Eurocode 1 Snow Load Calculator (EN 1991-1-3)

Compute characteristic ground snow load and roof snow load according to EN 1991-1-3, including exposure and thermal coefficients and shape factors for common roof types.

This tool follows the general rules of EN 1991-1-3. National Annex values (e.g. ground snow map, exposure and thermal coefficients) vary by country and must be confirmed from the relevant National Annex.

1. Ground snow load (sk)

Country / region (for guidance only)

This only pre-fills indicative sk values. Always verify with the official National Annex snow map.

Snow zone (indicative)

Characteristic ground snow load sk

kN/m²

Taken from the National Annex snow map for the site altitude.

Site altitude above sea level (optional)

Some National Annexes give formulas sk(z) depending on altitude z. Enter z for documentation; calculator does not modify sk automatically.

Result

Ground snow load sk: 0.75 kN/m²

Use this value as input for roof snow load calculations.

2. Roof snow load (s)

Ground snow load sk

kN/m²

Automatically synced from ground snow load tab but can be overridden.

Roof type

Roof pitch α

degrees

Used to suggest shape coefficient μi. Exact values must follow EN 1991-1-3 and the National Annex.

Shape coefficient μ_i

–

The calculator suggests μ_i, but you can override it to match the code tables (e.g. Table 6.2, 6.3).

Exposure coefficient C_e

–

Typically 0.8–1.2 depending on topography and wind exposure (see National Annex).

Thermal coefficient C_t

–

Usually 1.0 for normal roofs; may be < 1.0 for warm roofs or > 1.0 for cold roofs.

Partial factor γ_Q for snow (optional)

–

If provided, the calculator will also show the design snow load s_d = γ_Q · s.

Results

Shape coefficient μ_i (used): 0.80

Exposure coefficient C_e: 1.00

Thermal coefficient C_t: 1.00

Characteristic roof snow load s: 0.60 kN/m²

Design roof snow load s_d (if γ_Q given): 0.90 kN/m²

Formula: s = μ_i · C_e · C_t · s_k (EN 1991‑1‑3, Eq. (5.1)).

How the Eurocode 1 snow load calculation works

Eurocode 1, Part 1‑3 (EN 1991‑1‑3) defines how to determine snow loads on the ground and on roofs. This calculator implements the core equations and lets you adjust all coefficients to match your National Annex.

1. Ground snow load s_k

The characteristic ground snow load s_k is obtained from the National Annex snow map for your country. Many Annexes provide:

Snow zones (1, 2, 3, …) with base values s_k,0
Altitude-dependent formulas, e.g. s_k(z) = a + b·z for z above a reference altitude

Input: s_k [kN/m²] from the National Annex.

2. Roof snow load s

For most roofs without exceptional accumulation, Eurocode 1 uses the basic expression:

\( s = \mu_i \cdot C_e \cdot C_t \cdot s_k \)

where:
μ_i = shape coefficient for roof area i
C_e = exposure coefficient (wind / topography)
C_t = thermal coefficient (heat loss through roof)
s_k = characteristic ground snow load

3. Shape coefficient μ_i

The shape coefficient accounts for how snow accumulates on the roof. EN 1991‑1‑3 provides tables and figures for different roof types. Typical values (to be confirmed in the code) include:

Flat roofs (α ≤ 30°): μ_i ≈ 0.8
Monopitch roofs: μ_i decreases from about 0.8 at α = 0° to 0 at α ≥ 60°
Duopitch roofs: similar trend, sometimes with different μ₁ and μ₂ for each slope
Multispan / valley roofs: increased μ_i in valleys due to drifting

The calculator suggests μ_i based on roof type and pitch, but you can override it to exactly match the values from the relevant figure/table in EN 1991‑1‑3 and your National Annex.

4. Exposure coefficient C_e

C_e accounts for wind exposure and topography. Sheltered roofs may have C_e > 1.0, while very exposed roofs may have C_e < 1.0. The National Annex defines the categories and values.

5. Thermal coefficient C_t

C_t reflects how much heat escapes through the roof and melts snow:

Cold roofs / well insulated: C_t ≈ 1.0
Warm roofs / high heat loss: C_t < 1.0 (reduced snow load)

6. Design snow load s_d

For ultimate limit state (ULS) design, the characteristic roof snow load s is multiplied by the partial factor γ_Q for snow:

\( s_d = \gamma_Q \cdot s \)

γ_Q is given in EN 1990 / National Annex (often around 1.5 for snow).

Worked example

Assume:

Ground snow load s_k = 0.75 kN/m²
Flat roof (α = 0°), μ_i = 0.8
C_e = 1.0 (normal exposure)
C_t = 1.0 (cold roof)
γ_Q = 1.5

Then:

\( s = 0.8 \cdot 1.0 \cdot 1.0 \cdot 0.75 = 0.60 \,\text{kN/m}^2 \)

\( s_d = 1.5 \cdot 0.60 = 0.90 \,\text{kN/m}^2 \)

Limitations and responsibilities

This calculator is a supporting tool, not a substitute for professional engineering judgement.
Always check the latest version of EN 1991‑1‑3 and the applicable National Annex.
Special cases (drifting, sliding, exceptional snow loads, snow guards, parapets, etc.) are not fully covered here.