How Much Does Snow Weigh? The Math of Snow Load

Snow looks light because it is mostly air. The weight comes from the small share that is ice and water, and that share changes from storm to storm, which is why the answers you find online disagree. The math needs three numbers: depth, water content, and the weight of water. This page builds the formula, tests it on a roof and a driveway, and shows where it stops being reliable.

How heavy is 1 ft of snow?

Per square foot of ground or flat roof, a foot of new snow weighs about 3 to 12 pounds, and about 5 pounds at the average water content²¹. The spread comes from the water content. Newly fallen snow typically holds 5 to 20 percent water, with about 8 percent as the average across North America¹. Snow at about 7 percent or less counts as light and snow at 11 percent or more counts as heavy¹.

Worked example (our arithmetic): load in pounds per square foot, from depth × water fraction × 5.2²¹

Every cell is depth × water fraction × 5.2, rounded to one decimal place². For the 12-inch row at 8 percent, 12 × 0.08 × 5.2 = 4.99, which is the 5.0 in the table²¹. The water fractions are the typical 5 to 20 percent of new snow, the 8 percent average and the 11 percent heavy threshold¹; the 5.2 is explained next².

Where the formula comes from

The National Weather Service starts from the weight of water: 1000 kilograms per cubic meter, which is 62.4 pounds per cubic foot². Put that water in a column one square foot wide and one foot deep and it weighs 62.4 pounds, so each inch of depth weighs 5.2 pounds². Dividing 62.4 by 12 gives the same 5.2 (our arithmetic)².

The second ingredient is the water equivalent, the depth of water that would cover the ground if the snow were liquid⁴. The essential measurement for a snow load estimate is that water equivalent². Multiply the water equivalent in inches by 5.2 and you have the load in pounds per square foot². The NWS example: 2.0 inches of water equivalent gives 10.4 pounds per square foot against a flat roof².

When you only know the depth of snow, you convert it to water equivalent with the water fraction. That is the step in the table: 12 inches of snow at 8 percent water holds 12 × 0.08 = 0.96 inches of water (our arithmetic)¹. Then 0.96 × 5.2 = 4.99 pounds per square foot (our arithmetic)².

Why there is no single number for snow

Snow density has a wide range. Newly fallen snow is generally between 30 and 300 kilograms per cubic meter¹. The water-content shortcut divides the density by 10 and adds a percent sign, so the range is 3 to 30 percent (our arithmetic)¹. In weight per cubic foot, 3 percent water is 62.4 × 0.03 = 1.9 pounds and 30 percent is 62.4 × 0.30 = 18.7 pounds (our arithmetic)²¹. A sample of newly compacted snow on a race course was probably around 350 kilograms per cubic meter¹, which is 35 percent water (our arithmetic).

Several things push the density up or down:

• Temperature. The warmer it is, the denser new snow tends to be¹. The relationship holds down to about -15 degrees Celsius, and colder than that the density hardly changes¹.
• Wind. Faster winds go with denser new snow¹. Wind can also break flakes apart, which lowers the accumulation per unit of water³.
• The storm itself. Ratios can change dramatically within a single snow event³. The warmer the layer of air near the freezing point, the lower the ratio³.
• Cold air. Deep cold, in general, promotes higher snow ratios³.

The 10:1 rule and its limit

The old rule of thumb said 10 inches of snow holds 1 inch of water, a 10:1 ratio, which is the same as 10 percent water³. Recent studies suggest 12:1 is more representative on average for the Upper Midwest, and the NWS adds that a rule of thumb is usually off the mark³. NOAA’s constant 10:1 forecast product multiplies the model’s water amount by 10 and so overestimates snow in marginally warm air and underestimates it in very cold air⁵.

A ratio and a water fraction are two views of the same quantity (our arithmetic). A 10:1 ratio is 1 ÷ 10 = 0.10, or 10 percent water, and a 12:1 ratio is 1 ÷ 12 = 0.083, or about 8.3 percent water, close to the 8 percent North American average³¹.

Worked examples: roof, pitched roof and driveway

Worked example (our arithmetic): a flat roof of 1,500 square feet after 20 inches of snow at 11 percent water²¹

The same snow on a pitched roof presses less directly on the surface. The NWS method multiplies the flat load by the cosine of the roof pitch². In the agency’s example, a roof 35 degrees up from the horizon under a load of 10.4 pounds per square foot gives 10.4 × cos 35 = 8.5 pounds per square foot against the roof². Applied to our 11.44: 11.44 × 0.819 = 9.37 pounds per square foot (our arithmetic)². The weight along the slope still matters, since snow stays on a pitched roof only while friction holds it².

Worked example (our arithmetic): a driveway 12 feet wide and 40 feet long after 10 inches of snow at the 8 percent average²¹

A light dusting of snow is easy, and a heavy foot is not. The same driveway under 10 inches of 20 percent snow is 10 × 0.20 × 5.2 × 480 = 4,992 pounds (our arithmetic)²¹.

Measure the snow you have

Formulas give a range; a measurement gives your number. Take a core of the snow all the way to the ground with a long cylinder, melt it indoors and read the depth of water; that is the water equivalent². The NWS asks its observers to measure water equivalent, snowfall and snow depth, which it calls some of the most difficult but important weather elements to measure accurately⁶. Choose a spot where blowing and drifting are minimized, and leave the largest drifts out of the measurement⁶.

Roofs vary more than open ground. Measure the snow on your own roof if possible, because depth can vary a lot over a small area². The weight tables are a rough estimate to be used with caution, and snow that ages and settles does not stay uniform². Scientists weigh a known volume of snow to find its density, which is the same idea at a smaller scale⁷.

Snow load is a straight line

Plot load against depth and you get a straight line through zero, as in the chart above². The slope of the line is the load added by each extra inch: 0.416 pounds per square foot for each inch of 8 percent snow (0.08 × 5.2, our arithmetic)²¹. In calculus language that slope is the derivative of the load with respect to depth, and it is constant because the density is assumed constant². Real snowpacks are not that tidy: a snowpack gets denser over a season⁷, so the slope bends upward as the pile ages. For the idea of a slope as a rate of change, see what a derivative is.

For other places where one simple physical rule sets a size, see why seasons happen and how fast coffee cools, or browse the World section. The sources behind the numbers are the NWS Juneau snow load article, the NWS La Crosse snow ratio page and the UBC snow density notes.