About Wind Load Calculation
This calculator evaluates wind load by zones for a rectangular building, a gable roof, and a free-standing wall or fence. The method follows EN 1991-1-4 (wind actions) and applies the general safety factor approach from EN 1990.
Results are provided as zone coefficients and final design pressure by zone. Pressure is shown in kN/m² and can be positive or negative depending on the action direction on the building envelope element.
Guidelines and recommendations
Basic wind velocity is entered as v_b,0 in m/s. This is the regional basic value from the National Annex to EN 1991-1-4. It is used as the starting point for pressure evaluation with terrain and height effects.
Reference pressure is derived from the kinetic energy of the air flow. The calculator uses air density ρ = 1.25 kg/m³ and q0 = 0.5 · ρ · v_b,0² / 1000. Dividing by 1000 converts the value to kN/m².
Terrain and height effects are included through the exposure factor k(z) as a function of terrain category and reference height z. Heights are entered in mm and converted to meters by z = z_mm / 1000. For numerical stability, the height is limited to z ≥ z_min and z ≤ 200 m, where z_min depends on terrain category.
Exposure factor is computed using a logarithmic roughness profile. The sequence is ln = ln(z / z0), c_r = k_r · ln, I_v = 1 / ln, and k(z) = (1 + 7·I_v) · c_r², where z0 and k_r are chosen by terrain category.
Peak pressure at height for each zone is calculated as q_p(z) = q0 · k(z). The zone aerodynamic coefficient and the partial safety factor are then applied.
Aerodynamic coefficient in the table is shown as the final zone coefficient c. For the building and the roof it may include internal pressure. When internal pressure is enabled, the calculator uses the most unfavorable case by magnitude from c_pi = +0.2 and c_pi = -0.3, and applies c = c_pe - c_pi.
Design pressure by zone is computed as w = q_p(z) · c · γ, where γ is the partial factor for actions. The calculator uses γ = 1.5 as a typical value for the leading variable action in ULS according to EN 1990. The National Annex defines the final values and combination rules.
Building zoning depends on the ratio of height h to the depth of the windward face. For the selected wind direction, the depth is taken from the plan dimensions and reference heights z_e are assigned for several levels. These levels define k(z) and thus pressures for different zones.
Roof coefficients are determined by the roof pitch angle. The angle is computed geometrically as α = arctan((h - h1) / (d/2)) in degrees. Zone coefficients are taken from tabulated values versus angle and interpolated between adjacent points. The angle is limited to the tabulated range used by the interpolation.
Free-standing wall or fence is treated as a separate structure without an enclosed internal volume. Internal pressure c_pi is therefore not applied in this mode, and zone coefficients are used directly in w = q_p(z) · c · γ.
- Input units: geometry in mm,
v_b,0in m/s. - Output units: pressure in
kN/m². - The sign indicates action direction relative to the surface. Negative values commonly represent suction.
- Standards: EN 1991-1-4 (wind), EN 1990 (principles, safety factors, combinations).
FAQs
Why can the coefficients and pressures be negative
The sign indicates the direction of action on the surface. Negative values commonly correspond to suction, when the flow creates reduced pressure and pulls the element outward. For cladding and fasteners, the sign can be as important as the magnitude.
What changes when switching wind direction A and B
The windward face changes, so the depth, geometric ratios, and zoning change as well. For the roof, switching direction selects the corresponding set of tabulated coefficients in EN 1991-1-4 for wind along the ridge or across the ridge.
Why does terrain category affect the result so much
Terrain category controls roughness and the vertical profile of wind speed. It enters the calculation through k(z), which scales pressure at different heights. Open terrain and dense urban terrain can yield noticeably different pressures for the same v_b,0.
What does internal pressure cpi change
Internal pressure accounts for the pressure difference between outside and inside of a building envelope. EN considers both signs of c_pi because the internal pressure direction depends on openings and windward conditions. The calculator selects the most unfavorable case by magnitude using standard EN values.
Why is the partial factor γ used and can it be changed
The factor γ converts characteristic wind action into a design value for limit state checks. For many practical ULS checks, γ = 1.5 is used for the leading variable action under EN 1990, while the National Annex defines the final rules. If a characteristic value is needed, the same formula is used without multiplying by γ.