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Concrete Math

A friend of mine just called me ask how many cubic inches of concrete is a bag of concrete mix. So you can say he inspired this article.

In order to buy something close to the correct amount you need to know concrete math. That means you need to be able to convert inches, fractions of a foot to decimal form so you can use a calculator to do the math. Concrete is normally poured in slabs that are 4" or 6" thick. Footers are generally 8-12" thick.

Let's get the first set of conversions out of the way before we start:
2" = .17 feet(2/12=.1666)
4" = .33 feet (4/12=.3333)
6" = .50 feet (6/12=.5000)
12" = 1.0 feet (12/12=1.0)

So the answer to my friends question is there are 1037 cubic inches of concrete in an 80 pound bag of redi-mix (12*12*12/.60=1036.80)

An 80 pound bag of concrete mix yields 2/3 (.66) cubic feet of concrete according to the bag label. In reality if you use .60 cubic feet you will be much closer to the actual yield. The easier handled 60 pound bags will yield 75% of that amount or about .495 cubic foot per bag. If you are like me, the state of your back and the prevailing prices will determine which you choose to buy. As I get older a few extra cents per cubic foot is offset by how well I feel the next day.

A cubic yard of concrete is equal to about 45 - 80 pound bags (27/.60=45).

In a contractor grade wheelbarrow when mixed with the proper amount of water you can do 1 - 80 pound bag or 2 - 60 pound bags. It is very hard to properly mix the dry stiff mix you need when you exceed those limits. You can mix 2-80 pound bags but you will have to make a weak soupy mix to do that.

Important Note: Excess water greatly reduces the strength of any concrete.

Whether you are hand mixing or ordering a truck load of mixed concrete you need to understand the math so a to have enough and waste as little as possible. Lets take a look at a few simple examples that would be well within the range of a dedicated DIY person.

A sidewalk or sidewalk section.
This is probably the most common home concrete project that a homeowner will tackle. It might be a repair job, a new walk or just a pad to park the trash cans on. No matter what size your project the math remains the same. Let's look at the math for a 3 foot wide walk that is 12 feet long. For a yard path over a good rock base you can pour the slab as thin as 2" but we will do the math for a traditional 4" thick slab. It is framed with 2 x 4 stock and those are only 3.5" thick but use the stated thickness of 4" as some concrete will seep into the rock base and be lost.

4" is .33 feet so the math is .33 x 3 x 12. That equals 11.88 cubic feet. 11.88 divided by .60 equals 19.8 bags. Round that off to 20 and buy at least one extra bag. This little walk will take about 21 - 80 pound bags.

If it were my project I would plan on doing half one day and the other half another day. 880 pounds is a nice load on small truck or trailer and 10 bags is about all you will want to mix and finish in one day. This also gives you the chance to check your math and adjust your purchase as needed.

A small footer for a garden shed.
Often sheds are just built on a floating slab but sometimes due to the slope of the lot or local codes you might need to pour a footer and lay up some block to create a level base. If you want a poured foundation then refer to the next example; a garden wall and a poured foundation are computed in the same manner.

These specifications are just an example; more width or depth may be required by local codes. A footer should be at least twice as wide as what it will support. Concrete blocks are 8" so your footer needs to be a minimum of 16" and 6" thick. Simply measure the perimeter of your excavation. A 10 x10 shed will be approximately 11 x 11 or 44 feet. The math then looks like this 1.33 x .50 x 44 equals 29.26 cubic feet of concrete. There are 27 cubic feet in a cubic yard so you need just a little over a cubic yard.

A small poured retaining wall.
In my opinion garden walls are best built with retaining wall blocks but you may want to pour a curb or even a poured foundation for a shed or addition. Again the math is width x height x thickness yielding an answer in cubic feet. I am not going a lot of detail but I would be remiss if I did not mention that walls are best poured with the base wider than the top portion. Think of it as an integral footer.

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