Average End-Area Method

The Average End-Area method is a useful tool for estimating quantities in construction. It is an approximate method of calculating volume and is accurate enough for most situations.

The general concept is that you calculate the total volume (V) of a material given, the area of two ends (A) and the perpendicular distance between the two area-faces (L). For a volume comprised of several sections you sum them up:

$$ V = \sum{L \frac{A_1+A_2}{2}} $$

When to use the Average End-Area Method

You can use this anytime you need to quickly approximate the volume of a shape, both in-practice and on the test. On the test you will often be told explicitly to use this method.

Other giveaways are if you are given a table of data similar to this:

Or if you are provided a picture like this (this results in the same volume as above): And asked to calculate the total volume of material to excavate/fill the area. Here is the solution to the two examples above:

$$ V = (210-130) \frac{500+440}{2} + (340 – 210) \frac{440+520}{2} = 100000 \text{ ft}^3$$

These problems will sometimes be combined with soil bulkage/shrinkage problems so be familiar with that.

Stationing

Stationing is used often to represent distances. The big secret is that the number in front of the + sign represents hundreds of feet. This means you can usually just omit the + sign and read it like a normal number. For example: 1+50 ft is the same as 150 ft. Check out the example above of how I did this.