How to Figure the Number of Bricks for a Circular Border

Circular Brick Border Calculator
Radius of Slab inches
Width of Brick inches


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.

         rectangular partitions

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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