Corrections for air gaps and fixings (ISO 6946 Annex F)

A_{f} = \frac{π d_{f}^{2}}{4000000}

α = \frac{0.8 d_{1}}{d_{0}}

Δ U_{g} = Δ U ″ {(\frac{R_{1}}{R_{T}})}^{2}

Δ U_{f} = \frac{α λ_{f} n_{f} A_{f}}{d_{0} / 1000} {(\frac{R_{1}}{R_{T}})}^{2}

U_{c} = U + Δ U_{g} + Δ U_{f}

where
$A_{f}$: cross-section area of one fixing (m²)
$d_{f}$: fixing shank diameter (mm)
$α$: fixing coefficient
$d_{1}$: length of fixing inside the insulation (mm)
$d_{0}$: insulation layer thickness (mm)
${ΔU}_{g}$: air-gap correction (W/m²K)
$ΔU″$: air-gap level: 0, 0.01 or 0.04 (W/m²K)
$R_{1}$: resistance of the insulation layer with gaps or fixings (m²K/W)
$R_{T}$: total resistance ignoring bridging (m²K/W)
${ΔU}_{f}$: fixings correction (W/m²K)
$λ_{f}$: fixing thermal conductivity (W/mK)
$n_{f}$: fixings per m²
$U_{c}$: corrected U-value (W/m²K)
$U$: U-value before corrections (W/m²K)

Explain this equation

Adds the BS EN ISO 6946 corrections for small air gaps around insulation boards and for metal fixings that pass through the insulation.

Gaps between boards let air move around them; ΔU″ is a level from 0 (no gaps) to 0.04 (gaps that link warm and cold sides). Metal fixings are tiny thermal bridges: their effect grows with the steel's conductivity λ_f, the number per square metre and their cross-section, and falls with insulation thickness. α is 0.8 for a fixing right through the layer, less if recessed. Both corrections are scaled by (R₁/R_T)², because they matter more when the insulation layer does most of the work.

These are the simplified correction formulas of the standard's Annex F.

Sense check: six 4 mm steel fixings per m² through 100 mm of insulation add about 0.02 W/m²K to a 0.28 wall; with minor gaps the total correction is about 10%.

Watch out: if the total correction is under 3% of U it may be ignored. Stainless or plastic-headed fixings greatly reduce the penalty.

Adds the BS EN ISO 6946 Annex F corrections for air gaps in the insulation and for metal fixings that pass through it, as used for external wall insulation, warm roofs and mechanically fixed boards.

Enter your values to see the result.

Good to know

Air-gap levels (BR 443): level 0 (ΔU″ = 0) for well-fitted boards with staggered or sealed joints, or where insulation fills the space; level 1 (0.01, the default) where gaps may bridge the insulation without air movement; level 2 (0.04) where gaps link to air circulating on the warm side. The fixing formula uses α = 0.8 for a fixing that goes right through the insulation and α = 0.8 × d1/d0 for a recessed one. Fixings are ignored where they only pass through air or have λ under 1 W/mK (plastic). Use the manufacturer's or ETAG/EAD point thermal transmittance χ where given (ΔUf = nf × χ). Corrections below 3% of U may be left out.

Common mistake

Entering the anchor sleeve or washer size instead of the steel shank diameter, or using a corrected U from one build-up for another with a different R1/RT ratio.

Limits

Simplified Annex F method; not for fixings whose both ends contact metal plates. Roof-specific precipitation correction ΔUr for inverted roofs is not included. Some manufacturers publish χ values from 3D modelling that are more accurate.

Sources

Results are calculations from the published methods and figures shown, and depend on the data you enter. Follow BS EN ISO 6946, BS 5250, PAS 2035, Building Regulations Part L and manufacturers’ data. Whole-house retrofit needs a qualified retrofit assessor and coordinator.

Corrections for air gaps and fixings (ISO 6946 Annex F)

Good to know

Common mistake

Limits

Sources

Corrections for air gaps and fixings (ISO 6946 Annex F)

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