I was looking at some curved edging pavers online at the ‘orange box-store’ site, and saw a comment from “acer”: ‘Info needed on circle sizes and how many needed to make different size circles so as to make a round circle without ‘weaving’.
My curiosity aroused, a google Internet search turned up some rather difficult pages (like this one). Most people I know are not truly proficient at mathematics, so for ‘acer’, and other seekers, here is my simplified method for:
How to calculate a circle from a segment or chord:
To show you how to do this, we’ll construct an example.
Let us presume that we have 5 bricks laid out in an arc (‘s’ in the diagram) around a small bush at the center; ‘Θ’ [theta].
How many bricks do we need to completely circle the bush?
We measure the distance (length) between the inside corners of our arc (‘c’ in the diagram) to be 15½ inches (39.37 cm), and measure the inside height of our arc (‘h’ in the diagram) to be 4¼ inches (10.80 cm).
This is all the information we need.
We calculate the radius (‘R’) of the circle from (‘c’), the length of the ‘base‘ and (‘h’), the height of our ‘chord’.
Where c = 15.5 inches, and h = 4.25 inches, so …
Radius R =
Radius R =
Radius R = inches
So Circle Diameter = inches
The next step is to calculate the central angle of the arc segment, ‘Θ’ [theta], which is the angle of the circle used by our 5 bricks. Looking at the diagram (above) we see that this can be solved using the Trigonometry Law of Cosines: knowing 3 sides of a triangle, find an opposite angle.
Triangle sides a and b = Radius R, and side c = chord length c.
We now know all three sides of our triangle, and we want to know the angle opposite the long side, so let’s call the long ‘side c‘, which makes the opposite angle C, which is our ‘Θ’ [theta] segment angle.
Where sides a, b = Radius (9.25 inches)
Where c = chord segment length (15.5 inches)
And angle theta degrees
Since we used 5 bricks to create the arc, each brick is:
degrees per brick
So the total number of bricks we need is:
bricks in the circle.
So we should get 16 bricks (for a single layer).
Note that the ‘missing’ 0.21 (one-fifth) brick in the circumference can be rounded to the nearest full brick. This slight error will not visibly affect our circle due to the natural variance of the bricks, so it can be ignored (in this case).
REMEMBER: Mathematics is only as accurate as your data input, so always measure as accurately and as carefully as you can.
If there is enough interest, I may set a page to automatically calculate these.