Thermal resistance R, U-value: how to read a roof’s thermal report

The three quantities in a thermal report

The Th-bat rules, published by the French ministry responsible for construction, set the definitions and calculation methods that engineering consultancies use. Three quantities are enough to read a roof report.

• Thermal conductivity λ, in W/(m·K), is specific to a material: it is the heat flow that passes through one square metre of a one-metre thickness for one kelvin of difference between its faces. The smaller λ is, the better the material insulates. Related to a thickness d, it gives the conductance C = λ/d, in W/(m²·K), which describes a given layer.
• Thermal resistance R, in m²·K/W, is the inverse of conductance: for a homogeneous layer, R = d/λ, with d the thickness in metres; the resistance of a multi-layer element is the sum of the resistances of its layers. The higher R is, the more the element slows heat down.
• Thermal transmittance U (the U-value), in W/(m²·K), is the heat flow that passes through one square metre of the element, in steady state, for one kelvin of difference between the two environments. It equals the inverse of the total resistance: U = 1/(Rsi + ΣR + Rse), where Rsi and Rse are the internal and external surface resistances, which represent the exchanges by convection and radiation between the air and the faces of the element.

For a roof, the heat flow is upward in winter: the Th-bat rules use Rsi = 0.10 and Rse = 0.04 m²·K/W (0.13 and 0.04 for a vertical element, 0.17 and 0.04 for downward heat flow).

An example, calculated with these formulas: a double-skin steel deck with 100 mm of mineral wool of conductivity 0.040 W/(m·K) has a resistance R = 0.10/0.040 = 2.5 m²·K/W; with Rsi = 0.10 and Rse = 0.04, the total resistance is 2.64 m²·K/W and U ≈ 0.38 W/(m²·K). The steel sheets, which are highly conductive, add nothing.

What the regulations require in renovation

The French order of 3 May 2007 on the thermal characteristics of existing buildings, amended by the order of 22 March 2017, imposes a minimum total thermal resistance as soon as the insulation of a building element is installed or replaced. In the version in force since 1 January 2023: 4.5 m²·K/W for a flat roof in French climate zone H1 (4.3 in H2, 4.0 in H3 below 800 m of altitude), 5.2 for the floor of an unconverted loft, 5.2 for pitched roof slopes in H1 (4.5 in H2, 4.0 in H3), 3.2 for an external wall (2.2 in H3). The French CEE sheets for the insulation of tertiary-sector roofs set their own minimum resistances. These thresholds apply to insulation; a reflective coating adds no resistance and is not concerned.

Reading a report line by line

A thermal report presents each building element as a table: layers from the outside to the inside, thickness, λ, R of each layer, surface resistances, total R and U. Five points to check:

1. Is the thickness used the one that is actually in place? Insulation that is compressed, damp or discontinuous does not have the resistance on its data sheet; the Th-bat rules require “design” values, not catalogue values.
2. Is the λ a design λ? The “Materials” booklet of the Th-bat rules and product certifications distinguish the value declared by the manufacturer from the design value.
3. Are the surface resistances consistent with the direction of heat flow? For a roof: 0.10 on the inside and 0.04 on the outside.
4. Are the singular points dealt with? Through fixings, parapets, rooflights, kerbs: they are described by linear or point coefficients, outside the U-value of the main roof area, and they weigh heavily on a steel deck.
5. Does the report say anything about the surface? Generally not: U describes the path of heat through the element, not the amount of heat that arrives at its surface. Neither colour, nor solar reflectance, nor emissivity appears in it.

What insulation does, and does not do, against summer heat

The heat flow through a roof is the product of U and the temperature difference between its surface and the interior. Insulation acts on U; reflectance acts on the surface temperature. Take the roof from the example again, U ≈ 0.38 W/(m²·K), with 26 °C inside. Dark, its surface reaches 60 °C under the summer sun: the difference is 34 K and the incoming flow about 12.9 W per square metre. Reflective, its surface stays at around 35 °C: the difference falls to 9 K and the flow to 3.4 W/m². The same insulation lets nearly four times less heat through, because there is nearly four times less of it to slow down. For a single-skin steel deck, whose U-value is far above 1 W/(m²·K), the hot surface radiates almost directly onto the occupants and the difference is even more marked.

Measurement confirms the calculation. The Heat Island Group of the Lawrence Berkeley National Laboratory states that on a summer afternoon, a clean white roof that reflects 80 % of sunlight stays about 31 °C cooler than a grey roof that reflects only 20 %. A simulation study published in Energy and Buildings (Synnefa, Santamouris and Akbari, 2007, DOI 10.1016/j.enbuild.2007.01.004) crossed reflectance and U-value: for an increase in reflectance of 0.65, the annual reduction in cooling load ranges from 213 kWh/m² of roof for U = 3.24 W/(m²·K) to 22 kWh/m² for U = 0.39 in Abu Dhabi, and from 95 to 7 kWh/m² in Tokyo. The authors conclude that the gains are “more important for poorly or non-insulated buildings”, while remaining significant at high levels of insulation; in the climates studied, the winter heating penalty (0.2 to 17 kWh/m² per year) remains lower than the reduction in cooling (9 to 48 kWh/m² per year). Our article on the cool roof in winter deals with this objection for France.

So: insulation divides the flow, it does not remove it; it does nothing for the waterproofing that bakes at 65 °C, nor for the rooftop equipment, nor for the radiation from the ceiling in a poorly insulated building. And insulation is only installed when the roof is being renewed, as our comparison of external roof insulation and cool roofs (in French) explains.

Reflectance, the other column of the report

This is where the reflective coating comes in, without touching the U-value. The PrimaTherm® system applied by Hélios is a 4-layer coating (PH169 primer, PH107 reflective base coat in two passes, PH107TCL anti-soiling topcoat) whose values are measured according to test standards: solar reflectance of 95 % (ASTM E903-12), emissivity of 0.89 (ASTM C1371-15), SRI of 120 (ASTM E1980), SRI maintained after 4,000 h of accelerated QUV ageing — conventional service life of 20 years (French CEE sheet) —, Broof(t3) fire classification (CSTB report RA23-0010). The SRI combines reflectance and emissivity into a single surface-temperature index.

In practice, a dark roof goes from 50–70 °C to 25–35 °C, i.e. up to −30 °C on the roof surface; at Airbus Marignane, on 5,900 m² of bitumen membrane, the infrared handover measurement of 19 June 2026 showed 28.6 °C on the treated zone against 57.8 °C on the control zone, i.e. −29 °C. Indoors, the gain reaches up to −6 °C felt inside depending on insulation, and air-conditioning consumption falls by 15 to 25 % in French climate zone H1, 20 to 30 % in H2 and 25 to 40 % in H3, i.e. up to −40 % of this item.

The decision rule can be read in the thermal report:

• Low or zero R (single-skin steel deck, asbestos-free fibre cement, thin slab): the cool roof produces its maximum effect, in a few days, without lifting. See our guide to cool roofs on steel deck.
• Compliant R (insulated flat roof, double skin): a more modest indoor gain, but the waterproofing stops undergoing a daily thermal cycle of several tens of degrees and the air conditioning keeps part of the saving; see cool roof on bitumen roofs.
• Renewal decided: you insulate within the new build-up and finish with a reflective surface; the reflectance of the element can then be taken into account in the regulatory calculation.

The free roof study starts from your thermal report if there is one, and from a survey of the substrate otherwise: satellite measurement, nature and condition of the insulation, rooflights, answer within 48 h.

Sources

• Th-bat rules, Opaque elements booklet, French Ministry of Ecological Transition.
• French order of 3 May 2007 on the thermal characteristics of existing buildings, Légifrance.
• Synnefa, Santamouris and Akbari, Estimating the effect of using cool coatings on energy loads and thermal comfort in residential buildings, Energy and Buildings 39 (2007), copy hosted by the EPA.
• Cool roofs, Heat Island Group, Lawrence Berkeley National Laboratory.
• Using cool roofs to reduce heat islands, EPA.
• PrimaTherm® test reports, certifications page.