Although square feet and linear feet are measurements of different quantities, it makes sense to compare them in certain situations. Perhaps the most common is in building projects in which you have to cover a certain area, such as a floor, wall or fence panel, with lumber of a particular dimension. If the lumber is sold by the linear foot, which is often the case, converting the area you have to cover to the number of linear feet of lumber you need provides the information you need to estimate the cost of the project.

## A Real-World Example: Fence Building

When estimating materials for a fence, you usually start by calculating its total area "A." To do this, you measure the total length "L" of the fence and multiply that by its projected height "H." The area is then given by the formula:

A = LH.

Now suppose you plan to use fence boards with a certain width given by "W." To find the total number of linear feet "LF" of these fence boards you need, perform this division:

LF = A ÷ W.

For this calculation to work, you must first convert W from whatever units you've used to measure it (usually inches) into feet. In practice, you would also include the gap between the boards as part of W.

**Plugging in Some Numbers:** Suppose you're planning a 6-foot fence that will be 100 feet long, and you intend to use 6-inch redwood fencing boards, which are in reality 5 1/2 inches wide. You plan to space the boards with a 1-inch gap between them.

The area of the fence is 6 • 100 = **600 square feet**.

The width of the fence boards, including the 1-inch gap between them, is 6 1/2 inches. A foot has 12 inches, so the width can be expressed as 6.5 ÷ 12 = **0.54 feet**.

The number of linear feet of fencing boards you need is then 600 ÷ 0.54 = **1,111 feet**.