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This article gives details and formulas for calculating R-values, U-values U-coefficient of heat loss resistance, and K-values, all ways of looking at insulation values or building heat loss rates.

Related Building Heat Loss Articles

Beginning at HEAT LOSS in buildings article series explains how to insulate a building and how much insulation is needed including how to measure or calculate heat loss in a building, defines thermal terms like BTU and calorie, provides measures of heat transmission in materials, gives desired building insulation design data, and shows how to calculate the heat loss in a building with R values or U values

Also see HEAT LOSS INDICATORS (where is the building losing heat during the heating season, or gaining un-wanted heat during the cooling season),see HEAT LOSS DETECTION TOOLS for both tools and procedures, and see HEAT LOSS R U & K VALUE CALCULATION for a guide to calculating heat loss (or gain) rates for buildings and building insulation. At INSULATION R-Values & Properties we give a detailed table of insulating material R-values & properties.

Be sure to review the definitions of R, U, & K Values at Definition of Heating & Cooling Terms. Because no amount of insulation can keep a drafty building warm, also review ENERGY SAVINGS PRIORITIES. Also see our detailed table of Insulation R-Values & Properties and our list of building HEAT LOSS INDICATORS (where is the building losing heat during the heating season, or gaining un-wanted heat during the cooling season).

Formula-R™ and Owens Corning™ which may be visible in this photograph of pink Styrofoam™ insulation boards are registered trademarks of Owens Corning® and were photographed at a Home Depot® building supply center.

© Copyright 2012 InspectAPedia.com, All Rights Reserved. Information Accuracy & Bias Pledge is at below-left. Use page top links to major topics or use links at the left of each page to navigate within topics and documents at this website. Green links show where you are in a document series or at this website.

Definition of & How to Calculate the R value or R-coefficient of Resistance to Heat Loss in a Building or its Insulation

The "R" value of a material is defined as the material's resistance to heat flow through the material. For purposes of insulation, you might think of "R" value as the opposite of thermal conductance, since it's described as thermal resistance or resistance to heat flow. And you'd be correct. If thermal resistance to heat flow is "resistance" we can say that the thermal conductivity of a material is equal to the reciprocal of its thermal resistance.

More practically, by convention we use thermal resistance or R-value when buying various insulation materials. You will almost always see an "R" value quoted for the material. In general, higher "R" means more resistance to heat loss and therefore lower heating or cooling bills for the building. [Assuming all other fadctors like air leakage are either equal or have been factored into the R-value calculation.]

Mathematically, but in painfully circular reasoning, "R-value" is simply the reciprocal of the two measures of resistance to heat flow "K-value" (R = 1/K) or "U-value" (R_{(whole building)} = 1/U) that we define further below.

What do U and K values have to do with R-values?

As you'll read below "K" measures the heat flow through an individual substance and "U" as most folks use it measures the overall building heat loss by adding all of the various areas and substances together. U-values measure the thermal transmittance of heat in or out of a building and combines heat movement by all principles that are occurring at a building: radiation, convection, and conduction. So you can see that "U" values are more complex but really more complete than "R" values.

Escaping the Circular Reasoning of R=1/K

We can escape the horrible circular reasoning that appears in some writing about heat loss measurements if any one of the three values, R, U, K is defined independently. We'll take a stab at this just below.

The R-value of a material is typically expressed as R [resistance to heat flow] per inch of material thickness. More technically, "R-value" is measured in meter²·°C/Watt [metric system] or ft²·°F·h/Btu [U.S. measurement system].

Materials may be rated in R per inch or R per meter or similar measures.

Here are Some Basic Formulas for Calculating R-Values

R-value = temperature difference [in degF] x area [sq ft] x time [in hours] / heat loss[in BTUs]

Calculating R-Value [U.S. metrics]

R = (Heat Resistance x Degrees F x square feet) / BTUs

or stated in metric: (R-value) = t/k, measured in K·m²·W^{−1}

Definition of & How to Calculate the U value or U-coefficient of heat loss resistance

Computing "K" values tells us the heat loss rate for a specific material, thickness, area, and temperature difference but while we need to be able to calculate "K" values, those alone don't tell us what's going on in an actual building. We need to be able to combine all of the rates of heat loss (or gain) across all of the types of surfaces, insulation, and building material for the whole building - at least for all of its external or perimeter surfaces including roofs, walls, and floors as well as windows and doors. That's where the "U" value makes its appearance.

A building's "U" value or U-coefficient of resistance of heat loss is a related measure of resistance to thermal energy or heat flow out of a building (if it's warmer inside than outside) or conversely the same concept works in a warm climate where air conditioning is in use, except that we expect outside heat to be flowing into the building.

A building's "U" value is much more complete, and therefore useful than "K" values alone because a building's "U" value combines the "K" factors for all of the building's surfaces and materials. In other words, we add the effects of heat loss (or gain), still expressed in the number of BTU's per hour per square foot of area, and still expressed per degree of Fahrenheit of temperature difference and still expressed per inch of thickness of material (just as with "K" values), for all of the substantial areas and surfaces of the exterior of a building's floors, walls, windows, doors, ceilings, or roofs (if cathedral ceilings are present).

To calculate the "U" value, or overall heat loss (or gain if we're air conditioning) for a building, we need to add the "R" values for each material in the structure, and to factor in the total area of each material in the structure. We discuss this procedure in more detail below at "Calculating Heat Loss for a Building".

U-value = BTUs / (hours x Degrees F x Square Feet)

A building's "U" value or U-coefficient of resistance of heat loss is a related measure of resistance to thermal energy or heat flow out of a building (if it's warmer inside than outside) or conversely the same concept works in a warm climate where air conditioning is in use, except that we expect outside heat to be flowing into the building.

A building's "U" value is much more complete, and therefore useful than "K" values alone because a building's "U" value combines the "K" factors for all of the building's surfaces and materials. In other words, we add the effects of heat loss (or gain), still expressed in the number of BTU's per hour per square foot of area, and still expressed per degree of Fahrenheit of temperature difference and still expressed per inch of thickness of material (just as with "K" values), for all of the substantial areas and surfaces of the exterior of a building's floors, walls, windows, doors, ceilings, or roofs (if cathedral ceilings are present).

To calculate the "U" value, or overall heat loss (or gain if we're air conditioning) for a building, we need to add the "R" values for each material in the structure, and to factor in the total area of each material in the structure. We discuss this procedure in more detail below at "Calculating Heat Loss for a Building".

Formulas Used to Calculate the Rate of Building Heat Loss Per Hour for a Building Using it's "R" Values or "U" Values

Formulas and an explanation of how we use R U or K values to determine the rate of heat loss at a building (or heat gain if we are cooling it) are at HEAT LOSS in buildings or within that articler at section Formulas to Calculate the Rate of Heat Loss Per Hour for a Building Using it's "R" Values or "U" Values.

Definition of & How to Calculate the K value or K-coefficient of heat transmission

A building's K value or K-coefficient of heat transmission is one way to express the heat loss in a building. "K" is defined as the number of BTU's of heat moving through any material with these details:

• Per square foot of area of the material
• Per degree Fahrenheit of temperature difference
• Per inch of thickness of the material

So "K" takes a lot of variables into consideration and gives us the rate of heat loss per square foot of building surface, per inch of thickness of material in that building surface, per degree of temperature difference in Fahrenheit, in BTUs per hour.

By "degree of temperature difference in Fahrenheit" we mean that we are taking into consideration the difference in temperature on the two sides of our building surface. For example, if the indoor temperature in a building is 68 deg. F. and the outdoor temperature is 48 deg. F., then we have a 20 degree temperature difference on the two sides of the building (wall or roof for example).

This temperature difference on the two sides of a surface, say an insulated building wall, for example, is very important in understanding how a building loses heat (in the heating season) or gains heat (in the cooling season). That's because the rate of heat transfer through a material increases exponentially as a function of the temperature difference. This is intuitively obvious and is confirmed by physicists.

For example, if the temperatures on either side of a building wall were the same, there would be no heat loss or gain through the building wall. As the temperature difference on either side of that same wall increases, say from one degree of difference to 20 degrees of difference the rate of heat transfer increases.

An interesting version of this heat transfer theory was shared with the author in a class on how to minimize building heating costs when the instructor told us that "the thermal conductivity of finned copper heating baseboard is exponentially greater at higher temperatures".

He was saying that if we ran heating water from our heating boiler through the baseboards at 200 deg.F. we would see much more efficient heat transfer from the heating baseboards into the building. There are other factors involved in heating system efficiency such as the length of boiler "on" cycle (longer is more efficient), so there was more to think about, but the instructor was applying classic heat transfer theory that is reflected in the "K" values of building insulation as we've discussed here.

Computing "K" values tells us the heat loss rate for a specific material, thickness, area, and temperature difference but while we need to be able to calculate "K" values, those alone don't tell us what's going on in an actual building. We need to be able to combine all of the rates of heat loss (or gain) across all of the types of surfaces, insulation, and building material for the whole building - at least for all of its external or perimeter surfaces including roofs, walls, and floors as well as windows and doors. That's where the "U" value makes its appearance.

Sorting out the Definitions of U.S. k-values, lambda or λ values, and European k-values

Note: In the U.S. k-value when discussing the heat loss resistance of window glazing is equivalent to lamda λ value in Europe, and in case that's not confusing enough, an older European k-value (the total insulation value of a building) is currently referred to in Euripe as U-value. You'll recall from our notes above that U-value is a reciprocal or 1/R-value. - Wikipedia web search 03/11/2011 see "Thermal Conducitivity".

To convert U.S. R-values to European U-values:

[ (1 / R-value _USA) x 0.176 ] / 1 = U _Europe

and

U _Europe = [watts / kelvin x meters²]

Questions & Answers regarding this article

Questions & answers about how to calculate building heat loss rate, R-values, Insulation Values, Heating Efficiency.

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HEAT LOSS R U & K VALUE CALCULATION

• Thanks to Sanjiv Malkan for correcting our formula for R-values 3/22/2009.
• Thanks to Steven Muscato for correcting our formula for U-Values 7/31/2009

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• Building Research Council, BRC, nee Small Homes Council, SHC, School of Architecture, University of Illinois at Urbana-Champaign, brc.arch.uiuc.edu. "The Small Homes Council (our original name) was organized in 1944 during the war at the request of the President of the University of Illinois to consider the role of the university in meeting the demand for housing in the United States. Soldiers would be coming home after the war and would be needing good low-cost housing. ... In 1993, the Council became part of the School of Architecture, and since then has been known as the School of Architecture-Building Research Council. ... The Council's researchers answered many critical questions that would affect the quality of the nation's housing stock.
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• "Energy Savers: Whole-House Supply Ventilation Systems [copy on file as /interiors/Energy_Savers_Whole-House_Supply_Vent.pdf ] - ", U.S. Department of Energy energysavers.gov/your_home/insulation_airsealing/index.cfm/mytopic=11880?print
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• Steps and Stairways, Cleo Baldon & Ib Melchior, Rizzoli, 1989.
• "The Dimensions of Stairs", J. M. Fitch et al., Scientific American, October 1974.
• "The Elimination of Unsafe Guardrails, a Progress Report," Elliott O. Stephenson, Building Standards, March-April 1993
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• "Weather-Resistive Barriers [copy on file as /interiors/Weather_Resistant_Barriers_DOE.pdf ] - ", how to select and install housewrap and other types of weather resistive barriers, U.S. DOE
• Weaver: Beaver Board and Upson Board: Beaver Board and Upson Board: History and Conservation of Early Wallboard, Shelby Weaver, APT Bulletin, Vol. 28, No. 2/3 (1997), pp. 71-78, Association for Preservation Technology International (APT), available online at JSTOR.
• What Style Is It?: A Guide to American Architecture, Rev., John C. Poppeliers, S. Allen Chambers, Wiley; Rev Sub edition (October 6, 2003), ISBN-10: 0471250368, ISBN-13: 978-0471250364
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