The R-value is a measure of thermal resistance, specifically how well a two-dimensional barrier, such as a layer of insulation, a window, or a complete wall or ceiling, resists the conductive flow of heat, in the context of construction. The higher the R-value, the more insulating the material is. Higher R-values can reduce heating bills in cold weather and cooling bills in hot weather.
R-value can be expressed with in both metric and United States customary units. When expressed in metric, the term RSI-value is often used. R-values expressed in United States customary units are approximately 5.68 times as large as R-values expressed in metric.
An R-value can be given for a material (e.g., for polyethylene foam), or for an assembly of materials (e.g., a wall or a window). In the case of materials, it is often expressed in terms of R-value per metre, or per inch in the US. R-values are additive for multiple layers of materials. R-value is defined as the temperature difference needed to sustain one unit of heat flux between the warmer surface and colder surface of a barrier under steady-state conditions.
The U-factor or U-value is the overall heat transfer coefficient and can be found by taking the inverse of the R-value. It is a property that describes how well building elements conduct heat per unit area across a temperature gradient. The elements are commonly assemblies of many layers of materials, such as those that make up the building envelope. It is expressed in watts per square metre kelvin. The higher the U-value, the lower the ability of the building envelope to resist heat transfer. A low U-value, or conversely a high R-value, usually indicates high levels of insulation. They are useful as it is a way of predicting the composite behaviour of an entire building element rather than relying on the properties of individual materials.
R-value definition R-value is defined as
where (using SI units): (K⋅m2/W) is the R-value, (K) is the temperature difference between the warmer surface and colder surface of a barrier, (W/m2) is the heat flux through the barrier.
The R-value per unit of a barrier's exposed surface area measures the absolute thermal resistance of the barrier.
where (using SI units): is the R-value (m2⋅K⋅W−1) is the barrier's exposed surface area (m2) is the absolute thermal resistance (K⋅W−1)
Absolute thermal resistance, , quantifies the temperature difference per unit of heat flow rate needed to sustain one unit of heat flow rate. Confusion sometimes arises because some publications use the term thermal resistance for the temperature difference per unit of heat flux, but other publications use the term thermal resistance for the temperature difference per unit of heat flow rate. Further confusion arises because some publications use the character R to denote the temperature difference per unit of heat flux, but other publications use the character R to denote the temperature difference per unit of heat flow rate. This article uses the term absolute thermal resistance for the temperature difference per unit of heat flow rate and uses the term R-value for the temperature difference per unit of heat flux.
The greater the R-value, the greater the resistance, and so the better the thermal insulating properties of the barrier. R-values are used in describing the effectiveness of insulating material and in analysis of heat flow across assemblies (such as walls, roofs, and windows) under steady-state conditions. Heat flow through a barrier is driven by temperature difference between two sides of the barrier, and the R-value quantifies how effectively the object resists this drive: The temperature difference divided by the R-value and then multiplied by the exposed surface area of the barrier gives the total rate of heat flow through the barrier, as measured in watts or in BTUs per hour.
where (using SI units): is the R-value (K⋅m2/W), is the temperature difference (K) between the warmer surface and colder surface of the barrier, is the exposed surface area (m2) of the barrier, is the heat flow rate (W) through the barrier. As long as the materials involved are dense solids in direct mutual contact, R-values are additive; for example, the total R-value of a barrier composed of several layers of material is the sum of the R-values of the individual
For example, in winter it might be 2 °C outside and 20 °C inside, making a temperature difference of 18 °C or 18 K. If the material has an R-value of 4, it will lose 0.25 W/(°C⋅m2). With an area of 100 m2, the heat energy being lost is There will be other losses through the floor, windows, ventilation slots, etc. But for that material alone, 450 W is going out, and can be replaced with a 450 W heater inside, to maintain the inside temperature.
Terminology and units Note that the R-value is the building industry term for what is in other contexts called "thermal resistance" "for a unit It is sometimes denoted RSI-value if the SI (metric) units are used.
An R-value can be given for a material (e.g., for polyethylene foam), or for an assembly of materials (e.g., a wall or a window). In the case of materials, it is often expressed in terms of R-value per unit length (e.g., per inch of thickness). The latter can be misleading in the case of low-density building thermal insulations, for which R-values are not additive: their R-value per inch is not constant as the material gets thicker, but rather usually decreases.
The units of an R-value (see below) are usually not explicitly stated, and so it is important to determine from context which units are being used: an R-value expressed in I-P (inch-pound) units is about 5.68 times larger than when expressed in SI units, so that, for example, a window that is R-2 in I-P units has an RSI of 0.35 (since 2/5.68 = 0.35). For R-values there is no difference between US customary units and imperial units.
All of the following mean the same thing: "this is an R-2 window"; "this is an R2 "this window has an R-value of 2"; "this is a window with R = 2" (and similarly with RSI-values, which also include the possibility "this window provides RSI 0.35 of resistance to heat flow").
Apparent R-value The more a material is intrinsically able to conduct heat, as given by its thermal conductivity, the lower its R-value. On the other hand, the thicker the material, the higher its R-value. Sometimes heat transfer processes other than conduction (namely, convection and radiation) significantly contribute to heat transfer within the material. In such cases, it is useful to introduce an "apparent thermal conductivity", which captures the effects of all three kinds of processes, and to define the R-value more generally as the thickness of a sample divided by its apparent thermal conductivity. Some equations relating this generalized R-value, also known as the apparent R-value, to other quantities are: where: is the apparent R-value (K/W) across the thickness of the sample, is the thickness (m) of the sample (measured on a path parallel to the heat flow), is the apparent thermal conductivity of the material (W/(K⋅m)), is the thermal transmittance or U-value of the material (W/K), is the apparent thermal resistivity of the material (K⋅m/W).
An apparent R-value quantifies the physical quantity called thermal insulance.
However, this generalization comes at a price because R-values that include non-conductive processes may no longer be additive and may have significant temperature dependence. In particular, for a loose or porous material, the R-value per inch generally depends on the thickness, almost always so that it decreases with increasing thickness (polyisocyanurate (colloquially, polyiso) being an exception; its R-value/inch increases with thickness). For similar reasons, the R-value per inch also depends on the temperature of the material, usually increasing with decreasing temperature (polyisocyanurate again being an exception); a nominally R-13 fiberglass batt may be R-14 at and R-12 at . Nevertheless, in construction it is common to treat R-values as independent of temperature. Note that an R-value may not account for radiative or convective processes at the material's surface, which may be an important factor for some applications.
The R-value is the reciprocal of the thermal transmittance (U-factor) of a material or assembly. The U.S. construction industry prefers to use R-values, however, because they are additive and because bigger values mean better insulation, neither of which is true for U-factors.
U-factor/U-value
The U-factor or U-value is the overall heat transfer coefficient that describes how well a building element conducts heat or the rate of transfer of heat (in watts) through one square metre of a structure divided by the difference in temperature across the structure. The elements are commonly assemblies of many layers of components such as those that make up walls/floors/roofs etc. It is expressed in watts per meter squared kelvin W/(m2⋅K). This means that the higher the U-value the worse the thermal performance of the building envelope. A low U-value usually indicates high levels of insulation. These values are useful for predicting the composite behavior of an entire building element rather than relying on the properties of individual materials.
In most countries the properties of specific materials (such as insulation) are indicated by the thermal conductivity, sometimes called a k-value or lambda-value (lowercase λ). The thermal conductivity (k-value) is the ability of a material to conduct heat; hence, the lower the k-value, the better the material is for insulation. Expanded polystyrene (EPS) has a k-value of around 0.033 W/(m⋅K). For comparison, phenolic foam insulation has a k-value of around 0.018 W/(m⋅K), while wood varies anywhere from 0.15 to 0.75 W/(m⋅K), and steel has a k-value of approximately 50.0 W/(m⋅K). These figures vary from product to product, so the UK and EU have established a 90/90 standard which means that 90% of the product will conform to the stated k-value with a 90% confidence level so long as the figure quoted is stated as the 90/90 lambda-value.
U is the inverse of R. U is measured in SI units of W/(m2⋅K) and U.S. units of BTU/(h⋅°F⋅ft2) where is the heat flux, is the temperature difference across the material, k is the material's coefficient of thermal conductivity and L is its thickness. In some contexts, U is referred to as unit surface conductance.
The term U-factor is usually used in the U.S. and Canada to express the heat flow through entire assemblies (such as roofs, walls, and windows). For example, energy codes such as ASHRAE 90.1 and the IECC prescribe U-values. However, R-value is widely used in practice to describe the thermal resistance of insulation products, layers, and most other parts of the building enclosure (walls, floors, roofs). Other areas of the world more commonly use U-value/U-factor for elements of the entire building enclosure including windows, doors, walls, roof, and ground slabs.
Metric vs. inch-pound
The SI (metric) unit of R-value is kelvin square-metre per watt (K⋅m2/W or, equally, °C⋅m2/W),
whereas the I-P (inch-pound) unit is degree Fahrenheit square-foot hour per British thermal unit (°F⋅ft2⋅h/BTU).