Insulation

Warm deck flat roof U-value and insulation thickness

R_{t} = R_{s i} + \frac{d_{i}}{1000 λ_{i}} + \frac{d_{d}}{1000 λ_{d}} + R_{o} + R_{s e}

U = \frac{1}{R_{t}}

d_{n} = 1000 λ_{i} (\frac{1}{U_{t}} - (R_{t} - \frac{d_{i}}{1000 λ_{i}}))

where
$R_{t}$: total thermal resistance (m²K/W)
$R_{si}$: internal surface resistance (m²K/W)
$d_{i}$: insulation thickness (mm)
$λ_{i}$: insulation thermal conductivity (W/mK)
$d_{d}$: deck thickness (mm)
$λ_{d}$: deck thermal conductivity (W/mK)
$R_{o}$: other layers resistance (m²K/W)
$R_{se}$: external surface resistance (m²K/W)
$U$: U-value (W/m²K)
$d_{n}$: insulation thickness for the target (mm)
$U_{t}$: target U-value (W/m²K)

Explain this equation

Estimates the U-value of a warm deck flat roof and the insulation thickness needed to hit a target, such as 0.15 W/m²K for a new roof.

Each layer resists heat flow. For a solid layer the resistance is its thickness in metres divided by its conductivity λ, which is why millimetres are divided by 1000. The surface resistances R_si and R_se allow for the still air films on the inside and outside. Adding all the resistances gives R_t, and the U-value is its inverse. For the thickness, the target 1/U_t is the total resistance needed; take away everything except the insulation and convert the remainder back to a thickness.

Layers in series add their resistances, just like resistors in a single circuit.

Sense check: 120 mm of PIR at 0.025 on 18 mm ply gives about 5.08 m²K/W, a U-value of about 0.20. Reaching 0.15 needs about 160 mm.

Watch out: this is a simple layer sum. It ignores fixings and joints, so a full BS EN ISO 6946 calculation will come out slightly worse.

Simple layer-by-layer U-value for a warm deck flat roof, and the insulation thickness needed to reach a target U-value.

Enter your values to see the result.

Good to know

Each layer’s resistance is its thickness divided by its thermal conductivity. BS EN ISO 6946 gives surface resistances of 0.10 m²K/W inside for upward heat flow and 0.04 outside. Generic λ values: wood-based panels 0.13 and PIR board 0.025 W/mK; use the declared λ printed on the board, which is often lower. For extensions, building control commonly asks for 0.15 W/m²K on new flat roofs; Part L 2021 limits are 0.16 for roofs of new dwellings and renovated roofs of existing dwellings. Confirm the target with building control.

Common mistake

Counting the joists and ceiling void in a warm deck, or using a tapered scheme’s maximum thickness. Use the average thickness for tapered insulation and leave out anything below the vapour control layer unless you know its resistance.

Limits

Simple layer sum. It ignores the correction for mechanical fixings, any bridging, and tapered-insulation averaging, so it is slightly optimistic. Use the manufacturer’s calculation for building control.

Sources

Results are calculations from the published methods and figures shown, and depend on the data you enter. Follow the roof covering manufacturer’s fixing specification, BS 5534, BS 8000-6, BS 6229, the Lead Sheet Training Academy guidance and Building Regulations. Wind uplift and structural design need a competent designer.

Warm deck flat roof U-value and insulation thickness

Good to know

Common mistake

Limits

Sources

Warm deck flat roof U-value and insulation thickness

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