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The R value or R-value is a measure of thermal resistance [1] used in the building and construction industry. Under uniform conditions it is the ratio of the temperature difference across an insulator and the heat flux (heat flow per unit area, $\dot Q_A$) through it or $R = \Delta T/\dot Q_A$. The bigger the number, the better the building insulation's effectiveness[2]. R-value is the reciprocal of U-value.

Around most of the world, R-values are given in SI units, typically square-metre kelvins per watt or m²·K/W (or equivalently to m²·°C/W). In the United States customary units, R-values are given in units of ft²·°F·h/Btu. It is particularly easy to confuse SI and US R-values, because R-values both in the US and elsewhere are often cited without their units, e.g. R-3.5. Usually, however, the correct units can be inferred from the context and from the magnitudes of the values.

Heat transfer through an insulating layer is analogous to electrical resistance. The heat flows can be worked out by thinking of resistance in series with a fixed potential, except the resistances are thermal resistances and the potential is the difference in temperature from one side of the material to the other. The resistance of each material to heat transfer depends on the specific thermal resistance [R-value]/[unit thickness], which is a property of the material (see table below) and the thickness of that layer. A thermal barrier that is composed of several layers will have several thermal resistors in the analogous circuit, each in series. Like resistance in electrical circuits, increasing the physical length of a resistive element (graphite, for example) increases the resistance linearly; double the thickness of a layer means half the heat flow and double the R-value; quadruple, quarters; etc. In practice, this linear relationship may be only approximate some materials[citation needed].

Increasing the thickness of an insulating layer increases the thermal resistance. For example, doubling the thickness of fibreglass batting will double its R-value, perhaps from 2.0 m²K/W for 110 mm of thickness, up to 4.0 m²K/W for 220 mm of thickness. Heat transfer through an insulating layer is analogous to adding resistance to a series circuit with a fixed voltage. However, this only holds approximately because the effective thermal conductivity of some insulating materials depends on thickness. The addition of materials to enclose the insulation such as sheetrock and siding provides additional but typically much smaller R-value.

There are many factors that come into play when using R-values to compute heat loss for a particular wall. Manufacturer R values apply only to properly installed insulation. Squashing two layers of batting into the thickness intended for one layer will increase but not double the R-value. Another important factor to consider is that studs and windows provide a parallel heat conduction path that is unaffected by the insulation's R-value. The practical implication of this is that one could double the R value used to insulate a home and realize substantially less than a 50% reduction in heat loss. Even perfect wall insulation only eliminates conduction through the insulation but leaves unaffected the conductive heat loss through such materials as glass windows and studs as well as heat losses from air exchange.

The R-value is a measure of insulation's heat loss retardation under specified test conditions. The primary mode of heat transfer impeded by insulation is convection but unavoidably it also impedes heat loss by all three heat transfer modes: conduction, convection, and radiation. The primary means of heat loss across an uninsulated air-filled space is natural convection, which occurs because of changes in air density with temperature. Insulation greatly retards natural convection. Most insulations trap air so that significant convective heat loss is eliminated leaving only conduction and radiation transfer. The primary role of such insulation is to make the thermal conductivity of the insulation that of trapped, stagnant air. However this cannot be realized fully because the glass wool or foam is needed to prevent convection and increases the heat conduction compared to still air. Radiative heat transfer is minimised by having many surfaces interrupting a "clear view" between the inner and outer surfaces of the insulation. Such multiple surfaces are abundant in batting and porous foam. Radiation is also minimized by low emissivity (highly reflective) surfaces. Lower thermal conductivity and, therefore, high R-values can be achieved by replacing air with argon when practical such as between sealed double-glazed windows and within special closed-pore foam insulation.

UnitsEdit

The conversion between SI and US units of R-value is 1 h·ft²·°F/Btu = 0.176110 K·m²/W, or 1 K·m²/W = 5.678263 h·ft²·°F/Btu.[3]

To disambiguate between the two, some authors use the abbreviation "RSI" for the SI definition[2].

Example (SI units) Edit

To find the heat loss per square metre, simply divide the temperature difference by the R value.

If the interior of your home is at 20 °C, and the roof cavity is at 10 °C, the temperature difference is 10 °C (= 10 K). Assuming a ceiling insulated to R–2 (R = 2.0 m²K/W), energy will be lost at a rate of 10 K / 2 K·m²/W = 5 watts for every square metre of ceiling.

RelationshipsEdit

U-valueEdit

The U-value (or U-factor), more correctly called the overall heat transfer coefficient, describes how well a building element conducts heat. It measures the rate of heat transfer through a building element over a given area, under standardized conditions. The usual standard is at a temperature gradient of 24 oC, at 50% humidity with no wind[4] (a smaller U-value is better).

U is the inverse of R with SI units of W/(m²K) and US units of BTU/(h °F ft²)

$U=\frac{1}{R}=\frac{\dot Q_A}{\Delta T}$

ThicknessEdit

R-value should not be confused with the intrinsic property of thermal resistivity and its inverse, thermal conductivity. The SI unit of thermal resistivity is K·m/W. Thermal conductivity assumes that the heat transfer of the material is linearly related to its thickness.

Multiple layersEdit

In calculating the R-value of a multi-layered installation, the R-values of the individual layers are added:[5]

R-value(outside air film) + R-value(brick) + R-value(sheathing) + R-value(insulation) + R-value(plasterboard) + R-value(inside air film) = R-value(total).

To account for other components in a wall such as framing, an area-weighted average R-value of the whole wall may be calculated.