How to calculate the quantity of semi circular, full circular and segmental arches

In this construction video tutorial, the renowned engineer S.L. Khan, provides some useful tips to calculate the quantity for semi circular, full circular and segmental arches.

In this construction video, solution is given to the following problem:-

Problem:- Calculate the quantity of a semi circular arch with the following dimensions:-

Span = 10 feet

Height = 5 feet

Thickness = 13.5 inches

Breadth = 13.5 inches


Quantity = X-section area x Arch length

= T x B x Arch length (as x-section area = Thickness x Breadth)

= 13.5” x 13.5 x Arch length

= 1.125 x 1.125 x Arch length (after converting inches to feet)

Now, the question is which length should be taken as there are external and internal lengths. The external length is little bigger as compared to internal length.

So, Arch length = Circumference of half circle

We know circumference of full circle = 2πr

So, circumference of half circle = 2πr/2 = πr

Here, R = 5 + T/2 (half thickness and R = half of span)

After putting the value, we get the following:-

R = 5 + 1.125/2 = 5.5625 feet

So, arch length = π(5.5625) = 17.475 feet

After the value of arch length, we get the following :-

1.125 x 1.125 x Arch length = 1.125 x 1.125 x 17.475 = 22.117 cft

To get more details, go through the following video.

Video Courtesy : SL Khan

quantity arch