R-values of Materials

To calculate the R-value of an assembly (wall, ceiling), we must first know the R-values of the components: this document is about understanding what those R-value mean and to understand the limitations of using them.  Although most of this document is about the inaccuracies in the R-value number, you can still use the R-value as if it were accurate, since you have no other number, and for the most part they are accurate enough. Since we're generally interested in relative performance, not absolute, the key is being consistent about which R-values you pick: if you're pessimistic about one value and optimistic about another, your results will obviously be skewed in that direction.

The rest of this page could be titled "more things about R-values than you ever wanted to know". Regrettably, you actually want to know it all.¹⁰

R-values are calculated by means of a standard test (actually one of short list of approved very similar standard tests), done in a lab using special equipment under specific conditions that have come under scrutiny as not representative of real world conditions, or more specifically that the result of the test cannot be extrapolated to real world conditions.  The resulting R-value represents the total heat transfer thru the material (ie conduction, convection, radiation), although under the conditions of the test, there is virtually no radiation or convection (see R-value anomolies, below for when the real world varies from the lab).

While  R-values¹ have historically been treated as a constant, they are in fact at least somewhat dependent on the temperature on either side of the material.  Depending on the insulation type, factors such as moisture content, density, air pressure, age and errors in installation can also effect R-value.  While recent research⁹ indicates these factors can be quite large (10-30%), no one has fully characterized them, so in the meantime, there is really no choice but to consider R-value as a constant, and accept that its an approximation and move on to the next quandry.

Why do sources state different R-values?  There are a variety of reasons, and they vary by insulation material and type.   In loose fill, the main factor is how dense it is installed.  In foam board, it depends on what gas was used to make the foam and how much of the gas³ stays in place over the lifetime of the material (hence there is a "new" R-value and an "aged" R-value).  In spray foam it depends on what gas is used and whether it is open-cell or closed-cell.  The R-value given by the manufacturer for specific products at least is the result of a standard test, but beware of any other claims, especially when manufacturers or trade groups publish comparisons against the competition.  There are a variety of sources that list R-values for various product classes, and obviously in each case those numbers are an attempt to represent what a typical value is.  Needless to say, there is likely bias from each of those authors (for example my values tend to be more conservative).  The best bet is to believe the manufacturers value if you're using their product, and otherwise to look up in a variety of sources and pick a number that seems right.

How R-values are calculated: The most common way is to use either a hot box  or a hot plate, which are conceptually similar: each put the material between a hot and cold side and takes a measurement which represents the heat flow across the material.  In the hot box, the material being tested divides a box into two parts: on one side the air is kept at a "cool" temperature and the other side the air is "warm".  In the hot plate, the material is sandwiched between two plates, and the plates themselves are at controlled temperatures. In both cases, the test is then run long enough to get a steady state result.

The hot plate setup inherently limits heat transfer to only conduction (since there is no air gap, there is no radiation or convection),  and the hot box setup will only experience radiation and convection if the two surface temperatures of the test material are significantly different than the surrounding air, (ie the conduction transfer to the air is smaller than the transfer thru the material)--a thick enough sample with a higher total R-value will result in mostly conduction losses. Otherwise hot-box results will always be a lower R-value than when tested on a hot-plate, if for no other reason than a thin layer of air has an R-value as high a .7.

In the case of insulation within a wall cavity, air gaps are undesirable, so the hot-plate result is representative, other than the issue of what temperature its tested at. The worst case would be a metal plate, which would end up being uniformly the average temperature of the two sides, and hence have a large amount heat transfer due to radiation and conduction. However, keep in mind that when determining the R-value of a wall assembly that will exist in the real world, the conditions are often not the same as in the lab with the test setup (see R-value anomolies, below).

While the equipment for both tests are able to run at the full range of typical temperatures a building will experience, the FTC test specifies a mean temperatures of 75F, the tester is able to choose any combination of hot and cold temperatures that create the mean of 75, typically 50F and 100F are chosen. While this is a reasonable typical winter temperature difference, the specific temperatures are not exactly typical.

Although there is some controversy over the validity of the test results, the tests themselves are quite rigorous and controlled by a governing body such as ASTM.

R-values differences in detail

Temperature: For most materials, the R-value does not change that much with temperature, at least not across the range of temperatures that buildings are likely to experience. The exception to this are materials that contain large air gaps that result in convection currents as the temperature difference increases, and materials with an insulating gas that changes phase to a liquid at cold temperatures.  As for large air gaps, this is a claim particularly against very loose fill blown-in fiberglass ^2,  Although fiberglass batt insulation has a similar density, evidence is that it does not have the same problem.  High density fiberglass doesn't have the problem.  There is a separate effect that loose fiberglass is very poor air barrier (compared to other insulations), so if the building is not otherwise sealed correctly, fiberglass won't cover up the mistake, however this has no bearing on its R-value.

For materials with a blown in gas (foam insulation),  the gas may change R-value with temperature by changing phase to a liquid, for example HCFC142b has a boiling point of around 14°F, while HCFC245fa has a boiling point of 59°F.  How much of a problem this is might not be know for a few years, in which case, the industry will probably switch to new blowing agents anyhow, as HCFC142b is already being phased out.

Composition:  Even if two materials are essentially the same, if they're not identical, they won't have the same R-value. For materials that are substantially similar, like wood the difference might be significant, but not huge.  Light dry wood, for example a cedar board at less than 10% moisture content, will have a higher R-value than denser wood like oak or maple, and an even higher R-value yet if the denser wood has absorbed a bit of moisture.  While the R-values of two different pieces of wood might vary by as much as 20%, they're all so much lower than common insulation materials that using a median value (in this case R1/inch), no matter what the wood type will still yield a reasonably accurate result.  For materials like foam board that uses trapped gases, the difference in gases can be significant, hence the R-value difference between extruded polystyrene is not the same as expanded polystyrene, both because the structure of the foam is different and the trapped gases are different.  Likewise extruded polystyrene from one manufacturer might not be the same R-value as another if they don't use the same gas.

Age: Blown-in insulation can settle over time, and the gases in foam insulation will tend to escape over time, which is why those products often have an "aged" R-value and the "new" R-value.  Both spray foam and foam boards are subject to these effects.  For example,  polystyrene board (EPS) with no special gas has a R-value of somewhere between R3.7 and R4 per inch whether new or aged, while Polyisocyanurate (Polyiso) board has a "new" R-value of anywhere from R5.5 to R7 per inch, depending on what gas is used in the foam, and a somewhat lower "aged" R-value (which may be anywhere from 5% to 30% lower, depending on who you listen to.)  Dense polystyrene (XPS), which is blown with HCFCs has a stated new or aged R-value of 5, but  many suspect the aged R-value is closer to 4.5.

Density: For any insulation that is effectively built on site (ie blown-in and spray foam), the stated R-value is for a specific density, and it can be a challenge to get that density everywhere at a job site, although if installed correctly you should get a very close R-value.  Some board products, for example Roxul mineral wool boards come in various densities, so each version of the board is a different R-value.

Installation: batt insulation is difficult to install in any non-standard size cavity and when there are wires, pipes or other obstructions in the cavity.  Board insulation is often difficult to cut straight, so when fitting it in a cavity, there tends to be some gaps.

R-values Table

The following table gives approximate R-value of common building materials.  Materials are shown as a range of values, dependent on the specific material, installation density and of course, whose numbers you believe.⁵

R value anomalies

The conditions experienced by a real-world assembly (ie wall, ceiling, roof) often violate the assumptions made in both the expression of R-value and the heat loss calculations.  These effect don't change the R-value of the material, but they do change the amount of heat transferred thru the assembly.

Air layers/material boundary: in calculating the heat flow thru an assembly (wall, ceiling etc), there is an additional non-zero R-value of heat moving from inside air into the assembly, and then from the assembly into the outside air.   While this has no effect on the R-value of the materials themselves⁴, it increases the R-value for all the above ground assemblies.  Many sources add average R-values for these boundary layers into their calculation of an assembly's R-value, while others don't (including sensiblehouse, see more discussion in the heat loss section).

The R-value of this boundary layer depends on the density of air, the speed of the air movement, the mean radiant temperature of surrounding objects, and the emissivity of the material, and has a maximum value of approximately R.9.  The inside air layer of a wall is usually considered to be R.7, while the outside is R.2 (its only lower due to wind and convection).  For ceilings the inside layer has a slightly lower R-value.

Multi-pane windows make great use of this air layer R-value by trapping air between two panes of glass, which guarantees the air layers sitting on the inside of each pane stays at the higher R-values.

Radiant effects:  the heat loss equations assume the mean radiant temperature is the same as the air temperature, but this is often not the case.  A sun warmed surface can be much warmer than the surrounding air, and a roof surface can be significantly cooled due to radiant loss to the sky.  In both cases the radiant gain/loss is greater than it would otherwise be.  Likewise if the surrounding objects (eg ground, other buildings) are warmer than the air, radiant heat loss from the surface will be reduced, although how significant this is, isn't clear.

The R-value of the material doesn't really change, but the effective temperature difference does, hence, the concept of sol-air temperature⁶ was created to express what the actual effective temperature is. The effect of sol-air temperature can be quite significant, for example a dark roof can be over 140°F when the air temperature is only 90°F, but on a yearly basis, in most climates it will apparently not skew the results too much.  Since the roof surface is the one most affected, additional insulation is usually added there to compensate.⁷

Radiant barriers: these are effectively mirrors for infrared radiation.  Since radiation only travels thru a transparent medium (such as air), radiant barriers only work when facing such a medium.  More accurately, radiation only travels until it is absorbed by another atom, or is absorbed and re-emitted at the same energy level (frequency).

Aside:  Note that the term "radiation" is a bit confusing in that term also is used for energetic particles, such as the kind associated with nuclear power.  Radiation, in this context refers only to photons, and specifically only to photons who energy range is in the general infra-red range.  Non-metallic walls, for example, are transparent to radio and x-rays, but opaque to everything in the infrared thru UV range.

Typically radiant barriers are made of shiny metal, because it has a high reflectivity for infrared, and also a high emissivity (meaning that whatever energy is absorbed, it will soon be re-emitted).  Alas, they also have a very low specific heat, so they will get quite hot, and once they are hot, they will emit infrared radiation in both directions, with the greater amount going toward the colder side.  They stay reflective, but the reflection is far from perfect.

Dust accumulating on the surface of the metal renders it ineffective, because dust is not reflective, and since air all tends to be dusty, the long-term effectiveness of radiant barriers is questionable.   Either way, the metal foil will still have a near-zero R-value for conduction--the only resistance being the air layers on either side of the barrier.⁸

The low-e coating on window glass is a form of radiant barrier that works well, partially because the coating is in a sealed, dust free enclosure, and partially because being bonded

Convective effects: A windy day will remove heat faster than a still day, but this mostly results in greater air infiltration (the secondary effect is the reducing the boundary R-value, as described above).  From the perspective of modeling, the only effect is that on cold, windy days the outside boundary R-value should be considered to be 0, and the air infiltration amount should be increased.

If there is significant temperature stratification in a room (forced air, vaulted ceiling being the classic case, but also with wood stoves), there will be increased heat loss thru the ceiling due to the higher temperature that exists there.

Thermal mass: a high mass wall (for example, adobe, rammed earth, or even concrete) can have a significantly higher effective R-value than its measured R-value due to its ability to store heat. Needless to say, this only occurs when the actual conditions are very different from the test conditions, for example, when the wall surface temperature (or outdoor air temperature) gets warm enough to move heat to the interior.  Likewise any heat that the exterior of the mass absorbs during the day will leak out slowly during the course of the night, and hence stay warmer than air temperature.  The flip side of this is that the wall will stay cooler than it otherwise would well into the day, increasing the heat flow during that time period, at least within the wall.  If the air temperature rises fast enough, there will be a reduction is how much of that heat ends up leaking into the outside air.

Mass walls that are exposed to regular sunshine will obviously perform better than those that are not exposed, and clearly cloudy days with a lower diurnal temperature difference will cause the effective R-value to be much closer to the actual R-value.  If conditions cause a mass wall to get either quite hot or quite cold, they will stay that way for much longer than a low mass wall--how long depends mostly on how thick the walls are.

The thermal flywheel:  Heat moves thru thick mass walls at a specific rate which is largely determined by the specific heat of the material.   If the time it takes to move is approximately equal to the daylight hours, then as the day's heat begins reaching inside, the wall begins cooling to the outside as well.  The result is that the temperature of the wall on the inside has a much smaller change in temperature than at the outside.  Given a thick enough wall, the inside temperature will stay near the average outside temperature over the course of the day, or the last couple of days.  Walls that receive much sunshine will be much warmer than those that don't, since mass walls tend to be fairly good heat absorbers.  As with other aspects of heat movement, the exact performance depends on many factors.

When you read "equivalent R-value" for a mass wall somewhere, what it's referring to is the thermal flywheel, and hence it's a short term R-value that is only true when looked from the perspective of one (or a small number) of days of temperature fluctuations.   A mass wall will only achieve the "equivalent R-value" for time periods that are in the range of its time constant.  Over longer time periods, the interior temperature will move toward the average temperature over the last few days, so if that average isn't too far from 70F, mass wall will perform acceptably, otherwise it probably won't.  In most climates, mass is best kept on the inside of the envelope (see passive solar).

Metal components: in the context of insulated assemblies, the effective R-value of metal is lower than zero when there is a temperature difference from one side of the metal to the other.  Of course the actual R-value of metal is at least slightly greater than zero, but because it is so conductive, when it penetrates a non-conductive material it introduces lateral heat flow.  All our heat flow models assume that there is no lateral heat flow, ie that the heat movement is only between inside and outside, not sideways thru the assembly.  So the total heat flow due to the metal is greater than the heat flow thru just the metal (although how much greater isn't clear).

 Examples of this would be the nails used to hold plywood sheathing to a stud or steel studs.  A sheet of metal that is perpendicular to direction of heat flow would generally have no effect, because both surfaces would be the same temperature without the metal.  These effects are ignored in models, although if you consider how many nails, screws, metal clips, wires, staples, tie-down etc are in walls, its clear that the real world R-value of the wall will be at least a little bit less than what is calculated.

This effect can be used to advantage, for example in hydronic floor heating. In this case, placing pieces of sheet metal between the pipe and the wood flooring significantly increases the heat transfer by spreading the heat from the narrow pipe over a wide area.  So a 1/2" wide pipe placed on a foot wide piece of sheet metal will make the effective width of the heat transfer surface much closer to a foot than 1/2".

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Notes

1: The term R-value is used because more people are familiar with it, even though most of the heat loss calculations involve U-value.  Since one is just the inverse of the other, they are interchangeable.

2: This claim against fiberglass has been perpetuated by all their competitors, and apparently comes from a single test done by ORNL in 1992. The reference is here: http://www.ecp1.com/science/Oak-Ridge-Report.pdf

3: These gases are CFCs, HCFC, HFCs, and now Pentane and HOFCs. Don't be surprised if these change again in 5 years.

4: It is assumed here that in calculating the R-value from the hot box test, that the R-value associated with heat transfer from the material to the surrounding air has been adjusted for, since the intent is to measure the R-value of only the material itself, and typically insulation completely fills the cavity, meaning there is no air layer.  This boundary between the material and air is where convection and radiation would be the largest factors.  Note that a static air film (ie air not moving) can have an R-value as high at .7.

5: Manufacturers and trade associations tend to find ways to list more optimistic values, and the energy design community (including me), tend to be pessimistic about those values.  Exactly how pessimistic seems to depend on the how much you like the other properties of the insulation.  I'm pretty sure I'm guilty here.

For example, I found a site (run by a trade association) that listed spray foam as high as R6.7/inch, but to achieve that, they sandwiched the foam between two sheets of metal.  Since that's not a condition that's likely to occur in real life, I ignored this value. 

6. the definitions of sol-air temperature on the web are confusing at best, and as far as I can tell there is no readily available way to measure such a temperature.  I've stated the effect in more straightforward terms. Whether I got the definition exactly right or not, the principle is still correct.  When terminology like this generally makes principles clearer, this doesn't appear to be the case with sol-air temperature.

7: this is the reason for added attic insulation, is not because "heat rises"--heat moves from warm to cool with no sense of directoin. However, it is true that hot air rises due to having a lower density than cool air, and if there is a driving force that makes some air hotter than the rest (for example a woodstove or forced air heating), the temperature difference at the ceiling will be greater than at the walls which is another reason for more attic insulation.

8: While it would appear that the rear heat shield commonly installed on wood stoves is a radiant barrier, I think I doesn't really work quite the same way (mine is covered in highly absorbent black paint).  What I think happens is that it absorbs radiant heat from the stove, but then relies on air convection to keep it much cooler than the stove surface, and hence it radiates at a much lower temperature to the nearby wall.

9. See http://www.buildingscience.com/documents/special/thermal-metric

10: at least if you really want to understand what's going on, in particular if you want to whether a given R-value, or heat transfer related to that R-value is bogus or not.