R-value or thermal Resistance is the basic metric for insulation materials in construction. This R-value is calculated based on several measurements that include the area of a 2-dimensional barrier (wall, insulation batt, polyiso, etc.), the temperature difference between indoor and outdoor, and time.
When homeowners want to know how to calculate R-value, they usually have one of these two things in mind:
- How the R-value is calculated via measurement. Calculating R-value involves ASHRAE making measurements of heat flux over different insulation materials and determining the R-value of insulation based on how quickly (or slowly) this heat flows through the material. That’s how we come up with R-values for different materials; here is an extensive example of R-values for 51 materials used for insulation in construction.
- How to find R-value for walls, attics, and so on. More often, we want to know how to determine the R-value of insulation in our house. Example: How to calculate the R-value of our attic? What is the R-value of walls? To calculate these R-values, we have to specify all the insulation materials used, their thickness, and specific R-value per inch, and sum all individual layers of insulation to get an overall R-value of a wall, attic, ceiling, and so on.
Calculating R-values can be quite complex. That’s why we going to simplify it. We are going to take a structured step-by-step approach to illustrate how to calculate R-value. Here is a quick outline:
- R-value formula. We will start by explaining what R-value actually is by using a formula for calculating the R-value. This involves using thermal conductivity (insulation k-value); R-value is basically an inverse of the k-value (don’t worry, we’re going to explain all of this). On top of that, we will look at how to use the heat flux R-value formula (less often used in practice).
- R-value units. We are going to look at what does R-10, R-20, R-49, and so on actually mean in terms of units used to express R-value.
- How to calculate the R-value of insulation. We will explain how to find the R-value of walls, attics, basements, and so on. This involves summing all the R-values of individual layers that make up these construction elements.
Let’s start with the R-value formula and how is R-value calculated:
R-Value Formula (With k-value And Heat Flux)
Here is the basic R-value equation:
R-Value = 1 / k-Value
As we can see, the R-value is the inverse of the k-value (1 divided by the k-value). To fully understand what R-value is, we have to look at the k-value.
k-value is a measure of thermal conductivity; ie. the ability of heat to be transferred from one end of insulation material to the other end. Inversely, R-value is a measure of thermal resistivity; ie. how can an insulation material prevent the transfer of heat from one end of insulation material to the other end.
This thermal conductivity is a measure of the amount of heat that flows (we have 4 metrics here):
- Through 1 square foot of homogenous material (surface area component).
- This material is 1-inch thick (thickness component).
- In 1 hour (time component).
- For 1 degree of the temperature difference between indoor and outdoor temperatures (temperature component).
Let’s say we have a 1 sq ft and 1-inch thick board. The indoor temperature is 73°F and the outdoor temperature is 72°F (we have a 1-degree difference). We measure how much heat is transferred from indoors to outdoors in 1 hour. If we measure a heat transfer of 1 BTU/hour, that means that thermal conductivity or k-value is equal to 1. That also means that R-value is equal to R-1 since R-value = 1 / k-value; if k-value is 1, we have 1 / 1 = 1.
Alternatively, this RSI-value equation (SI unit using metric units) can be written using heat flux and temperature difference (instead of using the k-value to determine the R-value):
RSI-Value = ΔT / θ
Here the ΔT represents the temperature difference between indoors and outdoors. θ is a measure of heat flux, expressed in W/m2; that is heat is measured not in BTUs but in watts and the surface area is not measured in sq ft but in m2.
Before we check how to find R-value for walls, attics, windows, ceilings, and so on, let’s look at how the R-value equation can be used in practice:
Examples Of How To Calculate R-Values
Let’s say we have a brick wall. The outdoor temperature is 72°F and the indoor temperature is 73°F. We take a 1 sq ft 1-inch thick section of that wall and measure how much heat is transferred from indoors to outdoors in 1 hour. Realistically speaking, we are going to measure about 10 BTU of heat being transferred.
This means that the k-value or thermal conductivity is 10 (since 10 BTU of heat was transferred when we used a 1 sq ft 1-inch thick wall, 1 degree of difference, and 1 hour). Here is how we can calculate the R-value of this wall from the known k-value:
R-Value (Brick Wall) = 1 / k-Value = 1 / 10 = 0.1
That means that such a brick wall has an R-value of R-0.1 (this is for a 1-inch brick wall). If we have a 10-inch thick brick wall, the insulation R-value would be R-1.
Note: ASHRAE makes extensive measurements of heat loss across different construction materials and calculates the R-value for us. They usually present these metrics in big R-value charts.
R-0.1 is a very low insulation R-value. To increase the overall R-value of walls, we use wall insulation. Examples of wall insulation are insulation batts and rigid wall insulation like EPS, XPS, or ISO. You can check some R-values of rigid insulation materials here.
Now, let’s say that we add an insulation material like polyiso. Calculating the R-value of polyiso follows exactly the same procedure as calculating the R-value of a brick wall.
Here is how we can calculate the R-value of polyiso: Let’s say we have 1 sq ft 1-inch polyiso. The temperature difference is 1 degree and we measure the heat loss for 1 hour. Well, ASHRAE makes these measurements, and they tell us such a board of polyiso lost 0.25 BTU in 1 hour. How to determine R-value of polyiso?
Simple. We now know that the k-value of this polyiso board is 0.25. We use the R-value formula to calculate the R-value like this:
R-Value (polyiso) = 1 / k-Value = 1 / 0.25 = 4
As we can see, the calculated R-value of polyiso is R-4. This means that polyiso has 40 times higher insulation capability than simple brick walls; that’s precisely why we use it as insulation material.
R-Value Units (ft2×°F×h/BTU)
In many cases, it’s quite useful to understand what R-10 or R-19 and so on actually means in terms of units.
Units for measuring R-values are ft2×°F×h/BTU. Essentially, the R-value of R-1 is equal to 1 square foot times 1 degree Fahrenheit times 1 hour divided by BTU (British Thermal Units).
R-10 simply tells us that we have 10 ft2×°F×h/BTU insulation. These R-value units seem complex, right? That’s exactly why R-value was invented. It is much simple to write you have R-10 insulation than to write you have 10 ft2×°F×h/BTU insulation.
Now that we understand how R-value is measured, we can check how to determine the R-value of attics, ceilings, walls, and so on:
How To Find R-Value? (Summation Of All R-Values)
Alright, let’s say that you want to calculate the R-value of a wall. We will use some data from the previous two examples.
Example: We have a 12-inch brick wall insulated with a 2.5-inch thick polyiso (this polyiso has an R-value of R-4 per inch). To find the insulation R-value of such a wall, we have to summarize all the R-values of materials that constitute the wall. In this case, we have 2 materials the wall is made out of:
- 12 inches of bricks. Bricks have an R-value of R-0.1 per inch. In a 12-inch brick wall, the contributing R-value is thus R-1.2.
- 2.5 inches of polyiso. We know that polyiso has an R-value of R-4 per inch. That means that the contributing R-value for 2.5-inch ISO is R-10 (since 2.5 inches × R-4 per inch = R-10).
Here is how to calculate the overall R-value of such a wall:
Overall R-value (Brick + ISO Wall) = R-1.2 + R-10 = R-11.2
As you can see, we are adding up all the R-values of individual layers. A general equation for calculating the R-value of these multilayer construction objects looks like this:
Overall R-Value = R-Value (Material 1) + R-Value (Material 2) + R-Value (Material 3) + … + R-Value (Material n)
With this equation, we can calculate the R-value of any construction object. Let’s look at how to find the R-value of the attic as an example:
How To Find R-Value Of Attic
Attics usually have the highest R-values, ranging from R-30 up to R-49. If you have an attic and want to calculate the R-value, you have to summarize all the individual layers that the attic is made out of. Here is an example of attic insulation and construction materials:
- Roof shingles, asphalt, 1 inch thick. R-value = 0.45.
- Closed-cell foam spray, 2 inches thick. R-value = 10.6.
- Fiberglass batts, 2.5 inches thick. R-value = 11.2.
- Gypsum board, 1 inch thick. R-value = 1.1.
- Plywood, 3 inches thick. R-value = 2.9.
- Wood beams, 8 inches thick. R-value = 9.8.
When we have gathered all the materials that make our attic and roof, we can calculate the R-value of the attic like this:
R-Value (Attic) = R-0.45 (Material 1) + R-10.6 (Material 2) + R-11.2 (Material 3) + R-1.1 (Material 4) + R-2.9 (Material 5) + R-9.8 (Material 6) = R-36.05
This is just one example of how you can find an R-value.
The key problem we usually have calculating R-values in our homes is to correctly gather up all the R-values of individual layers that make up the attic, wall, ceilings, you name it. There are no shortcuts or hints here. You just have to check what layers you have and what R-values they have.
Hopefully, now you know how to calculate R-values, you know which units are used to express R-values, and will be able to calculate R-values yourself.