How to Calculate Snow Load on a Roof

Finds the weight of snow on a roof as the unit load × the depth of snow × a shape factor. Building codes set the unit load at 20 N/m² per centimetre of snow in ordinary regions and 30 N/m² in heavy-snow regions. A steeper roof sheds snow, which the shape factor accounts for.

This finds the weight of snow sitting on a roof, following the approach taken by building codes.

P = P_0 \times d \times \mu_b

$P_0$ is the unit load per centimetre of snow, $d$ the depth and $\mu_b$ the roof shape factor. Codes set the unit load at 20 N/m² in ordinary regions and at least 30 N/m² in heavy-snow regions.

The shape factor

A steeper roof sheds snow, so the load is reduced accordingly.

\mu_b = \sqrt{\cos(1.5\beta)}

$\beta$ is the pitch of the roof. Above 60 degrees snow does not settle and the factor is taken as 0. A flat roof gives 1, with no reduction at all.

Example

Take 30 cm of snow on a roof pitched 4 in 10, which is 21.8 degrees. The shape factor is 0.917, so the load is $20 \times 30 \times 0.917 = 550$ N/m². Over a footprint of 60 m² that totals 33.0 kN, a mass of 3.37 tonnes, or about two cars' worth of snow sitting on the roof.

Snow is heavier than it looks

Fresh snow runs around 100 kg per cubic metre, and settled snow passes 300. A metre of snow is therefore over 100 kg on every square metre, across the whole roof. This is why clearing it matters.

Notes

The design depth of snow is set locally by the authority for each area. Use the figure specified for the region when designing.