How Heavy Is the Snow on Your Roof?
― A Metre of Snow Puts the Weight of 20 Cars on Your House
Snow resting on your palm hardly weighs anything. But a metre of it across a whole roof can come to nearly 30 tonnes. Light snow can crush a house because of two things multiplied together: snow gets heavier as the days go by, and a roof is bigger than you think.
You may have seen it on the news from snowy regions: someone standing on a roof, shovelling snow off.
Snow looks soft and light. So why take the risk of climbing up to clear it?
The truth is that if you leave the snow, an old house may have doors that won't open, or a damaged roof. There is a weight up there that you would never guess from looking.
Only two reasons snow can get heavy enough to push on a house
Fresh snow is mostly air in the gaps. After several days it is squashed by its own weight, and the same volume can weigh two to four times as much.
The roof of an ordinary detached house is often said to cover around 100 square metres. Each square metre may be light, but multiply by the area and you reach tens of tonnes.
Each one is obvious on its own. But multiply them together and the numbers balloon. Let's take them in turn.
Even a metre of snow can weigh over three times as much, depending on its state
A snow crystal has branching arms. In fresh snow, these arms hook together and leave plenty of gaps. That is why new snow weighs only about a tenth as much as the same volume of water.
But snow keeps changing as it lies there. The fine arms of the crystals slowly round off, and the snow piled on top squashes them down. Packed snow like this is said to weigh about 30% as much as water. Melting snow that has soaked up water can reach nearly 50%.
Figure 1 compares the height of water you would get by melting a one-metre-square box full of snow. The boxes look the same, but what is inside weighs very different amounts.
On top of that, when rain falls on snow, it hardly runs off. It soaks in. Just 10 millimetres of rain adds about one tonne across the whole roof. This is why roofs are most at risk in early spring and on warm winter days.
Multiply by the roof's area and you get tens of tonnes
Next, the area. A metre of packed snow on one square metre weighs about 300 kilograms, as Figure 1 shows. That is about four adults, which is still easy to picture.
But a roof, seen from above, covers around 100 square metres. Multiply 300 kilograms by 100 and you get 30 tonnes. If a car weighs 1.5 tonnes, that is 20 cars. Use the slider in Figure 2 to change the snow depth and watch how the weight grows.
Houses are built to carry this weight. In regions with a lot of snow, builders expect heavy falls and make the posts and beams thicker. Even so, a year with more snow than expected, or an old and worn house, can be in danger.
When a house is designed, snow weight has to be allowed for as a number. In ordinary regions, it is said to be calculated as about 2 kilograms per square metre for every centimetre of snow. In heavy-snow regions, a larger value is used. So even in the design world, snow is treated as weighing "20 to 30% of water".
So what should we do?
- Never clear snow aloneAlways work with at least two people, so someone can call for help if you fall. Use a safety rope and a helmet.
- Notice the "signs" your house givesDoors or sliding screens that suddenly stick, or posts that creak, are said to be signals that the snow is too heavy.
- Don't walk under the eavesOn warm or rainy days, roof snow slides off in lumps. Nearly a tonne can come down at once.
Most people injured or killed in snow accidents are hurt during snow removal, by falling from the roof or being buried under snow that slides down. Before you climb up, secure the ladder, and remember that snow slides easily on warm, sunny days. If someone is buried in snow, call 119 (emergency services in Japan) right away and call for people nearby. If you are worried about the snow on an elderly relative's house, you can also ask your local government's snow-removal support desk.
Summary
A single flake is light, but snow packs down and gets heavier over the days, and when you multiply by the area of a roof it comes to tens of tonnes. A roof under a metre of packed snow may be carrying about the weight of 20 cars.
Light snow gets heavy when you multiply by time and area.
On your roof there is an invisible "car park".
Why snow on a slope suddenly starts to slide is explained in "Why Do Avalanches Strike Suddenly on Seemingly Calm Slopes?", and another job of the air between snow grains is covered in "Why Does the Ground Under Snow Stay at 0 °C When It's −20 °C Outside?". We also calculate the weight of clouds in the sky in "How Much Does a Single Cloud Weigh?".
- Fill a cup to the brim with fresh snow, gently, without pressing it down.
- Leave it in a warm room to melt, and see what fraction of the cup the water fills.
- Do the same with snow that is several days old, or snow you have pressed firm by hand, and compare the water heights.
With fresh snow, the water should reach only about a tenth of the height. The older the snow, the more water is left. If you have a kitchen scale, you can compare the weights too.
For those who want more ― Terms, formulas, and links to textbooksWe show which level each part belongs to, from middle-school science to university courses
- Middle schoolCovered in middle-school science
- High schoolCovered in high-school "Basic Physics" and "Physics"
- High school+Advanced high-school material, or textbook sidebars
- UniversityUniversity specialist subjects (snow and ice science, structural engineering), not taught in high school
- ResearchNot yet settled even at university level; researchers are still working on it
Middle schoolTerms: this phenomenon has names
- Density: mass per cubic metre. The difference in snow weight is a difference in density.
- Snow load: the weight of snow on a roof or building. It is the amount allowed for when a house is designed.
- Packed snow: snow squeezed by its own weight until the crystals join into rounded grains. It is denser than fresh snow.
Middle schoolHigh schoolChecking with a formula: the weight of roof snow
Treat the snow on the roof as a single slab of even thickness. Its mass is "density × volume", and the volume is "depth × area".
| In symbols | M ＝ ρ × h × A F ＝ M × g |
| In words | Mass of snow = snow density × snow depth × roof area. Force on the roof = mass × gravitational acceleration |
| Where it comes from | A combination of the definition of density (mass = density × volume) and the weight formula (gravity = mass × gravitational acceleration) |
| M | Mass of roof snow (kilograms) |
| ρ | Snow density (kilograms per cubic metre) |
| h | Snow depth (metres) |
| A | Roof area seen from above (square metres) |
| F, g | Force on the roof (newtons), gravitational acceleration (9.8 metres per second squared) |
| Density of packed snow ρ | Said to be about 300 kilograms per cubic metre |
| Density of fresh snow | Said to be about 100 kilograms per cubic metre |
| Snow depth h | 1 metre |
| Roof area A | 100 square metres (typical for a detached house) |
| Mass of one car | About 1500 kilograms |
| Volume of snow h × A | 1 × 100 ＝ 100 cubic metres |
| Mass of packed snow M | 300 × 100 ＝ 30000 kilograms |
| Mass of fresh snow | 100 × 100 ＝ 10000 kilograms |
| Force on the roof F | 30000 × 9.8 ＝ 294000 newtons |
| In cars | 30000 ÷ 1500 ＝ 20 cars |
| Mass of 10 mm (0.01 m) of rain (water density 1000) | 1000 × 0.01 ＝ 10 kilograms (per square metre) |
| Mass 10 mm of rain adds to the whole roof | 10 × 100 ＝ 1000 kilograms |
A metre of packed snow comes to about 30 tonnes, the weight of 20 cars. Fresh snow of the same depth is about 10 tonnes, so the snow's "age" alone changes the weight by a factor of three. If 10 millimetres of rain then soaks in, the whole roof gains another tonne.
High schoolHigh school+Roof slope, and why snow doesn't slide off
High schoolGravity acting on snow on a sloping roof splits into a component perpendicular to the roof and a component along it. As long as the force along the roof is smaller than the static friction between the snow and the roof, the snow does not slide off and keeps pressing on the roof.
High school+In the calculation above we used the area "seen from above" because snow falls straight down from the sky. Even if the roof is sloped, the amount of snow it catches is set by its horizontally projected area. This is why snow load is expressed per unit of horizontally projected area.
UniversityHow snow packs down (compaction and sintering)
The process by which lying snow packs down over time is called "compaction" in snow and ice science. Under the weight of the snow above, snow shrinks slowly, like a sticky material. How easily it shrinks is described by the "compactive viscosity coefficient", and it is said to shrink more easily when it is warmer and when its density is lower. At the same time, where ice grains touch, molecules move and join the grains with neck-like bridges. This is called "sintering", and it is why packed snow becomes hard. In building design, the snow load is set from the maximum snow depth and the expected density for each region, and a reduction for the roof pitch is also considered.
📖 Derivations and further reading: Snow cover (Wikipedia, in Japanese) ／ Roof snow removal (Wikipedia, in Japanese)
ResearchWhat is still not clear
- Predicting the weight of rain-soaked snow How far rain soaks into snow, and how much it holds, depends greatly on how the snow layers are stacked. Methods for estimating roof snow weight accurately from weather forecasts are said to be still improving.
- Heavy snow in warm winters In milder winters, wet, heavy snow can fall all at once. Some think that with global warming, the amount of snow may fall but heavy, wet snowfalls may actually become more common, and this is being studied.
- The moment roof snow starts to slide When, and in what amount, roof snow falls depends on the roof material and on the thin film of water between the snow and the roof. Research on predicting snowfall from roofs is under way.
In other words, this article too is "an explanation within what is known now". Snow density varies greatly with how it fell and how many days it has lain, so please take the numbers here as a guide.
Links to textbooks (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| Middle school | Grade 7 science, "States of matter (density)" | The weight difference between fresh and packed snow |
| High school | Basic Physics, "Balance of forces and friction" | The weight formula, and why snow stays put on the roof |
| High school+ | Basic Physics, advanced (resolving forces) | The amount of snow is set by the horizontally projected area |
| University | Snow and ice science, structural engineering | Compaction, sintering, how snow load is estimated |
| Research | Snow and ice disaster research | Rain soaking in, heavy wet snowfalls, predicting snow slides |
| ― | Links to daily life | Deciding when to clear snow, avoiding the eaves, signs from the house |
- National Research Institute for Earth Science and Disaster Resilience (防災科学技術研究所) (snow observation and research by its Snow and Ice Disaster Prevention Research Center)
- Snow cover (積雪) (Wikipedia, in Japanese)
- Roof snow removal (雪下ろし) (Wikipedia, in Japanese)
- Building Standard Law Enforcement Order, Article 86 (Snow load) (建築基準法施行令 第86条（積雪荷重）)
- Japanese Society of Snow and Ice (日本雪氷学会), ed., Shinpan Setsuhyō Jiten (新版 雪氷辞典, New Edition Dictionary of Snow and Ice), Kokon Shoin (古今書院)
※This article is a science explainer for general readers. The figures given are rough guides to help you understand how things work. When clearing roof snow, follow the instructions and warnings of your local government, fire department and others, and put safety first without pushing yourself.