Pricing Products by Linear Foot or Square Foot

Date: 06/29/2005 at 12:17:51
From: Dee
Subject: What is the difference between Linear foot and square foot

Please HELP.  What is the difference between linear foot and square 
footage?  I have received 2 prices for an item: $1.67 per square foot
or $19.67 per linear foot.  I am so confused.

I was under the understanding they were basically the same.  But then 
how can the same measursement be so far in price?

Date: 06/29/2005 at 23:31:56
From: Doctor Wilko
Subject: Re: What is the difference between Linear foot and square foot

Hi Dee,

Thanks for writing to Dr. Math!

Are you looking at carpet by chance?  Without knowing exactly what 
you're buying, I'll relate your question to something similar that
I've experienced.

I worked at a place that sold carpet and we had three price tags on 
each roll of carpet--Square Foot Price, Linear Foot Price, and Square
Yard Price.  The sticker might have looked like this:

==================================
12' wide Berber Carpet
==================================
 $1.67  per square foot

 $15.03 per square yard

 $20.04 per linear foot
==================================

This often confused customers, but in reality, the prices were the 
same, they were just expressed in different _units_.  

Maybe a simple example is 1 pound (16 oz) of candy costs $1.00, but 
32 ounces (2 lbs) costs $2.00.  The pricing strategy is the same, but 
it's expressed in two different ways.  

Does this make sense?  If so, then it's similar with the carpet prices 
above.  I'll elaborate more below.

The square foot price is kind of the "unit price" or base price that 
the other figures are derived from.  In our example, a piece of carpet 
1 foot by 1 foot (one square foot) would cost $1.67.  

People don't usually buy carpet in square feet like that, but it 
serves as a way to compare different types and sizes of carpets.

It's like if you see a sticker on cereal at the grocery store and it 
tells you how much you're paying per ounce (unit price) for the 
generic Crispy Rice versus the name brand Rice Krispies.  

If the two boxes are different sizes, sometimes it's hard to see which 
is the better deal, but if they give you a price per ounce for each of 
them, now you have a direct comparison between the two.  This is what 
the square foot carpet price does for you.

So, in our example, we said $1.67 per square foot is our starting 
price.

Now, a yard is 3 feet long, so a square yard is a square that is 3
feet by 3 feet, which gives you a total area of 9 square feet in one
square yard.

Since a square yard is nine square feet, the price per square yard
should be 9 times the price per square foot:

  $1.67 * 9 = $15.03 per square yard

A Linear foot of carpet would be if I pull out one foot of carpet from 
the roll and cut it off.  You only cut off one foot, but the carpet is 
twelve feet wide, so you have a piece of carpet that is 1 foot by 12 
feet wide, which gives you a total area of 12 square feet per linear 
foot.  

That means the price per linear foot should be 12 times the price per
square foot:

  $1.67 * 12 = $20.04 per linear foot

This linear foot pricing is easier if someone says, "I need 10 feet of
this carpet" (or a 10'x 12' piece) because a salesman can quickly tell
them that it'll cost,

  $20.04 * 10 = $200.40 (for a 10'x 12' piece of carpet)

instead of calculating how many square feet are in a 10'x 12' piece 
and then multiplying that by $1.67:

  10' x 12' = 120 sq ft * $1.67 = $200.40

So, the square foot price is our starting price.  Then we multiply the
square foot price by 9 to get the square yard price, and by 12 to get
the linear foot price.  Now does the pricing make more sense?  

If you want to relate this more to what you're purchasing, please 
write back and tell me what you're buying and any dimensions or other 
useful information about the product so we can compare their pricing 
strategy.  

Honestly, just knowing how they price stuff lets you be a smarter 
consumer and makes you less likely to be ripped off!  I'd suggest to 
always double-check any store's estimates for accuracy.

Does this help?  Please write back if you have further questions.

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

Date: 07/03/2005 at 14:36:17
From: Dee
Subject: Thank you (What is the difference between Linear foot and
square foot)

You were very helpful and precise, and I really appreciate the way you
explained everything.  My best friend is a math teacher and I will 
make sure she gets this address to give her students.  Again, thank
you for everything.  Dee