Linear and Board Feet

Date: 01/04/99 at 13:22:14
From: Sam
Subject: How many square feet are in a linear foot?

Hi, I'm trying to understand what a linear foot is. As I understand it, 
a linear foot is a foot long, but how wide is it? How can I calculate 
how many square feet are in a linear foot?

Thanks for your help!

Date: 01/04/99 at 17:06:28
From: Doctor Rick
Subject: Re: How many square feet are in a linear foot?

Hi, Sam, welcome to Ask Dr. Math!

The terms used in the lumber industry are a bit confusing. There are 
two terms that I think you might be mixing up.

A LINEAR FOOT is simply the length of a board. If you want to know the 
area or volume of the board, you need additional information. For 
instance, 6 linear feet of 1-by-12 has an area of 6 square feet (12 
inches = 1 foot, times 6 feet), and it's 1 inch thick, so the volume is 
1/2 cubic foot (6 square feet times 1/12 foot). But 6 linear feet of a 
1-by-6 board would have half the area and half the volume.

A BOARD FOOT is equivalent to one square foot of a 1-inch-thick board. 
In other words, it is a square-foot-inch (ft^2-in), or 1/12 cubic foot.

Linear feet are used for the pricing of a single size such as two-by-
fours. Board feet are used for larger lumber that you are more likely 
to want to compare directly with different size boards (is it cheaper 
to cover an area with 1x12's or 1x6's?). Today's Homeowher has a Web 
page that explains board feet from a practical standpoint:

   Board Foot: Lumber Lingo - Don Vandervort 
   http://www.todayshomeowner.com/buyerguide/19971284.word3.html   

To sum up, neither a linear foot nor a board foot can be converted 
directly to square feet. A linear foot is a linear (length) measure, 
and a board foot is a volume measure. You need to know your particular 
board to do anything more, such as find the area.

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/   

Date: 06/17/2003 at 13:57:17
From: Christine Van Horn
Subject: Conversion

How to convert square feet to linear feet?   A countertop is measured 
in square feet; however, certain hard surfaces are sold in linear 
feet.

If one hard surface in sold in square feet and another in linear feet, 
how would you compare pricing? It seems as if you would need to 
convert the square foot measurement to linear feet.

Date: 06/17/2003 at 17:40:50
From: Doctor Rick
Subject: Re: Conversion

Hi, Christine.

You can't convert between the two. All you have to do is to make the 
appropriate measurements so you can calculate the price of each item.

I am in the midst of getting a new kitchen myself, so I know how this 
works. The linear measurement is taken along the rear of the 
countertop, along the wall. If the countertop is to be an "L" shape, 
this is important: the measurement along the front will be different.

The area of an L-shaped countertop is most easily calculated by 
dividing the region into rectangles, like this:

                    80
   +---------------------------------+
   |                                 |
   |                                 |24
   |                                 |
   |                                 |
   |.........+-----------------------+
 60|         |          56
   |         |
   |         |36
   |         |
   |         |
   |         |
   +---------+
       24

The two rectangles are 24 by 80 inches and 24 by 36 inches. Thus the 
area is:

  24 * 80 + 24 * 36 = 24 * (80 + 36)
                    = 24 * 116
                    = 2784 sq. in.

To get it in square feet, divide by 144:

  2784 / 144 = 19.33 sq. ft.

The linear measure of this countertop would be

  60 + 80 = 140 inches
          = 140/12 feet
          = 11.67 feet

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/