# How to Figure the Number of Bricks for a Circular Border

Adding a brick border to a circular slab is an easy and cheap way to decorate indoor and outdoor fixtures. If you have a circular concrete pad in your yard, a brick border can help protect the edge of the circle. Indoors, many fireplaces have a semi-circular hearth that can be accented with a border of bricks.

To create a border from rectangular bricks, you arrange them around the circle so that the shorter sides are tangent to the edge of the circle.

If the short side has length **L** and the circle has a radius of **R**, you can use these numbers to compute the maximum number of bricks that will fit around a whole circle. (To compute the max number of bricks for a semi-circular border, just divide by two.)
The formula for the number of bricks is

Max # Bricks = π/[tan^{-1}(0.5L/R)] *radian formula*

where the output of the function tan^{-1} is in radians. If your calculator is set to degrees rather than radians, the equivalent formula is

Max # Bricks = 180/[tan^{-1}(0.5L/R)] *degree formula*

**Example 1:** A circular concrete patio has a diameter of 16 feet, and you want to create a border with bricks that are 3 inches wide. What is the maximum number of bricks you can arrange around the outside edge of the patio?

Since the diameter is 16 feet, the radius is 8 feet. This is equivalent to 96 inches. So you have R = 96 and L = 3. Using the radian formula, you compute

Max # = π/[tan^{-1}(0.5*3/96)]

= π/[tan^{-1}(0.015625)]

= 3.1415926536 / 0.015623729

= 201.078291

The absolute maximum number of whole bricks you can fit around the border is 201. If you leave some space between the bricks, you need fewer.

**Example 2:** A semi-circular concrete patio has a diameter of 16 feet, and you want to create a border with bricks that are 3 inches wide, leaving a 1/4 inch space between bricks. How many bricks do you need?

In this example, R = 96 as before, but now L = 3.25. Using the radian formula, the number of bricks needed for a whole circle is

Max # = π/[tan^{-1}(0.5*3.25/96)]

= π/[tan^{-1}(0.016927083)]

= 3.1415926536 / 0.016925467

= 185.61335

The number required for a semi-circle is 185.61335/2, or about 92 whole bricks.

© *Had2Know 2010
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