 333kg.
Keeping that in mind, a foot of snow would be about 6.75lb to 223.82lb.
The weight of snow can not be answered based on an area of a square foot of snow: the volume is required. It also depends on the kind of snow it is. Example- packing snow will have a different weight (because of its density) than other kinds of snow.
A square foot is a measure of area, not volume. So the answer depends on two things. One is the depth, which will give us the volume, and the other is the density of the snow, which tells us how much weight there is per volume.
Unpacked, fresh fallen snow can have a density roughly of only 5% of water. That will not have much depth, however. As snow packs it can get to 30% of the density of water, so a square foot of snow one foot deep (a cubic foot) might weigh roughly twenty pounds. With more packing and passage of time this might go up to thirty pounds per cubic foot. Finally, the snow can be compressed to become ice (with a lot of air inclusions), and this might be as more than fifty pounds per cubic foot.
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