Construction Design-The Effect of Windows on Wall R-Values

I’m about to start a remodel project of the family room in my home.  Not your normal fresh paint and new floor covering update, but a complete gut down to the stud renovation.  New electrical, new drywall and no more popcorn ceiling.  I’m curious as to what my effective R-value of the exterior walls will be when I’m done with the space.  This includes the windows.  I figured I’d share my calculations with you.  This post is math heavy, if you’d like to skip the math, read the final five paragraphs.

Progress picture of the exterior work on my small cape from 2019.

The needed information

The room is 13′-6″ x 18′-6″, 8 feet tall.  Framing is 16″ on center 2×4 construction.  Two walls are exterior.  There are two windows, one is 7′-6″ x 4′-6″ and a second is 4′-6″ x 4′-6″.  Both have a U-value of .26.  I will be replacing the existing insulation, which is original to the home from 1952, a mineral wool kraft faced batt that is R-7 with a new Rockwool ComfortBatt, R-15.  I will also be installing Siga’s Majrex as my air and vapor control layer.  Interior finishing will be 1/2″ drywall.

Calculating the opaque wall effective R-value

To begin the calculation, I first need to calculate the wall percentages, what percent is wall framing and what percentage is cavity insulation.  My wall is 14% framing and 86% cavity insulation.  The R-values of the 14% framing are:

Wood clapboard siding              R-.80

Board sheathing                           R-.80

2 x 4 wood framing                     R-4.25

Drywall                                              R-.45

Total framing wall R-value      R-6.30

And the 86% cavity insulation R-value:

Wood clapboard siding              R-.80

Board sheathing                           R-.80

Cavity insulation                           R-15.0

Drywall                                              R-.45

Total cavity wall R-value          R-17.05

The next step is to convert the two total wall R-values to U-values.  The math is simple: U-value = 1/R-value.  The R-6.30 of the areas of the wall containing the framing is U-.159 and the area with the cavity insulation is U-.059.

The formula to calculate the effective opaque wall R-value is (framing area x the u-value) + (cavity insulation area x u-value).  (14% or .14 x .159) + (86% or .86 x .059) = U-.022 + U-.051 = U-.073.  To convert the U-.073 back to an R-value. Simply use the formula 1/U-value = R-Value.  My total weighted or effective R-value for the opaque wall area is R-13.70.  Much better than what I calculated my current wall at, which is R-5.9.

Adding the windows

I’ve calculated the total area of windows in my living room at 21% of the total wall area and they have a U-value of .26.  (Better than average in my market.)  We use the same formulas to calculate the total weighted or effective R-value of the walls including the windows as we did for calculating the opaque wall R-value.

(79% or .79 x U-.073) + (21% or.21 x U-.26) = U-.113, convert to R-value 1/.133 = R-7.52.

Wow!  I started with thinking I would have an R-15 wall.  After the calculations, my effective R-value of the opaque wall, or wall without the windows was R-13.70.  Add in better than average windows, and we are down to a total effective R-value of 7.52.  When I purchased the home originally, my overall effective R-value for this room was closer to R-4.5.

Options to improve the overall R-value

There are three options to increase my overall wall insulation values from the calculated R-7.52.  The first is to add more insulation, maybe by using continuous exterior insulation.  Let’s say I add 3 inches of Rockwool’s ComfortBoard to the outside of the home.  That product has an R-value of 4.2 per inch, so I would be gaining R-12.6 more resistance to heat flow over my current plan.  Because it is added to the exterior, the entire R-value is added to the effective opaque portion of the wall.  That R-value now becomes R-26.3, the U-value is .038.  Recalculating the math for the effective R-value including the windows, we get R-11.8.  A nice increase over my wall without the exterior insulation.

The second option is to have less window area.  Let’s say I reduce the amount of window area from 21% to 15%, this would increase my effective overall R-value from R-7.52 to R-9.90.  An improvement, but the exterior insulation was greater.  Plus, I’ve loss some potential heat gain from the sun during the winter months by reducing my window size.

The third option is to install better windows.  If I improved the windows to units having a U-.15, or R-6.67, the total effective R-value goes up to R-11.5.  Almost the same as adding exterior insulation.

If I want the best R-value given my existing wall conditions, adding 3-inches of exterior insulation or replacing my better than average windows to extremely good windows are my best two options…I’m not doing either, my effective R-7.52 plus the gains I’ll be making in my air sealing will almost double what I currently have.  In my 70+ year old cape, that’s good enough for me.

2 Replies to “Construction Design-The Effect of Windows on Wall R-Values”

  1. Hi, Randy

    If I might ask, what is your heating fuel? Cost of heat is high these days if one is heating with oil ($4.90 per gallon) and will be part of my calculation when upgrading our farmhouse. Looking at the different options here, electricity is currently at 10.9 kWh so electric heat is about $32 per million Btu’s and heating oil is about $41 with an 85% efficient furnace. Our electric provider (Lake Region) has mentioned a possible rate increase due to higher natural gas prices used in generating electricity. Can’t seem to get away from the higher fossil fuel costs. They do have some off peak options including electric thermal storage that I would consider if we change out to an electric boiler.

    1. Hey Doug,
      Sorry for the slow response. My house has natural gas, and I added a standard air source heat pump this past summer. The heat pump cuts out at 20°F with the gas taking over then. So far this fall, the heat pump has been the main heat source. Electricity rates in Grand Rapids are tiered, the first 500 kWh are $.0888, after that, they rise to $.1144. There is also something called a power purchase adjustment which adds an additional $.01583 per kWh on all consumption. The local rural electric coop I contract energy audits with is closer to $.15 per kWh. I recently had a meeting with them, they are pushing thermal storage using ETS. If you have that option, look into Steffes ETS units, they are made in North Dakota. The local REA offers at least a 50% rate reduction for heating with ETS, putting the operating cost close to natural gas. Pair it with a cold climate air source heat pump, very nice system. Storage heating programs are only available with the rural electric coops in my area, the city of Grand Rapids only offers a water heating program that takes $5 off your monthly electric bill. I would think with the projected stresses on the grid, we would start seeing some of these off-peak programs being offered everywhere, but so far, it’s just the REA’s that seem to be ahead of the game.

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