The theory behind this wind load calculator: how the basic wind velocity, terrain roughness and orography combine into the peak velocity pressure q_p(z), how external and internal pressure coefficients give surface pressures, and how those are summed into the wind force on a building to Eurocode 1 (EN 1991-1-4).
Wind action on a structure is calculated to Eurocode 1, EN 1991-1-4by building up from a site wind speed to the pressure on each surface and finally the total force. The chain is: basic wind velocity → mean velocity at height → turbulence → peak velocity pressureqp(z)→ surface pressures via coefficients → forces. This calculator performs each step and reports the zone pressures and forces.
Basic wind velocity
The starting point is the fundamental basic wind velocityvb,0 - a 10-minute mean at 10 m above flat open country (terrain II), with a 0.02 annual probability of exceedance (50-year return). It is modified for wind direction and season:
vb=cdircseasonvb,0
The directional factor cdir and seasonal factor cseason are normally taken as 1.0 unless the National Annex permits a reduction.
Mean velocity, terrain and roughness
The mean wind velocity at height z grows from the ground up through the atmospheric boundary layer. It is the basic velocity scaled by a roughness factorcr(z) and an orography factorco(z) (1.0 on flat ground, higher on hills and escarpments):
The terrain factor kr=0.19(z0/z0,II)0.07 and the roughness length z0 come from the terrain category (0 = sea, I = flat, II = open, III = suburban, IV = urban - Table 4.1). Rougher terrain gives a lower velocity near the ground but a thicker boundary layer.
Turbulence and the peak velocity pressure
Wind is gusty, so a peak rather than the mean governs. The turbulence intensityIv(z) is the ratio of the velocity standard deviation to the mean:
Iv(z)=vm(z)σv=co(z)ln(z/z0)kl
The peak velocity pressureqp(z) then combines the mean dynamic pressure with the gust contribution. With air density ρ=1.25kg/m3:
qp(z)=[1+7Iv(z)]21ρvm2(z)=ce(z)qb
where qb=21ρvb2 is the basic velocity pressure and ce(z) the exposure factor. This qp(z) is the single most important wind quantity - every surface pressure is proportional to it.
Pressure coefficients
The pressure on a surface is qp(z) times a pressure coefficient. The wind pushes on the windward face and sucks on the leeward face, the side walls and most roofs:
we=qp(ze)cpe,wi=qp(zi)cpi
External coefficient cpe - depends on the surface zone (A–E on walls; F–I on roofs), the building proportions and the loaded area. cpe,10 is used for the overall structure, cpe,1 for small elements like fixings (Tables 7.1–7.5).
Internal coefficient cpi - set by the openings: it ranges from about −0.3 to +0.2, and for a dominant opening it follows the external coefficient at that opening.
The net pressure on an element is the difference of the external and internal pressures, wnet=we−wi - internal suction adds to external pressure on a windward wall, which is why the internal coefficient matters.
Wind force on the structure
The overall force is found either by summing surface pressures over the reference areas, or directly with a force coefficient:
Fw=cscdcfqp(ze)Aref+∑Ffr
Here cf is the force coefficient (for the whole shape - used for signboards, cylinders, lattices), Aref the reference area,cscd the structural factor (size + dynamic response, often 1.0 for ordinary buildings under 15 m), and Ffr the friction force on surfaces parallel to the wind. For buildings the pressure-summation route is usual; for slender or special shapes the force-coefficient route is used.
Zones, roofs and special cases
Real surfaces are not uniformly loaded. EN 1991-1-4 divides walls into zones A–E and roofs (flat, monopitch, duopitch, hipped) into zones with their own cpe, with strong local suction near edges and corners. Canopies and free-standing walls use net pressure coefficients cp,net that capture both faces at once. This calculator covers vertical walls, flat/mono/duopitch roofs, canopies, free-standing walls and parapets, signboards and rectangular/circular sections, applying the correct table for each.
Values such as cdir, the air density and the terrain parameters can be set by the National Annex - always confirm them for your country before issuing a design.
Frequently asked questions
The peak velocity pressure q_p(z) is the design wind pressure at height z, including the effect of gusts. It is q_p(z) = [1 + 7·I_v(z)]·½·ρ·v_m²(z), where I_v is the turbulence intensity, ρ ≈ 1.25 kg/m³ is the air density and v_m(z) the mean wind velocity at height z. Equivalently q_p(z) = c_e(z)·q_b, the exposure factor times the basic velocity pressure. Every external and internal surface pressure in the Eurocode is q_p(z) multiplied by a pressure coefficient, so it is the central wind quantity.
EN 1991-1-4 Table 4.1 defines terrain categories 0 to IV by roughness length z₀: 0 (sea/coastal, z₀ ≈ 0.003 m), I (flat open, 0.01), II (open with scattered obstacles, 0.05 - the reference terrain), III (suburban/forest, 0.3) and IV (dense urban, 1.0). Rougher terrain reduces the wind speed near the ground (through the roughness factor c_r(z) = k_r·ln(z/z₀)) but the boundary layer is deeper, so the speed catches up at height. The terrain category therefore changes q_p(z) at every level.
External pressure coefficients depend on the loaded area. c_pe,10 applies to loaded areas of 10 m² or more and is used for the overall load on the structure and large elements. c_pe,1 applies to areas of 1 m² or less and is larger (more onerous) - it is used for small elements and their fixings, such as cladding panels and their fasteners, where high local suction near edges governs. For areas between 1 and 10 m² the coefficient is interpolated logarithmically.
The internal pressure coefficient c_pi depends on the distribution of openings in the building envelope. For a building without a dominant opening, c_pi is taken as the more onerous of +0.2 and −0.3 (EN 1991-1-4 §7.2.9). If there is a dominant opening (its area at least twice the sum of the other openings on the other faces), c_pi follows the external coefficient at that opening, scaled by a factor that depends on how dominant it is. Internal suction combines with external pressure, so the worst case for the net pressure must be checked.
Two routes are allowed. The pressure-summation route multiplies the net pressure (external minus internal) on each surface by its area and sums over the structure, scaled by the structural factor c_s·c_d. The force-coefficient route uses F_w = c_s·c_d·c_f·q_p(z_e)·A_ref plus friction forces, where c_f is a force coefficient for the whole shape - used for signboards, free-standing walls, cylinders and lattice structures. For ordinary low-rise buildings c_s·c_d is usually 1.0.
The structural factor c_s·c_d accounts for two effects: c_s (the size factor) reduces the load because peak gust pressures do not act simultaneously over a large surface, while c_d (the dynamic factor) increases it to allow for resonant response of the structure to turbulence. For most buildings below 15 m tall the combined value may be taken as 1.0 (EN 1991-1-4 §6.2). Slender, tall or flexible structures need the detailed calculation of Annex B or C, because their dynamic response is significant.
Ready to compute your own wind loads? Get q_p(z), the pressure coefficients and zone pressures for walls, roofs, canopies and more.
