Calculate how many bricks or blocks you need for a circle, fire pit ring or round patio from its radius or diameter, using typical brick sizes plus waste.

Estimate bricks around a circle.

Ring: inner-face radius or diameter. Patio: outside edge.

8 in is a typical standard brick; landscape and fire-pit blocks are often 12 or 16 in. Enter yours if different.

Courses, joints and waste
Blank means one course.

Blank means no joint.

Blank means 10%. Enter 0 for no extra bricks.

Brick Circle Formula

The following formula is used to calculate the total number of bricks needed to create a circle of a certain size.

N = π / arctan((s + j) / (2r))

Geometry source: U. H. Kurzweg, Areas of Regular n-Sided Polygons (2023). Rearranging the apothem relation gives the continuous ring count; angles here are in radians.

  • Where N is the number of bricks needed to make the circle
  • s is the length of the long side of the brick
  • r is the inner-face radius, measured from the center to the midpoint of a brick face; j is the joint width (zero if omitted).

In this case, the radius and length of the brick must be in the same units, for example, both in inches.

How many bricks make a circle?

The number of bricks that make a circle depends on both the length of the brick and the radius of the circle you are trying to make.

The larger the circle, the more bricks it will require. Conversely, the larger the brick, the smaller number of bricks needed to make the circle.

How to calculate the number of bricks in a circle?

Example Problem:

The following example problem outlines the steps required to calculate the number of bricks in a circle.

First, determine the radius of the circle. In this example, the person is trying to make a circle with a diameter of 40 inches. Dividing by 2 yields a radius of 20 inches.

Next, measure the long edge of the brick. The bricks being used for this circle have a length of 4 inches.

Finally, calculate the number of bricks needed using the formula above:

#B = π/arctan((s+j)/(2*r))

#B = π/arctan(4/(2*20))

#B ≈ 31.52, rounded up to 32 bricks per course before waste, or 36 with the default 10% waste. This example uses a 20-inch inner-face radius and no joint. Cuts or adjusted joints are needed to close the ring.