Choose what to find (board feet, or working backward) and the input units, then enter the thickness, width, length and number of pieces (up to 6 kinds; rows with no sizes are ignored). The price can be left blank.
Row
Name (optional)
Thick. (mm)
Width (mm)
Length (m)
Pieces
A
B
C
D
E
F
Board feet are calculated from the sizes you enter, as a rectangular block. A blank number of pieces counts as 1, and blank names become "Part A" to "Part F". To match lumber yard prices, enter nominal sizes for dimensional lumber (a 2×4 as 2 and 4).
Result and figure
Enter the thickness, width, length and number of pieces on the left and press "Calculate". The board feet and a drawing will appear here.
Table of Contents
-
What you can do on this page
-
What is this calculation used for?
-
How to Use
-
Formulas and figures
-
Board feet of one piece (thickness × width × length ÷ 12)
-
What one board foot is (144 cubic inches)
-
Converting board feet to cubic feet and cubic meters
-
Total board feet (multiply by pieces and add)
-
Working backward (length and pieces from a target in board feet)
-
Estimated cost and price conversion ($/bf and $/MBF)
-
-
Symbols and terms
-
Good to know before you start
-
How to calculate it in Excel
-
How to calculate it in Google Sheets
-
How to calculate it in Python
-
How to write it in LaTeX and other math languages (copy and paste)
-
How to have ChatGPT do the calculation
-
DataChef Features
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Related Features
-
NumberChef Calculators List
What you can do on this page
- Enter the thickness, width, length and number of pieces (up to 6 kinds of lumber), and get the board feet for one piece and the total. Enter thickness and width in inches and length in feet, or switch to millimeters and meters
- The total is also shown in cubic feet (1 ft³ = 12 bf) and cubic meters (1 m³ ≈ 423.78 bf), so you can compare with metric prices and imported lumber
- Work backward from a target, such as "how many 12 ft 2×6s make 500 board feet?". You get the total length, the pieces (rounded up), the value before rounding and the board feet you actually buy
- Enter a price per board foot or per 1,000 board feet (MBF) to get the estimated cost, along with the price converted to the other unit
- A drawing compares the cross-section with 1 in × 12 in and the length with 1 ft, so you can see how board feet are counted. A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are also on this page
Board feet are calculated as the volume of a rectangular block, thickness × width × length, using the sizes you enter. Lumber yards count softwood dimensional lumber (2×4s, 2×6s and so on) by its nominal size, and hardwood by its rough thickness in quarters (4/4 = 1 in), so enter the sizes the price list uses. Shrinkage, milling waste and weight are not included, and log scaling (board feet from log diameter) is not covered. To find how many parts you can cut from stock lengths, use the "Lumber Cut List Calculator", then find the board feet and cost of those boards on this page.
What is this calculation used for?
Buying hardwood priced per board foot
Hardwood dealers sell lumber by the board foot. A 4/4 red oak board 1 in thick, 8 in wide and 10 ft long is \(1 \times 8 \times 10 \div 12 \approx 6.667\) bf, so at $6.50 per board foot it costs about \(6.667 \times 6.50 \approx 43.33\) dollars.
Boards of different sizes, such as a 4/4 board and an 8/4 plank, can be compared with the same yardstick once they are in board feet. That is why lumber is priced by volume.
Framing lumber takeoffs and quotes per MBF
A takeoff for a framing job adds up all the studs, joists and rafters. For example, ten 8 ft 2×4s, six 12 ft 2×6s and five 8 ft 1×6s total 145.333 bf. Framing lumber quotes and market prices are often in dollars per thousand board feet (MBF). At $500 per MBF, 2,400 bf of lumber costs \(2.4 \times 500 = 1200\) dollars.
Knowing the total board feet lets you see how a change in the market price per MBF affects the whole job.
Estimating wood for a furniture project
A walnut tabletop made of five 5/4 boards, each 7 in wide and 6 ft long, needs \(1.25 \times 7 \times 6 \div 12 = 4.375\) bf per board, or 21.875 bf in all. At $12 per board foot that is \(21.875 \times 12 = 262.50\) dollars. Woodworkers often buy about 20% or more extra to allow for defects and milling.
Enter every board on this page to see the total board feet and cost, and check how a change such as 4/4 instead of 5/4 affects the price before you order.
Comparing board foot prices with metric prices
Lumber from outside North America, and many international price lists, use cubic meters. Since 1 m³ ≈ 423.78 bf, a price of $600 per m³ is about \(600 \div 423.78 \approx 1.42\) dollars per board foot, and you can compare it with local prices.
Remember that softwood board feet use nominal sizes. An 8 ft 2×4 is counted as \(2 \times 4 \times 8 \div 12 \approx 5.333\) bf, but its actual size (1-1/2 × 3-1/2 in) holds only \(1.5 \times 3.5 \times 8 \div 12 = 3.5\) bf of wood. Use the nominal size to compare prices and the actual size to find the real amount of wood.
Planning a lumber delivery or storage space
Board feet are also the basis for truck loads and storage. Working backward on this page, 500 bf of 2×6 is 500 ft of board, or 42 boards 12 ft long (504 bf).
Knowing the pieces ahead of time tells you how big the bundle will be and whether it fits in your space. Wood weight depends on the species and how dry it is. Multiply the cubic feet (board feet ÷ 12) by the density in pounds per cubic foot to estimate it.
Formulas and figures
Board feet of one piece (thickness × width × length ÷ 12)
Figure
Standard notation
(the usual math form)
\(F\)
\(=\)
\(t\)
\(\times\)
\(w\)
\(\times\)
\(L\)
\(\div 12\)
In words
(symbols replaced with words)
④
\(F\): board feet of one piece
\(=\)
①
\(t\): thickness (in)
\(\times\)
②
\(w\): width (in)
\(\times\)
③
\(L\): length (ft)
\(\div 12\)
The formula in words
①
Multiply the
\(t\): thickness (in)
by the
②
\(w\): width (in)
to get the cross-section in square inches, then multiply by the
③
\(L\): length (ft)
and divide by 12 to get the
④
\(F\): board feet of one piece
Quick example
The board feet in one 2×6 that is 8 ft long are
board feet \(F\)
\(=\)
thickness (2 in)
\(\times\)
width (6 in)
\(\times\)
length (8 ft)
\(\div 12\)
\(2 \times 6 \times 8 \div 12 = 96 \div 12 = 8\)
Key idea
A board foot is a unit of volume for lumber: a piece 1 in thick, 12 in wide and 1 ft (12 in) long. Board feet are simply the volume of a rectangular block, but with mixed units. Thickness and width are in inches and length is in feet, so thickness × width × length gives "square inches × feet". One board foot is 12 of those (1 in × 12 in × 1 ft), so divide by 12.
A handy way to see it: every foot of a board with a 12 in² cross-section (a 1×12 or a 2×6) is exactly 1 board foot. A 2×4 has 8 in², so each foot of it is 8 ÷ 12 ≈ 0.667 bf.
For softwood dimensional lumber, lumber yards count board feet from the nominal size, not the actual size. A 2×4 really measures 1-1/2 × 3-1/2 in, but an 8 ft 2×4 is counted as \(2 \times 4 \times 8 \div 12 \approx 5.333\) bf, not \(1.5 \times 3.5 \times 8 \div 12 = 3.5\) bf. Hardwood is sold by its rough thickness in quarter inches (4/4 is 1 in, 5/4 is 1-1/4 in, 8/4 is 2 in), with the actual width and length. Enter the sizes that your price list uses.
What one board foot is (144 cubic inches)
Figure
Standard notation
(the usual math form)
\(F\)
\(=\)
\(V\)
\(\div\)
\(144\)
\(V\)
\(=\)
\(t\)
\(\times\)
\(w\)
\(\times\)
\(\ell\)
In words
(symbols replaced with words)
③
\(F\): board feet
\(=\)
①
\(V\): volume (in³)
\(\div\)
②
volume of 1 bf (144 in³)
⑦
\(V\): volume (in³)
\(=\)
④
\(t\): thickness (in)
\(\times\)
⑤
\(w\): width (in)
\(\times\)
⑥
\(\ell\): length (in)
The formula in words
①
Divide the
\(V\): volume (in³)
by the
②
volume of 1 bf (144 in³)
(that is, count how many board feet fit in it) to get the
③
\(F\): board feet
. The volume in cubic inches is the
④
\(t\): thickness (in)
times the
⑤
\(w\): width (in)
times the
⑥
\(\ell\): length (in)
, all in inches, which gives the
⑦
\(V\): volume (in³)
(with the length in feet instead, divide by 12, as in the first formula)
Quick example
The same 2×6 that is 8 ft (96 in) long has a volume in cubic inches and board feet of
board feet \(F\)
\(=\)
volume (1,152 in³)
\(\div\)
1 bf (144 in³)
\(2 \times 6 \times 96 = 1152\)
\(1152 \div 144 = 8\)
Key idea
One board foot is a board 1 in thick, 12 in wide and 12 in long: \(1 \times 12 \times 12 = 144\) cubic inches. So board feet are just the volume in cubic inches divided by 144. The figure compares the 2×6 with one board foot. Its cross-section, 2 in × 6 in = 12 in², is the same area as 1 in × 12 in, and it is 8 times as long as 1 ft, so it is 8 bf.
This form is useful when all your sizes are in inches, such as a hardwood board 1 in × 8 in × 120 in: \(1 \times 8 \times 120 \div 144 \approx 6.667\) bf. With the length in feet, \(1 \times 8 \times 10 \div 12\) gives the same 6.667 bf, because 144 in³ ÷ 12 in per foot = 12.
Board feet are a volume, even though the name says "feet". A 12 ft 2×6 and a 6 ft 2×12 are both 12 bf.
Converting board feet to cubic feet and cubic meters
Standard notation
(the usual math form)
\(C\)
\(=\)
\(F\)
\(\div\)
\(12\)
\(M\)
\(=\)
\(F\)
\(\times\)
\(0.0023597\)
In words
(symbols replaced with words)
②
\(C\): cubic feet
\(=\)
①
\(F\): board feet
\(\div\)
\(12\)
③
\(M\): cubic meters
\(=\)
\(F\): board feet
\(\times\)
\(0.0023597\)
The formula in words
①
Divide the
\(F\): board feet
by 12 (1 ft³ is 12 in × 12 in × 12 in, or 12 bf) to get the
②
\(C\): cubic feet
. Multiply the same board feet by the volume of 1 bf, 0.0023597 m³, to get the
③
\(M\): cubic meters
Quick example
145.333 bf (the total of the studs, joists and boards in the example below) in cubic feet and cubic meters is
\(145.333 \div 12 \approx 12.111\ \mathrm{ft^3}\)
\(145.333 \times 0.0023597 \approx 0.3429\ \mathrm{m^3}\)
Key idea
A cubic foot is a cube 12 in on each side, which is a stack of twelve 1 in boards 12 in × 12 in, so 1 ft³ = 12 bf. Cubic feet are handy for storage space, truck loads and wood weight (weight = cubic feet × density in pounds per cubic foot).
One board foot is \(0.0254^3 \times 144 = 0.002359737216\) m³, so 1 m³ ≈ 423.78 bf. Imported lumber and prices from other countries are often in cubic meters. For example, $600 per m³ is about \(600 \div 423.78 \approx 1.42\) dollars per board foot. Note that this page's board feet use the sizes you enter, so if a price list counts nominal sizes, enter nominal sizes too.
Total board feet (multiply by pieces and add)
Standard notation
(the usual math form)
\(F_{\text{total}}\)
\(=\)
\(F_1\)
\(\times\)
\(q_1\)
\(+\)
\(F_2\)
\(\times\)
\(q_2\)
\(+ \cdots\)
In words
(symbols replaced with words)
③
\(F_{\text{total}}\): total board feet
\(=\)
①
\(F_1\): board feet of one piece of part 1
\(\times\)
②
\(q_1\): pieces of part 1
\(+\)
\(F_2\): board feet of one piece of part 2
\(\times\)
\(q_2\): pieces of part 2
\(+ \cdots\)
The formula in words
①
Multiply the
\(F_1\): board feet of one piece of part 1
by the
②
\(q_1\): pieces of part 1
, do the same for each kind of lumber, and add them all up to get the
③
\(F_{\text{total}}\): total board feet
Quick example
For ten 8 ft 2×4 studs (5.333 bf each), six 12 ft 2×6 joists (12 bf each) and five 8 ft 1×6 boards (4 bf each), the total board feet are
\(5.333 \times 10 + 12 \times 6 + 4 \times 5 = 53.333 + 72 + 20 = 145.333\)
Key idea
Board feet can be added up. Studs, joists and boards have different shapes, but in board feet they add together simply, which is why lumber yards and mills quote and track mixed orders as "a total of so many board feet". The table on this page lists, for each part, the board feet of one piece and of all its pieces, and then the total.
The cubic feet and cubic meters of the total are found from the total board feet (÷ 12 and × 0.0023597), so they match the sum of the parts except for rounding in the last digit.
Working backward (length and pieces from a target in board feet)
Standard notation
(the usual math form)
\(L_{\text{total}}\)
\(=\)
\(F\)
\(\div\)
\((\)
\(t\)
\(\times\)
\(w\)
\()\)
\(\times 12\)
\(n\)
\(=\)
\(\lceil\)
\(L_{\text{total}}\)
\(\div\)
\(L_1\)
\(\rceil\)
In words
(symbols replaced with words)
④
\(L_{\text{total}}\): total length needed (ft)
\(=\)
①
\(F\): target board feet
\(\div\)
\((\)
②
\(t\): thickness (in)
\(\times\)
③
\(w\): width (in)
\()\)
\(\times 12\)
⑥
\(n\): pieces needed
\(=\)
\(\lceil\)
\(L_{\text{total}}\): total length needed
\(\div\)
⑤
\(L_1\): length of one piece (ft)
\(\rceil\)
The formula in words
①
Divide the
\(F\): target board feet
by the cross-section, the
②
\(t\): thickness (in)
times the
③
\(w\): width (in)
, and multiply by 12 to get the
④
\(L_{\text{total}}\): total length needed (ft)
. Divide it by the
⑤
\(L_1\): length of one piece (ft)
and round up (the symbol \(\lceil\ \rceil\) stands for "round up") to get the
⑥
\(n\): pieces needed
Quick example
How many 12 ft 2×6 boards make 500 board feet?
total length needed
\(=\)
target (500 bf)
\(\div\)
\((\)
thickness (2 in)
\(\times\)
width (6 in)
\()\)
\(\times 12\)
\(500 \div (2 \times 6) \times 12 = 500 \div 12 \times 12 = 500\)
\(\lceil 500 \div 12 \rceil = \lceil 41.67 \rceil = 42\)
Key idea
This is the board foot formula \(F = t \times w \times L \div 12\) solved for the length. It finds how many feet of lumber with a cross-section of \(t \times w\) make the target, then divides by the length of one piece. You cannot buy part of a board, so the pieces are rounded up. Because of rounding up, you buy a little more than the target, so the result also shows the board feet in the rounded-up pieces (42 pieces × 12 bf = 504 bf in the example).
If the number of pieces is fixed first ("I want 40 pieces"), divide the total length by the pieces to get the length of each (500 ft ÷ 40 = 12.5 ft). You can enter the piece length, the number of pieces, or both.
The target can be entered in board feet, cubic feet or cubic meters. It is first changed to board feet (1 ft³ = 12 bf, 1 m³ ≈ 423.78 bf) and then used in the formula.
Estimated cost and price conversion ($/bf and $/MBF)
Standard notation
(the usual math form)
\(T\)
\(=\)
\(F\)
\(\times\)
\(u\)
\(u_{\text{M}}\)
\(=\)
\(u\)
\(\times\)
\(1000\)
In words
(symbols replaced with words)
③
\(T\): estimated cost ($)
\(=\)
①
\(F\): board feet
\(\times\)
②
\(u\): price per board foot ($/bf)
⑤
\(u_{\text{M}}\): price per 1,000 bf ($/MBF)
\(=\)
\(u\): price per board foot ($/bf)
\(\times\)
④
1,000 bf in 1 MBF
The formula in words
①
Multiply the
\(F\): board feet
by the
②
\(u\): price per board foot ($/bf)
to get the
③
\(T\): estimated cost ($)
. Also, multiplying the price per board foot \(u\) by
④
1,000 bf in 1 MBF
gives the
⑤
\(u_{\text{M}}\): price per 1,000 bf ($/MBF)
(divide a price per MBF by 1,000 to get back to the price per board foot).
Quick example
For a total of 145.333 bf at $1.25 per board foot, the estimated cost and the price per MBF are
\(145.333 \times 1.25 \approx 181.67\)
\(1.25 \times 1000 = 1250\)
Key idea
Hardwood dealers usually price lumber per board foot, while mills, wholesalers and market reports for framing lumber use dollars per thousand board feet (MBF, where M is the Roman numeral for 1,000). Both are prices per volume, so you can move between them by multiplying or dividing by 1,000. For example, $500 per MBF is $0.50 per board foot, and 2,400 bf of framing lumber at that price costs \(2400 \div 1000 \times 500 = 1200\) dollars.
The cost is for the lumber only. Delivery, cutting, drying or treatment, and sales tax are extra. Home centers usually sell dimensional lumber per piece, and in that case pieces × price per piece is more accurate.
Board feet are the volume of lumber, thickness (in) × width (in) × length (ft) ÷ 12, where 1 board foot is 1 in × 12 in × 1 ft = 144 in³. 12 board feet make a cubic foot, and 1 m³ is about 423.78 board feet. To work backward, multiply the target board feet by 12, divide by the cross-section to get the total length, and divide by the length of one piece, rounding up, to get the pieces.
Symbols and terms
Symbols
| \(F\) | F | Board feet. From the "foot" in board foot. Used for one piece, a total and a target. |
| \(t\) | t | The thickness of the lumber (in). From "thickness". For square timbers, it does not matter which side you call the thickness. |
| \(w\) | w | The width of the lumber (in). From "width". |
| \(L\) | L | The length of the lumber (ft). From "length". \(L_1\) is the length of one piece entered when working backward, and \(L_{\text{total}}\) is the total length needed for the target. |
| \(V\) | V | The volume in cubic inches (\(V = t \times w \times \ell\) with all sizes in inches). From "volume". \(F = V \div 144\). |
| \(\ell\) | script l | The length in inches, written as a script l to tell it apart from the length in feet \(L\) (\(\ell = 12L\)). |
| \(C\) | C | The volume in cubic feet. From "cubic". \(C = F \div 12\). |
| \(M\) | M | The volume in cubic meters. From "meter". \(M = F \times 0.0023597\), because 1 bf = 144 in³ ≈ 0.0023597 m³. |
| \(q_i\) | q sub i | The number of pieces of part \(i\). From "quantity". \(i\) is the number of the kind of lumber (because there are several kinds, such as studs, joists and boards). |
| \(n\) | n | The pieces needed when working backward. From "number". It is a whole number, rounded up. |
| \(u\) | u | The price per board foot ($/bf). From "unit price". |
| \(u_{\text{M}}\) | u sub M | The price per 1,000 board feet ($/MBF). The price per board foot \(u\) times 1,000. |
| \(T\) | T | The estimated cost ($). From "total". Lumber only, without delivery or cutting charges. |
| \(\lceil x \rceil\) | ceiling of x | The ceiling function: round up to a whole number (for example \(\lceil 41.67 \rceil = 42\) and \(\lceil 10 \rceil = 10\)). The pieces to buy use it, because a shortfall calls for one more board. |
| \(\sum\) | sigma | The symbol for "add them all up". \(\sum_i F_i \, q_i\) tells you to work out \(F_i \times q_i\) for each kind of lumber \(i\) and add them all. It is the Greek letter sigma, the S of "sum". |
Terms
| board foot | The US and Canadian unit of lumber volume, written bf or BF. One board foot is a piece 1 in thick, 12 in wide and 1 ft long, which is 144 in³ = 1/12 ft³ ≈ 0.0023597 m³. Hardwood, lumber yard quotes and log volumes are measured in it. The name says "foot", but it is a volume, not a length. |
| MBF | One thousand board feet (M is the Roman numeral for 1,000). Mills, wholesalers and lumber market prices quote framing lumber in dollars per MBF. |
| cubic foot | The volume of a cube 1 ft on each side, 1,728 in³. It equals 12 board feet. It is used for storage space and for wood weight (density in pounds per cubic foot). |
| cubic meter | The metric unit of volume, a cube 1 m on each side. Lumber outside North America is measured in it. 1 m³ ≈ 423.78 bf ≈ 35.31 ft³. |
| nominal size | The name size of dimensional lumber, such as 2×4 or 2×6. The actual size after drying and planing is smaller (a 2×4 is 1-1/2 × 3-1/2 in, a 2×6 is 1-1/2 × 5-1/2 in), but softwood lumber is priced in board feet from the nominal size. |
| actual size | The measured size of a finished board. Use it when you need the real amount of wood, for example for weight. An 8 ft 2×4 is 5.333 bf by nominal size but only 3.5 bf by actual size. |
| stock length | A standard length that lumber is sold in, usually in 2 ft steps such as 8, 10, 12, 14 and 16 ft. Enter it as the length of one piece when working backward to get the pieces needed. |
| stud | A vertical framing member in a wall, usually a 2×4 or 2×6 set 16 in on center. It is used in the first row of the input example. |
| SPF | Spruce-pine-fir, a group of North American softwoods sold together as one grade of dimensional lumber. Many 2×4s at home centers are SPF. |
| dimensional lumber | Softwood lumber cut to standard nominal sizes, such as 2×4, 2×6 and 2×10, for framing. It is 2 to 4 in thick (nominal). |
| hardwood | Wood from broad-leaved trees, such as oak, maple, cherry and walnut, used for furniture and floors. It is sold by the board foot, in random widths and lengths. |
| quarter system | The way hardwood thickness is named, in quarter inches of rough (unplaned) thickness. 4/4 ("four quarter") is 1 in, 5/4 is 1-1/4 in, 6/4 is 1-1/2 in and 8/4 is 2 in. Board feet are counted from this rough thickness. |
| rough lumber | Lumber as it comes from the saw, before planing. Hardwood is often bought rough and planed smooth later, which removes some thickness. |
| cross-section | The shape you see when you cut the lumber straight across its length. For a board it is a thickness × width rectangle. Board feet are "cross-section × length", so for the same cross-section they grow in proportion to the length. |
| cross-section area | The area of the cross-section (thickness × width). A 2×6 is 2 in × 6 in = 12 in² by nominal size. Working backward, 12 × the target board feet divided by this area gives the length needed in feet. |
| S4S | Surfaced four sides, lumber planed smooth on all four sides. Its actual thickness is less than the rough thickness (4/4 S4S is usually about 13/16 in), but hardwood board feet are still often counted from the rough size. |
| 2×4 | The most common piece of dimensional lumber, 2 in × 4 in by nominal size and 1-1/2 × 3-1/2 in (38 × 89 mm) actual. An 8 ft 2×4 is counted as \(2 \times 4 \times 8 \div 12 \approx 5.333\) bf. |
| unit price | The price for one unit of volume. Hardwood dealers use dollars per board foot and mills use dollars per MBF, so multiply or divide by 1,000 to convert. |
| round up | If there is any decimal part, drop it and add 1 (41.67 pieces → 42 pieces; a whole number stays as it is). The pieces needed are rounded up, because a shortfall calls for one more board. |
Good to know before you start
Here is what helps to understand before you start, so that you can use the calculations on this page with a clear understanding.
| Converting units of length (Grade 4 to 5) |
|
| Volume of a rectangular prism (Grade 5) |
|
| Multiplying and dividing decimals (Grade 5 to 6) |
|
| Rounding (Grade 4) |
|
| Unit rates (Grade 6) |
|
| Fractions (Grade 5 to 6) |
|
How to calculate it in Excel
Copy the whole table below and paste it into cell A1 in Excel. It works as is.
Table for the board feet of one piece
| Thickness (in) | 2 |
| Width (in) | 6 |
| Length (ft) | 8 |
| Board feet of one piece | =B1*B2*B3/12 |
Table for board feet from cubic inches
| Thickness (in) | 2 |
| Width (in) | 6 |
| Length (in) | 96 |
| Board feet | =B1*B2*B3/144 |
Table for cubic feet and cubic meters
| Board feet | 145.333 |
| Cubic feet | =B1/12 |
| Cubic meters | =B1*0.002359737216 |
Table for the price per board foot from a price per cubic meter
| Price ($ per m³) | 600 |
| Board feet in 1 m³ | =1/0.002359737216 |
| Price ($ per bf) | =B1/B2 |
Table for the total board feet
| Board feet of one piece of part 1 | 5.333333 |
| Pieces of part 1 | 10 |
| Board feet of one piece of part 2 | 12 |
| Pieces of part 2 | 6 |
| Total board feet | =B1*B2+B3*B4 |
Table for working backward (length and pieces)
| Target (bf) | 500 |
| Thickness (in) | 2 |
| Width (in) | 6 |
| Length of one piece (ft) | 12 |
| Total length needed (ft) | =12*B1/(B2*B3) |
| Pieces needed | =ROUNDUP(B5/B4,0) |
Table for the estimated cost and price conversion
| Board feet | 145.333 |
| Price ($ per bf) | 1.25 |
| Estimated cost ($) | =B1*B2 |
| Price ($ per MBF) | =B2*1000 |
After you paste, the upper rows of column B are the inputs and the last rows are the calculated results.
B4 in the 1st table is 8 bf, B4 in the 2nd table is also 8 bf, the 3rd table gives about 12.111 ft³ and 0.3429 m³, the 4th table gives about 423.78 bf per m³ and $1.42 per bf, B5 in the 5th table is 125.33 bf, the 6th table gives a total length of 500 ft and 42 pieces, and the 7th table gives about $181.67 and $1,250 per MBF.
"/12" turns thickness (in) × width (in) × length (ft) into board feet, and "/144" does the same when the length is in inches. 0.002359737216 is the volume of 1 bf in m³. ROUNDUP(value, 0) rounds up to a whole number (the ⌈ ⌉ in the formulas).
B4 in the 1st table is 8 bf, B4 in the 2nd table is also 8 bf, the 3rd table gives about 12.111 ft³ and 0.3429 m³, the 4th table gives about 423.78 bf per m³ and $1.42 per bf, B5 in the 5th table is 125.33 bf, the 6th table gives a total length of 500 ft and 42 pieces, and the 7th table gives about $181.67 and $1,250 per MBF.
"/12" turns thickness (in) × width (in) × length (ft) into board feet, and "/144" does the same when the length is in inches. 0.002359737216 is the volume of 1 bf in m³. ROUNDUP(value, 0) rounds up to a whole number (the ⌈ ⌉ in the formulas).
How to calculate it in Google Sheets
Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.
Table for the board feet of one piece
| Thickness (in) | 2 |
| Width (in) | 6 |
| Length (ft) | 8 |
| Board feet of one piece | =B1*B2*B3/12 |
Table for board feet from cubic inches
| Thickness (in) | 2 |
| Width (in) | 6 |
| Length (in) | 96 |
| Board feet | =B1*B2*B3/144 |
Table for cubic feet and cubic meters
| Board feet | 145.333 |
| Cubic feet | =B1/12 |
| Cubic meters | =B1*0.002359737216 |
Table for the price per board foot from a price per cubic meter
| Price ($ per m³) | 600 |
| Board feet in 1 m³ | =1/0.002359737216 |
| Price ($ per bf) | =B1/B2 |
Table for the total board feet
| Board feet of one piece of part 1 | 5.333333 |
| Pieces of part 1 | 10 |
| Board feet of one piece of part 2 | 12 |
| Pieces of part 2 | 6 |
| Total board feet | =B1*B2+B3*B4 |
Table for working backward (length and pieces)
| Target (bf) | 500 |
| Thickness (in) | 2 |
| Width (in) | 6 |
| Length of one piece (ft) | 12 |
| Total length needed (ft) | =12*B1/(B2*B3) |
| Pieces needed | =ROUNDUP(B5/B4,0) |
Table for the estimated cost and price conversion
| Board feet | 145.333 |
| Price ($ per bf) | 1.25 |
| Estimated cost ($) | =B1*B2 |
| Price ($ per MBF) | =B2*1000 |
The same formulas as in Excel work as they are (ROUNDUP has the same name). 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
from fractions import Fraction
# 1 board foot = 1 in x 12 in x 12 in = 144 cubic inches; 1 in = 0.0254 m exactly
BF_M3 = Fraction(254, 10000) ** 3 * 144 # 0.002359737216 m3
price_per_bf = Fraction(5, 4) # price ($ per board foot)
# lumber: (name, thickness in, width in, length ft, pieces), nominal sizes
parts = [("Stud", 2, 4, 8, 10), ("Joist", 2, 6, 12, 6), ("Board", 1, 6, 8, 5)]
total_bf = Fraction(0)
for name, t_in, w_in, length_ft, qty in parts:
bf = Fraction(t_in * w_in * length_ft, 12) # thickness x width x length / 12
total_bf += bf * qty
print(f"{name}: {float(bf):.3f} bf per piece -> {qty} pieces: {float(bf * qty):.3f} bf")
print(f"Total: {float(total_bf):.3f} bf = {float(total_bf / 12):.3f} ft3 = {float(total_bf * BF_M3):.6f} m3")
print(f"Estimated cost: ${float(total_bf * price_per_bf):,.2f} (= ${float(price_per_bf * 1000):,.2f} per MBF)")
# working backward: how many 12 ft 2x6 boards make 500 bf?
target_bf = 500
total_length_ft = Fraction(12 * target_bf, 2 * 6)
pieces = math.ceil(total_length_ft / 12)
print(f"Total length needed: {float(total_length_ft):.3f} ft -> {pieces} pieces of 12 ft ({float(total_length_ft / 12):.3f} before rounding up)")
It runs with the standard library only. fractions.Fraction keeps values as exact fractions, so dividing by 12 or converting with 0.0254 adds no rounding error (float() turns them into decimals for printing). Replace the parts list and the price at the top with your own numbers and run it. Working backward uses math.ceil() to round the pieces up.
How to write it in LaTeX and other math languages (copy and paste)
Board feet of one piece (thickness × width × length ÷ 12)
F = t × w × L ÷ 12
F = \frac{t \times w \times L}{12}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>F</mi>
<mo>=</mo>
<mfrac>
<mrow><mi>t</mi><mo>×</mo><mi>w</mi><mo>×</mo><mi>L</mi></mrow>
<mn>12</mn>
</mfrac>
</mrow>
</math>
F = (t * w * L)/12
F = t*w*L/12
F := t*w*L/12;
F = t*w*L/12;
F = (t × w × L)/12
What one board foot is (144 cubic inches)
F = V ÷ 144, V = t × w × ℓ
F = \frac{V}{144},\quad V = t \times w \times \ell
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>F</mi>
<mo>=</mo>
<mfrac><mi>V</mi><mn>144</mn></mfrac>
<mo>,</mo>
<mi>V</mi>
<mo>=</mo>
<mi>t</mi>
<mo>×</mo>
<mi>w</mi>
<mo>×</mo>
<mi>ℓ</mi>
</mrow>
</math>
F = V/144, V = t * w * l
{V/144, t*w*l}
F := V/144; V := t*w*l;
F = V/144; V = t*w*l;
F = V/144, V = t × w × ℓ
Converting board feet to cubic feet and cubic meters
C = F ÷ 12, M = F × 0.0023597
C = \frac{F}{12},\quad M = F \times 0.0023597
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>C</mi>
<mo>=</mo>
<mfrac><mi>F</mi><mn>12</mn></mfrac>
<mo>,</mo>
<mi>M</mi>
<mo>=</mo>
<mi>F</mi>
<mo>×</mo>
<mn>0.0023597</mn>
</mrow>
</math>
C = F/12, M = F * 0.0023597
{F/12, F*0.002359737216}
C := F/12; M := F*0.002359737216;
C = F/12; M = F*0.002359737216;
C = F/12, M = F × 0.0023597
Total board feet (multiply by pieces and add)
F_total = F₁ × q₁ + F₂ × q₂ + …
F_{\text{total}} = \sum_i F_i \, q_i
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>F</mi><mtext>total</mtext></msub>
<mo>=</mo>
<munder><mo>∑</mo><mi>i</mi></munder>
<msub><mi>F</mi><mi>i</mi></msub>
<mo>⁢</mo>
<msub><mi>q</mi><mi>i</mi></msub>
</mrow>
</math>
F_"total" = sum_i F_i q_i
Total[F*q]
Ftotal := add(F[i]*q[i], i = 1 .. n);
Ftotal = sum(F .* q);
F_total = ∑_i F_i q_i
Working backward (length and pieces from a target in board feet)
L_total = 12 × F ÷ (t × w), n = ⌈L_total ÷ L₁⌉
L_{\text{total}} = \frac{12F}{t \, w},\quad n = \left\lceil \frac{L_{\text{total}}}{L_1} \right\rceil
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>L</mi><mtext>total</mtext></msub>
<mo>=</mo>
<mfrac><mrow><mn>12</mn><mi>F</mi></mrow><mrow><mi>t</mi><mo>⁢</mo><mi>w</mi></mrow></mfrac>
<mo>,</mo>
<mi>n</mi>
<mo>=</mo>
<mo>⌈</mo>
<mfrac><msub><mi>L</mi><mtext>total</mtext></msub><msub><mi>L</mi><mn>1</mn></msub></mfrac>
<mo>⌉</mo>
</mrow>
</math>
L_"total" = (12F)/(t w), n = |~ L_"total"/L_1 ~|
{12 F/(t*w), Ceiling[12 F/(t*w*L1)]}
Ltotal := 12*F/(t*w); n := ceil(Ltotal/L1);
Ltotal = 12*F/(t*w); n = ceil(Ltotal/L1);
L_total = 12F/(t w), n = ⌈L_total/L_1⌉
Estimated cost and price conversion ($/bf and $/MBF)
T = F × u, u_M = u × 1000
T = F \times u,\quad u_{\text{M}} = u \times 1000
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>T</mi>
<mo>=</mo>
<mi>F</mi>
<mo>×</mo>
<mi>u</mi>
<mo>,</mo>
<msub><mi>u</mi><mtext>M</mtext></msub>
<mo>=</mo>
<mi>u</mi>
<mo>×</mo>
<mn>1000</mn>
</mrow>
</math>
T = F * u, u_"M" = u * 1000
{F*u, u*1000}
T := F*u; uM := u*1000;
T = F*u; uM = u*1000;
T = F × u, u_M = u × 1000
How to have ChatGPT do the calculation
You are an assistant for lumber volume calculations. Do the following calculation by actually running Python code, and base your answer only on the numbers from the run (do not answer from mental math or guesses). One board foot is 1 in × 12 in × 12 in = 144 cubic inches, board feet = thickness (in) × width (in) × length (ft) ÷ 12, 1 ft³ = 12 bf, and 1 bf = 0.002359737216 m³. Use nominal sizes. For ten 2×4 studs 8 ft long, six 2×6 joists 12 ft long and five 1×6 boards 8 ft long, find each of the following. 1. The board feet of one piece of each part, and of all its pieces 2. The total board feet, cubic feet and cubic meters 3. The estimated cost at $1.25 per board foot, and that price per 1,000 board feet (MBF) 4. Working backward: the total length (ft) of 2×6 needed for 500 board feet, and how many 12 ft boards that is (rounded up) Show the code you used and the numbers from the run. Also mention in one sentence that softwood lumber is priced by nominal size, while the actual size is smaller.
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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