Enter the area to insulate, the insulation thickness, the package size and the waste factor. The thermal conductivity and the price can be left blank (then those items are not calculated).
A waste factor of 5–10% is common. Use more for walls with many cutouts around wiring, pipes and blocking, and less for batts simply laid on an attic floor. If left blank, 0% (no waste) is used.
Result and figure
Enter the area to insulate, the thickness and the product size in the fields on the left and press "Calculate". The result will appear here.
Table of Contents
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What you can do on this page
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What is this calculation used for?
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How to Use
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Formulas and figures
-
Symbols and terms
-
Good to know before you start
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How to calculate it in Excel
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How to calculate it in Google Sheets
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How to calculate it in Python
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How to write it in LaTeX and other math languages (copy and paste)
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How to have ChatGPT do the calculation
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DataChef Features
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Related Features
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NumberChef Calculators List
What you can do on this page
- Enter the area to insulate (as length × width or as a total area), the insulation thickness and the package size, and you get the number of batts and bags you need on the spot
- Enter the package as "batt width × length × batts per bag" or as "coverage per bag" (ft²). The area needed with a waste factor for cutouts and scraps, and the bags before rounding up, are shown too
- You also see the area the bags will actually cover and how much is left over, so it works backward too: "how many square feet will these bags cover?"
- Enter the thermal conductivity \(k\) (or pick a typical value for the material from the list), and the R-value for that thickness, \(R = t \div k\), is calculated too
- Enter a price (per bag or per ft²) to get the material cost. A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page
The number of batts and bags is an estimate based on area. The amount of scrap depends on the stud spacing and the cutouts around wiring, pipes and blocking, so a waste factor adds some extra. For walls, it is easiest to find the net area (the walls minus windows and doors) first with the "Wall, Ceiling and Floor Area Calculator" and enter it as the total area. The thermal conductivity values in the list are typical figures, so use the value on the product label or data sheet when you have it.
What is this calculation used for?
Adding insulation in the attic (DIY)
Adding insulation on the attic floor is one of the most popular DIY energy upgrades, and the U.S. Department of Energy recommends about R-30 to R-60 for attics, depending on the climate zone. For the attic over an 18 ft × 12 ft room (216 ft²) with a 5% waste factor, the area needed is \(216 \times 1.05 = 226.8\) ft². If, for example, each bag covers 60 ft² at the depth you want, you need \(\lceil 226.8 \div 60 \rceil = \lceil 3.78 \rceil = 4\) bags.
Knowing the number of bags helps you plan the trip to the home center. Attics are dark with poor footing, so step only on the joists (never between them, or you can break through the ceiling), and wear a dust mask, gloves and long sleeves.
Working out batts for walls during a remodel
When you open up walls and insulate them, the area to insulate is the net wall area after subtracting windows and doors. For the two exterior walls of a corner bedroom, 12 ft and 14 ft long and 8 ft high, the wall area is \((12 + 14) \times 8 = 208\) ft². Subtract two 3 ft × 5 ft windows (30 ft²) to get 178 ft². With a 10% waste factor and R-13 bags that cover 106.56 ft², you need \(178 \times 1.1 = 195.8\) ft², and \(195.8 \div 106.56 \approx 1.84\), rounded up to 2 bags.
Walls have many cutouts around wiring, pipes, electrical boxes and blocking, so allowing more waste than for an attic keeps you from running short halfway. You can find the net wall area with the "Wall, Ceiling and Floor Area Calculator".
Counting rigid foam boards for basement walls
The same formula works for rigid foam boards on basement walls. For 36 ft of wall 7 ft high (252 ft²) with 4 ft × 8 ft boards (32 ft² each) and no waste factor, you need \(\lceil 252 \div 32 \rceil = \lceil 7.875 \rceil = 8\) boards.
Foam boards are usually sold one at a time, so set "batts per bag" to 1, and the number of bags equals the number of boards. Boards are cut around windows, pipes and outlets, so in practice allow a waste factor for the cutouts too.
Comparing materials and thicknesses by R-value
Which insulates better, 3.5 in of high-performance fiberglass (typical k = 0.263) or 2 in of XPS foam board (typical k = 0.194)? Compare the R-values: \(3.5 \div 0.263 \approx 13.3\) for the first and \(2 \div 0.194 \approx 10.3\) for the second, so in this example the 3.5 in fiberglass insulates better.
The same formula also tells you that where there is no room for thickness, a material with a lower conductivity gets you the same R-value in less space. Conductivity differs by product, so use the product data sheet values when you compare.
Checking the quantities in a quote
An insulation quote often lists the area, the R-value and the number of bags, such as "attic, R-38, 1,200 sq ft, 25 bags". If you know the area and the coverage per bag, these formulas let you follow where the number of bags comes from, and ask how much waste the contractor has allowed for.
A real quote also covers air sealing, baffles, vapor retarder and labor, so the number of bags alone does not tell you whether the price is fair.
Formulas and figures
Area to insulate
Standard notation
(the usual math form)
\(S\)
\(=\)
\(L\)
\(\times\)
\(W\)
\(S\)
\(=\)
\(P\)
\(\times\)
\(H\)
In words
(symbols replaced with words)
③
\(S\): area to insulate
\(=\)
①
\(L\): length of the space
\(\times\)
②
\(W\): width of the space
\(S\): area to insulate
\(=\)
④
\(P\): total wall length
\(\times\)
⑤
\(H\): wall height
The formula in words
①
Take the
\(L\): length of the space
②
multiply it by the
\(W\): width of the space
③
and you get the
\(S\): area to insulate
④
For walls, multiply the
\(P\): total wall length
by the
⑤
\(H\): wall height
to get the area (then subtract windows and doors)
Quick example
The area of the attic floor over an 18 ft × 12 ft room, which is the same as a wall 27 ft long and 8 ft high, is
\(S\): area to insulate
\(=\)
length (18 ft)
\(\times\)
width (12 ft)
\(18 \times 12 = 216\,\mathrm{ft^2}\)
\(27 \times 8 = 216\,\mathrm{ft^2}\)
Key idea
For batts laid in an attic or under a floor, the area to insulate is the floor area of the room (measured wall to wall). For walls, it is "the total wall length × the height" minus the openings such as windows and doors. You can find the net area of all the walls with the "Wall, Ceiling and Floor Area Calculator" and enter it here as the total area. For exterior walls, count only the walls that face the outside (or an unheated space such as a garage).
Area needed with waste
Figure
Standard notation
(the usual math form)
\(S_r\)
\(=\)
\(S\)
\(\times\)
\((\)
\(1\)
\(+\)
\(r\)
\()\)
In words
(symbols replaced with words)
③
\(S_r\): area needed with waste
\(=\)
①
\(S\): area to insulate
\(\times\)
\((\)
\(1\)
\(+\)
②
\(r\): waste factor
\()\)
The formula in words
①
Take the
\(S\): area to insulate
②
multiply it by "1 plus the
\(r\): waste factor
" (1.05 for 5%)
③
and you get the
\(S_r\): area needed with waste
Quick example
The area needed for 216 ft² with a 5% waste factor is
\(S_r\): area needed
\(=\)
area to insulate (216 ft²)
\(\times\)
\((\)
\(1\)
\(+\)
waste factor (0.05)
\()\)
\(216 \times (1 + 0.05) = 216 \times 1.05 = 226.8\,\mathrm{ft^2}\)
Key idea
Insulation is cut and fitted between studs, joists and rafters, so the exact area is not enough. Batts have to be cut around pipes, wiring, blocking and electrical boxes, and the pieces cut off at the ends cannot always be used elsewhere. So the amount needed is taken as "the area plus a waste factor". A waste factor of 5–10% is common: less for batts simply laid on an attic floor, more for walls with a lot of wiring, pipes and blocking. You enter the waste factor in %, and the formula uses it as a decimal (5% = 0.05).
Area of one batt and coverage per bag
Standard notation
(the usual math form)
\(a\)
\(=\)
\(w\)
\(\times\)
\(l\)
\(A\)
\(=\)
\(a\)
\(\times\)
\(k\)
In words
(symbols replaced with words)
③
\(a\): area of one batt
\(=\)
①
\(w\): batt width
\(\times\)
②
\(l\): batt length
⑤
\(A\): coverage per bag
\(=\)
\(a\): area of one batt
\(\times\)
④
\(k\): batts per bag
The formula in words
①
Take the
\(w\): batt width
②
multiply it by the
\(l\): batt length
③
and you get the
\(a\): area of one batt
④
Multiply that by the
\(k\): batts per bag
⑤
and you get the
\(A\): coverage per bag
Quick example
For R-13 fiberglass batts 15 in wide and 93 in long, 11 batts per bag, the area of one batt and the coverage per bag are
\(A\): coverage per bag
\(=\)
width (15 in)
\(\times\)
length (93 in)
\(\times\)
batts (11)
\(15 \times 93 \div 144 = 9.6875\,\mathrm{ft^2}\)
\(9.6875 \times 11 = 106.5625\,\mathrm{ft^2}\)
Key idea
Batt sizes are given in inches, so to get square feet, divide width × length in square inches by 144 (1 ft² = 12 in × 12 in = 144 in²). This calculator converts the units for you. Batts are made to fit the stud spacing: 15 in wide for studs 16 in on center, and 23 in wide for 24 in on center. A 93 in batt fits a standard 8 ft wall, which has about 93 in between the plates. The coverage printed on the package (106.56 sq ft for this bag) is width × length × count, so if the package gives the coverage, you can skip this formula and enter it as "coverage per bag".
Number of batts needed
Figure
Standard notation
(the usual math form)
\(N\)
\(=\)
\(\lceil\)
\(S_r\)
\(\div\)
\(a\)
\(\rceil\)
In words
(symbols replaced with words)
④
\(N\): batts needed
\(=\)
③
\(\lceil\)
①
\(S_r\): area needed with waste
\(\div\)
②
\(a\): area of one batt
\(\rceil\)
The formula in words
①
Take the
\(S_r\): area needed with waste
②
divide it by the
\(a\): area of one batt
to see how many batts' worth it is
③
round up to the next whole number (the symbol \(\lceil\ \rceil\) means "round up")
④
and you get the
\(N\): batts needed
Quick example
The number of batts needed to fill 226.8 ft² (with waste) with 9.6875 ft² batts is
\(N\): batts needed
\(=\)
\(\lceil\)
area needed (226.8 ft²)
\(\div\)
area of one batt (9.6875 ft²)
\(\rceil\)
\(226.8 \div 9.6875 \approx 23.41\)
\(\lceil 23.41 \rceil = 24\)
Key idea
Batts come only in whole pieces, so if the division leaves a decimal, always round up (23.41 batts → 24). Rounding down or to the nearest whole number would leave you short. The symbol for rounding up is \(\lceil\ \rceil\) (the ceiling function). Set the waste factor to 0 to get the net number of batts, and compare to see how many batts the waste factor adds.
Number of bags needed
Standard notation
(the usual math form)
\(B\)
\(=\)
\(\lceil\)
\(N\)
\(\div\)
\(k\)
\(\rceil\)
\(B\)
\(=\)
\(\lceil\)
\(S_r\)
\(\div\)
\(A\)
\(\rceil\)
In words
(symbols replaced with words)
③
\(B\): bags needed
\(=\)
\(\lceil\)
①
\(N\): batts needed
\(\div\)
②
\(k\): batts per bag
\(\rceil\)
\(B\): bags needed
\(=\)
\(\lceil\)
④
\(S_r\): area needed with waste
\(\div\)
⑤
\(A\): coverage per bag
\(\rceil\)
The formula in words
①
Take the
\(N\): batts needed
②
divide it by the
\(k\): batts per bag
and round up
③
and you get the
\(B\): bags needed
④
With the coverage per bag, take the
\(S_r\): area needed with waste
⑤
divide it by the
\(A\): coverage per bag
and round up to get the number of bags
Quick example
If you need 24 batts and they are sold 11 to a bag, the number of bags needed is
\(B\): bags needed
\(=\)
\(\lceil\)
batts needed (24)
\(\div\)
batts per bag (11)
\(\rceil\)
\(24 \div 11 \approx 2.18\)
\(\lceil 2.18 \rceil = 3\)
Key idea
Fiberglass and mineral wool batts are sold several to a bag, so the number of bags is rounded up just like the number of batts. If you buy rigid foam boards one at a time, set "batts per bag" to 1, and the number of bags equals the number of boards. For products that list a coverage per bag, divide the area needed with waste by the coverage per bag and round up, as in the second line. This calculator also shows the value before rounding up (2.18 in the example), so you can see how much the rounding adds.
Area the bags cover and what is left over
Standard notation
(the usual math form)
\(S_c\)
\(=\)
\(B\)
\(\times\)
\(A\)
\(D\)
\(=\)
\(S_c\)
\(-\)
\(S\)
In words
(symbols replaced with words)
③
\(S_c\): area covered
\(=\)
①
\(B\): bags needed
\(\times\)
②
\(A\): coverage per bag
⑤
\(D\): left over
\(=\)
\(S_c\): area covered
\(-\)
④
\(S\): area to insulate
The formula in words
①
Take the
\(B\): bags needed
②
multiply it by the
\(A\): coverage per bag
③
to get the
\(S_c\): area covered
, then
④
subtract the
\(S\): area to insulate
⑤
and you get the
\(D\): left over
Quick example
If you buy 3 bags that cover 106.5625 ft² each for 216 ft² of area, the area covered and what is left over are
\(S_c\): area covered
\(=\)
bags (3)
\(\times\)
coverage per bag (106.5625 ft²)
\(3 \times 106.5625 = 319.6875\,\mathrm{ft^2}\)
\(319.6875 - 216 = 103.6875\,\mathrm{ft^2}\)
Key idea
Because the bags are rounded up, you end up with more insulation than the area needs. The area covered also works backward: for example, "how much attic floor can the 2 spare bags cover?" is \(B \times A\). The amount left over \(D\) includes the waste factor too. Here it is almost a whole bag, because 24 batts is just over 2 bags of 11. When the amount left over is large, think about how many cutouts and scraps you really expect before deciding how much to buy. Many home centers also accept returns of unopened bags.
Volume of insulation
Standard notation
(the usual math form)
\(V\)
\(=\)
\(S\)
\(\times\)
\(t\)
In words
(symbols replaced with words)
③
\(V\): volume
\(=\)
①
\(S\): area to insulate
\(\times\)
②
\(t\): thickness
The formula in words
①
Take the
\(S\): area to insulate
②
multiply it by the
\(t\): thickness (in the same unit, feet)
③
and you get the
\(V\): volume
Quick example
The volume of 3.5 in (= 3.5/12 ft) insulation over 216 ft² is
\(V\): volume
\(=\)
area to insulate (216 ft²)
\(\times\)
thickness (3.5 in)
\(216 \times 3.5 \div 12 = 63\,\mathrm{ft^3}\)
Key idea
Area (ft²) times thickness (ft) gives volume (ft³). The thickness is entered in inches, so divide by 12 to turn it into feet before multiplying (3.5 in → 0.2917 ft). Volume is useful for materials measured by volume and density, such as blown-in cellulose (pounds per cubic foot), and for estimating how much space the material takes up to haul and store. Bagged batts are compressed, so the bag size does not match the installed volume.
R-value (thermal resistance)
Figure
Standard notation
(the usual math form)
\(R\)
\(=\)
\(t\)
\(\div\)
\(\lambda\)
In words
(symbols replaced with words)
③
\(R\): R-value
\(=\)
①
\(t\): thickness
\(\div\)
②
\(\lambda\): thermal conductivity (k)
The formula in words
①
Take the
\(t\): thickness (in)
②
divide it by the
\(\lambda\): thermal conductivity (k)
③
and you get the
\(R\): R-value
(larger for thicker material and for lower conductivity)
Quick example
The R-value of 3.5 in high-performance fiberglass (typical conductivity k = 0.263 BTU·in/(h·ft²·°F)) is
\(R\): R-value
\(=\)
thickness (3.5 in)
\(\div\)
conductivity (0.263)
\(3.5 \div 0.263 \approx 13.3\ \ (\text{R-}13)\)
Key idea
Thermal conductivity, written \(k\) in the US (\(\lambda\), lambda, in metric countries), tells how easily heat passes through a material. The smaller it is, the better the material insulates. But the same material twice as thick lets through half as much heat. The R-value \(R\) combines both: it tells how well a layer of a given thickness resists heat, and it is the thickness divided by the conductivity. In the US it is given in h·ft²·°F/BTU and printed on the package as "R-13", "R-19" and so on. If two layers have the same R-value, they insulate equally well even if the materials differ, so you can compare "2 in of XPS foam board" with "3.5 in of fiberglass". The conductivity values in the list are typical figures, so use the R-value on the product label when you have it. The U.S. Department of Energy recommends about R-30 to R-60 for attics, depending on the climate zone. The performance of a whole wall also depends on the studs and the other layers, so the R-value of one insulation layer alone does not tell the whole story.
Estimated cost
Standard notation
(the usual math form)
\(T\)
\(=\)
\(u\)
\(\times\)
\(Q\)
In words
(symbols replaced with words)
③
\(T\): estimated cost
\(=\)
①
\(u\): unit price
\(\times\)
②
\(Q\): quantity
The formula in words
①
Take the
\(u\): unit price (per bag or per ft²)
②
multiply it by the
\(Q\): quantity (bags or area, to match the price)
③
and you get the
\(T\): estimated cost
Quick example
The cost of 3 bags of insulation at $50 a bag is
\(T\): estimated cost
\(=\)
unit price ($50)
\(\times\)
quantity (3 bags)
\(50 \times 3 = 150\)
Key idea
The key is to match the units of the price and the quantity. For a price per bag, multiply by the number of bags \(B\). For a price per square foot, multiply by the area needed with waste \(S_r\). Besides the insulation itself, vapor retarder, sealant, staples, protective gear and labor cost extra.
To find how much insulation you need, round up "area × (1 + waste factor) ÷ area of one batt" to get the number of batts, then divide by the batts per bag and round up to get the number of bags. The waste factor covers cutouts and scraps, usually 5–10%. Working backward from the bags to the area they cover shows what is left over, and dividing the thickness by the conductivity gives the R-value, which lets you compare how well different materials insulate.
Symbols and terms
Symbols
| \(S\) | S | The area to insulate (the net size of the space). Said to come from "square" or "surface". Enter it as length × width or as a total area. |
| \(L\), \(W\) | L, W | The length and width of the space (ft), from "length" and "width". Measure wall to wall. |
| \(P\) | P | The total length of the walls to insulate (ft). The letter comes from "perimeter". |
| \(H\) | H | The wall height (ft), from "height". 8 ft is common for rooms in US houses. |
| \(r\) | r (lowercase) | The waste factor, from "rate". The value entered in % is divided by 100 before use (5% → 0.05). |
| \(S_r\) | S sub r | The area needed with waste: the area \(S\) plus the waste factor \(r\). Found with \(S_r = S \times (1 + r)\). |
| \(w\), \(l\) | w, l (lowercase) | The width and length of one batt. Lowercase, to tell them apart from the room \(L\) and \(W\). Batt sizes are in inches (for example, 15 in × 93 in). |
| \(a\) | a | The area of one batt, from "area". Found with \(a = w \times l\). |
| \(k\) | k | The number of batts in one bag (package). (On this page, the thermal conductivity k is written \(\lambda\) in the formulas to keep the two apart.) |
| \(A\) | A (capital) | The coverage per bag. Found with \(A = a \times k\), or enter the coverage printed on the package directly. |
| \(N\) | N (capital) | The number of batts needed, from "number". Found with \(N = \lceil S_r \div a \rceil\). |
| \(B\) | B | The number of bags needed, from "bag". Found with \(B = \lceil N \div k \rceil\) (or \(\lceil S_r \div A \rceil\)). |
| \(S_c\) | S sub c | The area the bags cover. Found with \(S_c = B \times A\). The c stands for "cover". |
| \(D\) | D | What is left over beyond the area to insulate. \(D = S_c - S\), from "difference". |
| \(t\) | t | The insulation thickness, from "thickness". Entered in inches (for example, 3.5 in for a 2×4 wall). |
| \(V\) | V | The volume of insulation (ft³), from "volume". Found with \(V = S \times t\). |
| \(\lambda\) | lambda | The thermal conductivity. In the US it is usually written k, in BTU·in/(h·ft²·°F); metric countries use the Greek letter lambda, in W/(m·K). The smaller it is, the better the material insulates. |
| \(R\) | R (capital) | The R-value (thermal resistance), from "resistance". Found with \(R = t \div \lambda\). In the US it is in h·ft²·°F/BTU and printed as "R-13" and so on. The larger it is, the better the layer insulates. |
| \(u\) | u | The unit price of the insulation (per bag or per ft²), from "unit price". |
| \(Q\) | Q | The quantity that matches the price unit (bags or area), from "quantity". |
| \(T\) | T (capital) | The estimated cost (the insulation only, without vapor retarder or labor), from "total". |
| \(\lceil x \rceil\) | ceiling of x | The ceiling function: rounds up to the next whole number. (Examples: \(\lceil 23.41 \rceil = 24\), \(\lceil 2 \rceil = 2\)) |
Terms
| insulation | Material placed in walls, ceilings and floors to slow the flow of heat between inside and outside. The main types are fibers (fiberglass, mineral wool, cellulose) and foam plastics (polystyrene, polyurethane and polyiso, phenolic foam). |
| fiberglass | Insulation made of glass spun into fine fibers, like cotton. It is inexpensive and the most widely used. Batts come in widths that fit the stud spacing (15 in and 23 in) and are sold by R-value, such as R-13, R-15 and R-19 for walls and R-30 and up for attics. |
| mineral wool | Insulation made by melting rock such as basalt and spinning it into fibers (also called rock wool). It is a fiber type like fiberglass, and it resists fire well. |
| extruded polystyrene | Rigid foam board made by pushing foamed polystyrene out into sheets (XPS), often pink or blue. It resists water and is stiff, so it is often used on basement walls, under slabs and around foundations. About R-5 per inch. |
| expanded polystyrene | Rigid foam made by expanding polystyrene beads and molding them together (EPS), the white foam also used for packaging. It is lighter and cheaper than XPS, and its conductivity depends on its density. |
| polyurethane foam | Foam insulation made from polyurethane. Boards (and polyiso boards) have low conductivity and work where there is little room for thickness. It is also sprayed on site as spray foam, which often has a higher conductivity than boards, so enter the value from the product data sheet rather than the board value in the list. |
| phenolic foam | Rigid foam board made from phenolic resin. It has one of the lowest conductivities among common insulation, and is chosen for a high R-value in a thin layer. |
| cellulose | Insulation made from recycled paper such as newspaper, turned into fibers. It is mostly blown into attics and walls with a machine, and the amount comes from the volume (area × depth) and the installed density (pounds per cubic foot). |
| thermal conductivity | How easily heat passes through a material, called the k-value in the US (BTU·in/(h·ft²·°F)) and lambda in metric (W/(m·K)). The smaller it is, the better the material insulates. It differs by density and product, so use the product data sheet value. |
| R-value | How well a layer of a given thickness resists heat, found by dividing the thickness by the conductivity. In the US it is in h·ft²·°F/BTU (R-13, R-30 and so on); the metric R-value in m²·K/W is about 5.68 times smaller. The larger it is, the better the layer insulates, and it lets you compare different materials on the same scale. |
| waste factor | The extra share of material added to the area for cutouts, scraps and a spare. 5–10% is common, more for walls with a lot of wiring, pipes and blocking. |
| scrap | The pieces left over when batts are cut to fit between studs or at the ends. Not all of them can be used elsewhere, so the waste factor allows for them. |
| net area | The area without any extra or spare. On this page, "Area to insulate (net)" is the area before the waste factor. |
| inside dimensions | Measurements from the inside face of one wall to the inside face of the opposite wall. The area of an attic floor or a floor is measured this way. |
| stud | One of the vertical framing members in a wall, usually 2×4 or 2×6 lumber set 16 in or 24 in on center. Wall insulation fits between the studs, so batts are made in widths that match the spacing. |
| joist | One of the horizontal framing members that hold up a floor or a ceiling, set at regular spacing. Insulation under a floor or on an attic floor fits between the joists. |
| blocking | Short pieces of lumber fixed between studs or joists for support, fire blocking or mounting. Insulation has to be cut around them, which is one reason scraps are produced. |
| openings | Windows, doors and other holes in a wall. The wall area to insulate is the whole wall area minus the openings. |
| flange | The paper edges on both sides of a kraft-faced batt. They are stapled to the sides or faces of the studs, and the listed batt width usually matches the stud spacing. |
| cavity insulation | Insulation fitted into the spaces between studs, joists or rafters. It is the most common method in wood-frame houses, and the batt count on this page assumes it. Foam boards fastened over the outside of the framing are called continuous insulation. |
| area to insulate | The size of the space to fill with insulation. For an attic or a floor, the floor area of the room; for walls, the net wall area after subtracting windows, doors and other openings. |
| rounding up | Changing a value with a decimal part to the next whole number. Insulation comes only in whole batts and bags, so always round up the number of batts and bags. |
| density | The weight per unit of volume (pounds per cubic foot, or kg/m³). For fiberglass, a higher density means the fibers are packed more tightly and the material insulates somewhat better per inch. |
Good to know before you start
Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.
| Area of a rectangle (Grades 3–4) |
|
| Volume of a rectangular prism (Grade 5) |
|
| Converting units of length, area and volume (Grades 4–6) |
|
| Multiplying and dividing decimals (Grades 5–6) |
|
| Percentages (Grades 6–7) |
|
| Rounding (Grades 3–4) |
|
| How heat moves (elementary and middle school science) |
|
How to calculate it in Excel
Copy the whole table below and paste it into cell A1 in Excel. It works as is.
Table to find the area to insulate
| Length (ft) | 18 |
| Width (ft) | 12 |
| Area to insulate (ft²) | =B1*B2 |
Table to find the area needed with waste
| Area to insulate (ft²) | 216 |
| Waste factor (%) | 5 |
| Area needed with waste (ft²) | =B1*(1+B2/100) |
Table to find the area of one batt and the coverage per bag
| Batt width (in) | 15 |
| Batt length (in) | 93 |
| Batts per bag | 11 |
| Area of one batt (ft²) | =B1*B2/144 |
| Coverage per bag (ft²) | =B4*B3 |
Table to find the number of batts needed
| Area needed with waste (ft²) | 226.8 |
| Area of one batt (ft²) | 9.6875 |
| Batts needed | =ROUNDUP(B1/B2,0) |
Table to find the number of bags needed
| Batts needed | 24 |
| Batts per bag | 11 |
| Bags needed | =ROUNDUP(B1/B2,0) |
Table to find the area covered and what is left over
| Bags | 3 |
| Coverage per bag (ft²) | 106.5625 |
| Area to insulate (ft²) | 216 |
| Area covered (ft²) | =B1*B2 |
| Left over (ft²) | =B4-B3 |
Table to find the volume
| Area to insulate (ft²) | 216 |
| Thickness (in) | 3.5 |
| Volume (ft³) | =B1*B2/12 |
Table to find the R-value
| Thickness (in) | 3.5 |
| Thermal conductivity k (BTU·in/(h·ft²·°F)) | 0.263 |
| R-value (h·ft²·°F/BTU) | =B1/B2 |
Table to find the estimated cost
| Unit price ($) | 50 |
| Quantity (bags or ft²) | 3 |
| Estimated cost ($) | =B1*B2 |
After pasting, the upper rows in column B are your inputs and the last rows are calculated automatically.
"ROUNDUP(value, 0)" rounds up to a whole number (the ⌈ ⌉ in the formulas).
The third table divides the batt size in square inches by "/144" to get square feet (B4 shows 9.6875 and B5 shows 106.5625).
B3 in the first table shows 216, B3 in the second 226.8, B3 in the fourth 24 batts, B3 in the fifth 3 bags, the sixth table 319.6875 and 103.6875, B3 in the seventh 63, B3 in the eighth about 13.31 (R-13), and B3 in the ninth 150. Just replace the numbers in column B with your own.
"ROUNDUP(value, 0)" rounds up to a whole number (the ⌈ ⌉ in the formulas).
The third table divides the batt size in square inches by "/144" to get square feet (B4 shows 9.6875 and B5 shows 106.5625).
B3 in the first table shows 216, B3 in the second 226.8, B3 in the fourth 24 batts, B3 in the fifth 3 bags, the sixth table 319.6875 and 103.6875, B3 in the seventh 63, B3 in the eighth about 13.31 (R-13), and B3 in the ninth 150. Just replace the numbers in column B with your own.
How to calculate it in Google Sheets
Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.
Table to find the area to insulate
| Length (ft) | 18 |
| Width (ft) | 12 |
| Area to insulate (ft²) | =B1*B2 |
Table to find the area needed with waste
| Area to insulate (ft²) | 216 |
| Waste factor (%) | 5 |
| Area needed with waste (ft²) | =B1*(1+B2/100) |
Table to find the area of one batt and the coverage per bag
| Batt width (in) | 15 |
| Batt length (in) | 93 |
| Batts per bag | 11 |
| Area of one batt (ft²) | =B1*B2/144 |
| Coverage per bag (ft²) | =B4*B3 |
Table to find the number of batts needed
| Area needed with waste (ft²) | 226.8 |
| Area of one batt (ft²) | 9.6875 |
| Batts needed | =ROUNDUP(B1/B2,0) |
Table to find the number of bags needed
| Batts needed | 24 |
| Batts per bag | 11 |
| Bags needed | =ROUNDUP(B1/B2,0) |
Table to find the area covered and what is left over
| Bags | 3 |
| Coverage per bag (ft²) | 106.5625 |
| Area to insulate (ft²) | 216 |
| Area covered (ft²) | =B1*B2 |
| Left over (ft²) | =B4-B3 |
Table to find the volume
| Area to insulate (ft²) | 216 |
| Thickness (in) | 3.5 |
| Volume (ft³) | =B1*B2/12 |
Table to find the R-value
| Thickness (in) | 3.5 |
| Thermal conductivity k (BTU·in/(h·ft²·°F)) | 0.263 |
| R-value (h·ft²·°F/BTU) | =B1/B2 |
Table to find the estimated cost
| Unit price ($) | 50 |
| Quantity (bags or ft²) | 3 |
| Estimated cost ($) | =B1*B2 |
The same formulas as in Excel (including the ROUNDUP function) work as is. Copy the whole table, paste it into cell A1, and replace the numbers in column B with your own.
How to calculate it in Python
import math
room_length_ft = 18 # length of the space (ft)
room_width_ft = 12 # width of the space (ft)
thickness_in = 3.5 # insulation thickness (in)
batt_width_in = 15 # batt width (in)
batt_length_in = 93 # batt length (in)
batts_per_bag = 11 # batts per bag
waste_percent = 5 # waste factor (%)
k_value = 0.263 # thermal conductivity k (BTU·in/(h·ft²·°F)). Use the product data sheet value
price_per_bag = 50 # price per bag ($)
area_ft2 = room_length_ft * room_width_ft # area to insulate (net)
required_area_ft2 = area_ft2 * (1 + waste_percent / 100) # area needed with waste
batt_area_ft2 = batt_width_in * batt_length_in / 144 # area of one batt (in² to ft²)
bag_area_ft2 = batt_area_ft2 * batts_per_bag # coverage per bag
batts_needed = math.ceil(required_area_ft2 / batt_area_ft2) # batts needed (rounded up)
bags_needed = math.ceil(batts_needed / batts_per_bag) # bags needed (rounded up)
coverable_area_ft2 = bags_needed * bag_area_ft2 # area these bags cover
surplus_area_ft2 = coverable_area_ft2 - area_ft2 # left over beyond the area
volume_ft3 = area_ft2 * thickness_in / 12 # volume (ft³)
r_value = thickness_in / k_value # R-value (h·ft²·°F/BTU)
cost = bags_needed * price_per_bag # estimated cost ($)
print(f"Area to insulate: {area_ft2:.4f} ft², with waste: {required_area_ft2:.4f} ft²")
print(f"Area of one batt: {batt_area_ft2:.4f} ft², coverage per bag: {bag_area_ft2:.4f} ft²")
print(f"Batts needed: {batts_needed}, bags needed: {bags_needed}")
print(f"Area covered: {coverable_area_ft2:.4f} ft², left over: {surplus_area_ft2:.4f} ft²")
print(f"Volume: {volume_ft3:.4f} ft³, R-value: R-{r_value:.2f}")
print(f"Estimated cost: ${cost:,.2f}")
Runs with the standard library only. math.ceil() rounds up (the ⌈ ⌉ in the formulas). Replace the sizes, thickness, product details and price at the top with your own numbers and run it (the example gives 24 batts, 3 bags and R-13.31).
How to write it in LaTeX and other math languages (copy and paste)
Area to insulate
S = L × W, S = P × H
S = L \times W,\quad S = P \times H
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>S</mi><mo>=</mo><mi>L</mi><mo>×</mo><mi>W</mi>
<mo>,</mo>
<mi>S</mi><mo>=</mo><mi>P</mi><mo>×</mo><mi>H</mi>
</mrow>
</math>
S = L xx W, S = P xx H
{L*W, P*H}
S := L*W; S := P*H;
S = L*W; S = P*H;
S = L × W, S = P × H
Area needed with waste
Sr = S × (1 + r)
S_r = S \times (1 + r)
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>S</mi><mi>r</mi></msub>
<mo>=</mo>
<mi>S</mi>
<mo>×</mo>
<mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>r</mi><mo>)</mo></mrow>
</mrow>
</math>
S_r = S xx (1 + r)
s*(1 + r)
S_r := S*(1 + r);
S_r = S*(1 + r);
S_r = S × (1 + r)
Area of one batt and coverage per bag
a = w × l, A = a × k
a = w \times l,\quad A = a \times k
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>a</mi><mo>=</mo><mi>w</mi><mo>×</mo><mi>l</mi>
<mo>,</mo>
<mi>A</mi><mo>=</mo><mi>a</mi><mo>×</mo><mi>k</mi>
</mrow>
</math>
a = w xx l, A = a xx k
{w*l, w*l*k}
a := w*l; A := a*k;
a = w*l; A = a*k;
a = w × l, A = a × k
Number of batts needed
N = ⌈Sr ÷ a⌉
N = \left\lceil \frac{S_r}{a} \right\rceil
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>N</mi>
<mo>=</mo>
<mo>⌈</mo>
<mfrac><msub><mi>S</mi><mi>r</mi></msub><mi>a</mi></mfrac>
<mo>⌉</mo>
</mrow>
</math>
N = |~ S_r / a ~|
Ceiling[sr/a]
N := ceil(S_r/a);
N = ceil(S_r/a);
N = ⌈S_r/a⌉
Number of bags needed
B = ⌈N ÷ k⌉, B = ⌈Sr ÷ A⌉
B = \left\lceil \frac{N}{k} \right\rceil,\quad B = \left\lceil \frac{S_r}{A} \right\rceil
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>B</mi><mo>=</mo>
<mo>⌈</mo><mfrac><mi>N</mi><mi>k</mi></mfrac><mo>⌉</mo>
<mo>,</mo>
<mi>B</mi><mo>=</mo>
<mo>⌈</mo><mfrac><msub><mi>S</mi><mi>r</mi></msub><mi>A</mi></mfrac><mo>⌉</mo>
</mrow>
</math>
B = |~ N / k ~|, B = |~ S_r / A ~|
{Ceiling[n/k], Ceiling[sr/A]}
B := ceil(N/k); B := ceil(S_r/A);
B = ceil(N/k); B = ceil(S_r/A);
B = ⌈N/k⌉, B = ⌈S_r/A⌉
Area the bags cover and what is left over
Sc = B × A, D = Sc − S
S_c = B \times A,\quad D = S_c - S
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>S</mi><mi>c</mi></msub><mo>=</mo><mi>B</mi><mo>×</mo><mi>A</mi>
<mo>,</mo>
<mi>D</mi><mo>=</mo><msub><mi>S</mi><mi>c</mi></msub><mo>−</mo><mi>S</mi>
</mrow>
</math>
S_c = B xx A, D = S_c - S
{b*A, b*A - s}
S_c := B*A; D_s := S_c - S;
S_c = B*A; D = S_c - S;
S_c = B × A, D = S_c − S
Volume of insulation
V = S × t
V = S \times t
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>V</mi><mo>=</mo><mi>S</mi><mo>×</mo><mi>t</mi>
</mrow>
</math>
V = S xx t
s*t
V := S*t;
V = S*t;
V = S × t
R-value (thermal resistance)
R = t ÷ λ
R = \frac{t}{\lambda}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>R</mi><mo>=</mo>
<mfrac><mi>t</mi><mi>λ</mi></mfrac>
</mrow>
</math>
R = t / lambda
t/\[Lambda]
R := t/lambda;
R = t/lambda;
R = t/λ
Estimated cost
T = u × Q
T = u \times Q
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>T</mi><mo>=</mo><mi>u</mi><mo>×</mo><mi>Q</mi>
</mrow>
</math>
T = u * Q
u*q
T := u*Q;
T = u*Q;
T = u × Q
How to have ChatGPT do the calculation
You are a quantity calculation assistant for home insulation jobs. Do the following calculation by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing). I am insulating an area of 18 ft × 12 ft with R-13 fiberglass batts, 3.5 in thick (each batt 15 in wide × 93 in long, 11 batts per bag, thermal conductivity k = 0.263 BTU·in/(h·ft²·°F)). The waste factor is 5%. Find each of the following: 1. The area to insulate (ft²) and the area needed with the 5% waste factor (ft²) 2. The area of one batt (ft²) and the coverage per bag (ft²) 3. The number of batts needed (area needed ÷ area of one batt, rounded up) and the number of bags (batts ÷ batts per bag, rounded up) 4. The area those bags cover (ft²) and how much is left over beyond the area to insulate (ft²) 5. The R-value for 3.5 in (thickness in inches ÷ k) Show the formulas you used and the numbers from the execution result.
How to Use
-
1Enter your numbersType the numbers you want to calculate with into the input fields
-
2CalculatePress the "Calculate" button
-
3Check the resultThe result appears on the spot. The same page also explains the idea behind the calculation and the formula
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