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Foundation insulation, above ground, Maine © Daniel Friedman How to Calculate Building Heat Loss Rate,

Insulation Values & Heating Efficiency, Calculate R, U & K Values for insulation & buildings

The rate of un-wanted heat loss or gain in buildings or the effectiveness of any material serving as insulation can be expressed using several different measures such as R, U and K or in Europe, k-values, or as Kws (Kilowatts per square meter per hour) or in BTUs.

The best measurement of the rate at which heat is transferred through a building floor, walls, ceilings or roofs is best expressed as a U-value, as we explain here.

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.

Our page top photo of above-ground building perimeter & foundation insulation using styrofoam board was observed at a home Maine - Ed.

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- Daniel Friedman, Publisher/Editor/Author - See WHO ARE WE?

Building Heat Loss or Gain Rate Measurements & How to Calculate & Use Them

How to measure heat transmission in materials: definition of R-values, U-values, K-values, BTU, calorie, and rates of heat loss or gain. Building design temperatures & how to use a home energy audit or heat loss analysis. What insulation "R" values should be used in a building insulation?

We also discuss 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.

Article Contents

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

Infrared scan of attic hatch (C) D Friedman S Bliss PEP

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 factors 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.

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]

Calculate the 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 [editing needed]

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 a way to express the heat loss in a building.

K Value is defined as the number of BTU's of heat moving through any material with these details:

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.

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

A building's "U" value can be defined as the rate of unwanted heat loss or gain of an entire building.

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.

Why do we need to compute the "U" value for a building, wall, ceiling, floor or other material? The "U" value is the most broad or comprehensive view of a building's heat loss or gain rate.

Computing "K" values alone 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.

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".

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).

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

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".

Relationship of R, U, and K Values

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.

How to Escape 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 mete Watt [metric system] or h/Btu [U.S. measurement system].

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

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

Note: In the U.S. k-value when discussing the heat loss resistance of window glazing is equivalent to lambda 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 Europe 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 Conductivity".

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]

 

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

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.

How to Calculate Heat Loss & Electric Heater Size in Watts

For a typical building we compute the total building surface area, adding the area in square meters of the roof surfaces, wall surfaces and floor surfaces. Then using simple constants for typical building roofs, floors and walls we calculate the total surface area heat loss.

Watch Out: this is a simplifed example making quite a few assumptions. Your building's heat loss rate may vary significantly depending on your local climate, outdoor weather, wind, and building insulation and infiltration losses.

We add a factor for estimated rate of heat loss through air leaks or deliberate building outdoor ventilation.

Finally, expressing the heat loss in watts we can calculate the necessary electric heater size by multiplying the heat loss rate in Watts times the desired temperature "lift" in degrees.

This example is from Tombling cited below.

Example heat loss calculation

This example, by Tomblilng, assumes a simple building with the following dimensions, U-values, and design temperatures

Building Dimensions in Meters

Building U Values (Watts/M2 deg.C)

Building Design Temperature

Surface Heat Loss Calculation

Assuming 20% for heat loss through ventilation

Heater size required = total heat loss x temperature lift = 2901 x 25 = 72525 W

In this example 4 - 20kW Activair Ace electric fan heaters , 5 - 15kW Activair portable heaters or 4- 21kW Activair wall mounted electric heaters are needed.

References

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 article

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

Also see additional research citations at the page bottom REFERENCES section.

Formula for Evaporation As a Factor in Heat Loss

Useful in understanding heat loss at swimming pools or solar ponds is the formula for evaporation losses, given just below.

Pevaporationa = (25+19Vw) x S x (X - X') x LvA x t/1000c

Where:

In some expert sources that we reviewed we read that in general, evaporation from a pool or pond surface explains about 30% to one half of the total heat loss.

Surface evaoration in summer will remove about 50 mm of water in seven days. In energy this is about 150 Kwh or Kilowatt hours. Higher wind velocity and location in a dry climate such as Arizona will increase the evaoration rate significantly. Use of a pool cover will significantly reduce both evaporation loss of water and heat.

References

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