Formulas for Concreting

In this post I’m going to share some formulas I have worked out for calculating amounts of materials.

This post is long and has lots of maths, but it is useful if you are pricing a job off a plan or if you want to create a spreadsheet that calculates all of this stuff for you automatically.

Terminology Notes

Below you will see some words that have specific meanings, or there may be some abbreviations. I will list the meanings here with any notes to explain what they mean.

• Allowance Factor: An allowance factor is a factor that gets applied to a total quantity of material to allow for average real world expectations. If you measure out material quantities from a plan you will always find that when you do the job, your material quantities are short, especially with concrete. An allowance factor tries to estimate more accurately what happens in the real world compared to things drawn on paper. Each element of a job will have it’s own Allowance Factor as the factor amount varies depending on the job element.
• BOF: Bottom of footing
• Centre: A Centre is how often a product needs to be placed along a single lineal run. In the industry we often use this term. For example: “The starter bars are at 400mm centres.” means “there is a starter bar every 400mm along this stretch of the job”.
• EB: Edge Beam. This is a beam that runs around the perimeter of a slab. There can be variations of an EB depending on what the engineer requires, which may affect calculations accordingly. (Example: EB1 might be 500mm deep, EB2 might be 400mm deep)
• Element / Job Element: An element is one particular part of a job that is measurable in 2 or 3 dimensions. An element will have many attributes that allow you to calculate how much material is required to build the element. An easy example of an element is the “Slab” element of a job, which is the total square metres of concrete to be done. If we multiply a Slab’s area by the Slab’s thickness, we can see how many cubic metres of concrete the Slab will require. We can also multiply the Slab’s area by 12.5 (which is how many square metres we get from a 6×2.4m sheet of mesh allowing for laps) to determine how many sheets of mesh the Slab will require.
• Estimate: An estimate total is the amount of material you should price the job with. The estimate total of a product quantity for a job element is the element’s tight quantity total multiplied by the element’s allowance factor.
• IB: Internal Beam. This is a beam that runs through the internal area of a slab. There can be variations of an IB depending on what the engineer requires, which may affect calculations accordingly. (Example: IB1 might be 500mm deep, IB2 might be 400mm deep)
• LCP: Lineally Centred Product. This is any physical product (not mathematical product) that spans lineally at a given centre.
• Slab: In this article, ‘Slab’ most often refers to the Slab element of a job (see Element above). This specifically refers to the top portion of a physical, structural concrete slab which begins at the main slab’s subgrade height and ends at the top of concrete (TC).
• Stock Lengths: Stock Length refer to any steel product that comes in a 6m length. This includes products like N12 & N16 stock bars which will commonly be used as trimmer or rib bars above edge or internal beams, 3 or 4 bar trench mesh and Z cages which are all commonly used in edge and internal beams.
• Subgrade: The subgrade refers to the height of the product that a concrete Slab sits on. Often the subgrade height is 100mm below the TC but slab thickness’ can vary so this is not always true. On formed suspended slabs the subgrade height is equivalent to the formed deck height.
• SUP: Single Unit Product. These are products that can’t be calculated using an existing job Element. Examples of SUPs are corner bars and re-entrant bars.
• TC: Top of Concrete. This refers to specifically the finished height of the main slab area of a job. Wet areas, patios, hobs and stepped down areas are not the same as the TC height, they all have relative differences when compared to the TC height. Sometimes I can refer to FFL (Finished Floor Level) as well which may be the same as TC, however I prefer to use FFL to include any additional products than may go on top of TC, such as pavers, tiles or floating floor products.
• Tight: A tight measurement means it has been calculated from a plan.
• TOF: Top of footing
• Units: When using these formulas you must
  

  always remember to keep all the factors in the same units of measure!

  Your high school or primary school math teacher probably harped on about this and you probably didn’t listen, but none of this stuff works if you don’t keep all the numbers in the same units of measure.
  A common example: If you know you have 65 lineal metres of footing, and you want to know the concrete quantity for the footing, and the footing width is 800mm and the depth is 400mm, you don’t calculate: 65 x 800 x 400.
  Why? Because you would be calculating: metres x millimetres x millimetres. See how they aren’t all the same units of measure?
  Always ask: “What unit of measure do you want to end up with?” It is almost always going to be some type of (cubic, square, lineal) metres.
  Make it easy for yourself and convert everything to metres to begin with: 65 x 0.8 x 0.4 is what you would calculate, because 800mm is 0.8 of a metre and 400mm is 0.4 of a metre.

  If there’s one thing you should remember from this article it is to keep all the factors the same unit of measure.

  Without this base rule you will never calculate anything using formulas!

Job Element Formulas

Below I will detail formulas for specific, common job elements.

Beams or Footings

Beam – Concrete Quantities

(Total Lineal Metres x Width x Depth)
= Tight Cubic Metres x Allowance Factor
= Estimate Cubic Metres

Beam – Stock Length Steel Products

(Total Lineal Metres x 5.4)
= Total Number of Stock Lengths w/ Laps (600 max lap)

Sometimes this formula calculates out short. You should double check this to ensure it allows enough product.

Beam – Trench Chair Quantities

(Total Lineal Metres x Trench Chair Spacing)
= Total Number of Individual Chairs Required for Element

Notes

• ‘Depth’ should be the measurement from BOF to TOF, do not include the slab thickness at the top of this calculation. That concrete quantity will be included in the square metres of the slab element.
• ‘Allowance Factor’ for footings in ground I like to allow 30% so the factor is 1.3. If you are doing footings in sand, the allowance factor could need to be higher.
• ‘Trench Chair Spacing’ can vary, but you can usually work off 800 or 900 mm spacing of trench chairs which is 0.8 or 0.9 in metres.
• If you are calculating for formed beams (like on a suspended deck) instead of dug in the ground footings the Allowance Factor will be far lower. Something like 5 to 10% maximum.

Slabs

The Slab element is the main, top section of a slab, not including beams or thickenings. It begins at the main slab’s subgrade height and ends at the top of concrete (TC).

Slab – Area

Break an irregularly shaped job up into square, rectangle or triangle shapes and calculate the area (square metres) of each section. Add all those area totals up to get a job’s total Slab area.

Square and Rectangle Areas

(Length x Width)

(Right Angle) Triangle Areas

(Length x Width / 2)

Perfectly Circular Areas

(3.14 x Radius x Radius)

Slab – Concrete Quantity

Once you have your area total(s) you can multiply by the depth of each area to get concrete quantity:

Slab Area x Slab Thickness 
= Tight Slab Concrete Quantity x Allowance Factor
= Estimate Slab Concrete Quantity

For Slab concrete areas, I like to allow 10% Allowance Factor, so Allowance Factor would be 1.1 in this case.

Slab – Viscrine / Black Plastic

If the slab area is flat, without deep beams, you can simply use the Slab total area to determine the amount of viscrine required.

If you have beams, use the following formula:

Slab Total Area + (Total EB Length x EB Depth x 1.5) + (Total IB Length x IB Depth x 2)
= Tight Total Area for Viscrine

You may also like to apply an Allowance Factor to the beam sections of the formula, as beams notoriously use more material in real life compared to calculations done on paper.

Slab – Waffle Pods (added July 2022)

Calculating out the total number of waffle pods in an area can be done approximately (it’s pretty close to being exact, maybe a little over which is what we want realistically) by getting the footprint of a pod and dividing it into the area size. 

Most pods are 1.1m x 1.1m – check the size your supplier has. However, I found it’s more accurate to include half of the rib beam’s width in with the pod size. Including all of the rib beam’s width seemed to yield too low a number of pods and not including it seemed to yield too high a number of pods. 

Usually the rib beam will be 100mm or 0.1m, so the final ‘standard’ size for a pod in m2 is:

1.15 x 1.15
= 1.32m2

To calculate how many pods for any given area, just do: 

Area / 1.32
or
Area * 1.32^-1

You can change division to multiplication by raising the divisor value to the power of -1. This can be useful in spreadsheets or programs where ordering of values may become an issue.

I tried this formula and it seemed to work out even though the Slab Area included the 300mm wide Edge Beam in it. I was assuming that the engineering plan was drawn to scale and was showing the exact number of pods in their location (which a pod plan usually does).

Slab – Waffle Pods – Spacers

Spacers can be calculated just like chairs. They are intersections at a fixed interval in a grid pattern. Therefore, the formula to find how many spacers in a given area is: 

Area / Center^2
or
Area * Center^-2

Ensure Area and Center are in the same units of measure, ie meters: square meters for area and meters apart for the Center spacing. 50m2 and 0.6m centers (600mm) for example. (See Chairs section below for update comments)

Slab – Waffle Pods – Rib Bars

Rib bars run both directions between pods and sit on top of the spacers. This is similar to calculating for saw cuts so the following formula will work to apply to an area: 

(Length / Center + 1) * Width * 2 / 5.4

Where: Length and Width are the Area’s length and width, Center is how far apart each rib bar is laid (1.2m typically). This formula will calculate the number of 6m stock bars required, including lap (up to 0.6m). You should RoundUp() the result. If you want to know the lineal meters instead, remove the “/ 5.4” from the end of the formula. 

Rib Bars – Calculate Length and Width runs separately

If you want to calculate ribs along only one axis, you can use the following formulas.

Along the Length (Ribs that are spanning the Width of the Area)

(Length / 1.2 * Width) / 5.4

Across the Width (Ribs that are spanning the Length of the Area)

(Width / 1.2 * Length) / 5.4

Both formulas above will calculate out to number of 6m stock bars required, including lap (up to 0.6m). To calculate the lineal meters only, remove “/ 5.4” from the end of the formula.

Slab – Mesh

On the Gold Coast you can buy 2 sizes of mesh mats: 

• Full Size Mesh: 6.0m x 2.4m
• Ute Mesh: 4.0m x 2.0m

If mesh is laid out in a grid-like fashion, you can determine exactly how many square metres a mat of mesh should cover. You have to allow for the laps in this, and I work off the following amounts for the Mesh Coverage Factor: 

• Full Size Mesh: 12.5m2 per mat
• Ute Mesh: 6.9m2 per mat

If the engineer requires lap that is more than the standard “2 bars and 40mm” you might need to calculate the mesh coverage factor, especially if it’s a large area being done.

To determine how many mats of mesh you need: 

RoundUp( (Total Slab Area x Mesh Coverage Factor) )
= Total Number of Mats of Mesh Required

Notice the RoundUp() to be applied to the result. If you calculate 12.6 mats of mesh, you will need to price and order 13 mats.

Slab – Mesh – Chairs

To calculate how many mesh chairs will be required, you need to decided on the Chair Centre value first. How far apart will you place the chairs? Every metre? Every 800mm or every 600mm? Once you have decided this, you can determine how many square metres you will get from 100 chairs using this formula: 

(Chair Centre x 9)^2

Chair Centre	Formula	Result (Chair Coverage Factor)
1 metre	(1.0 x 9)^2	81 m2
800mm	(0.8 x 9)^2	51.84 m2
600mm	(0.6 x 9)^2	29.16 m2

We can now use the Chair Coverage Factor with the Slab Area to determine how many bags of 100 chairs we will need: 

RoundUp( (Slab Area / Chair Coverage Factor) )
= Total Number of Bags of 100 Chairs Required

Update 20220723

I recently revisited this formula when working out spacers for waffle pod slabs. I found this formula a little confusing, but I worked out why. The “9” in the formula is factoring in a 10% wastage I guess. Also, what is being created above is a Chair Coverage Factor. This formula is not initially telling you how many chairs – or more generally speaking – how many intersections we are needing. That is done in the formula above with the RoundUp() function involved with it. Because the original formula uses 9 in it for wastage, that’s why the round up is needed. I mean, you can still get fractional answers depending on the Center value, but if you’re using simple values like 1m or 0.5m centers a RoundUp might not be needed.

So here is a much simpler formula for this, and we’ll call it Intersections Within An Area

The formula is: 

Area / Center^2
or
Area * Center^-2

This will give you how many intersection points there are in an Area, given that the Center distance is the same on both axes (ie: same center spacings on both the length and width of the area). Just remember that this is giving you total number of intersections which will represent the number of individual chairs or pod spacers, or whatever other product you’re using this formula to calculate quantity for. You may want to RoundUp() the result to get a whole value.

Note that you can change this formula from division to multiplication by making the exponent value negative. It gives the same answer and allows you to use multiplication, which I think is better as it doesn’t matter which order the factors are presented in the operation.

End of Update

Notes

• Mesh and Chairs don’t really need an Allowance Factor as they are minimal loss products and we RoundUp() their Tight calculated values so we have that much as an allowance anyway.
• These Chair Formulas are only for chairs that come in Bags of 100! If the bag quantity differs the Chair Coverage Formula needs to be adjusted.
• ^2 means “to the power of 2” or “squared” which mathematically means “multiply this by itself” so: (0.8 x 9)^2 = 7.2^2 = 7.2 x 7.2 = 51.84

Lineally Centred Products

What is a lineally centred product (LCP)? The easiest way to identify one of these is to ask if we say the product “can be at at X centres”. Try it:

• Can mesh be at 600 centres? No (doesn’t make sense). It’s not a LCP.
• Can concrete be at 600 centres? No (doesn’t make sense). It’s not a LCP.
• Can dowel bars be at 600 centres? Yes. It can be a LCP.
• Can starter bars be at 400 centres? Yes. It can be a LCP.
• Can slab ties be at 1 metre centres? Yes. It can be a LCP.

There are two factors we need when calculating quantities of LCPs:

1. The total lineal metres that this product spans over
2. The Centre that this product will be placed at

If you imagine doing a house renovation slab the new slab will join onto the existing slab in places. Usually, along these runs where the 2 slabs join the engineer will require dowel bars. Let’s say the engineer wants dowel bars at 600mm centres and the length of the join is 12.5m. We can use the following formula to calculate how many dowel bars are required: 

RoundUp( (Total Length / Product Centre) ) + 1
= Tight Total Units of Product

Example: The product is N16 Galvanized Dowel Bars. The centre for them are 600mm and the Total Length we require them over is 12.5m: 

RoundUp(12.5 / 0.6) + 1
= RoundUp(20.83) + 1
= 21 + 1
= 22 N16 Galvanized Dowel Bars are needed to cover 12.5m lineally at 600mm centres

Notes

• This formula can be applied to any LCP, just change the name of the product and the values accordingly:

  N12 Starter Bars at 400mm centres over 24m
  RoundUp( (24 / 0.4) ) + 1
  = 61 starter bars

  R10 Slab Ties at 1 metre centres over 68m of footings
  RoundUp( (68 / 1.0) ) + 1
  = 69 slab ties

• Why do we + 1? If you look at the slab ties example above, you can see we have 68m lineal of footing and a slab tie at each metre. If we place a bar at metre 1, then metre 2 … up to metre 68 we need 68 bars right? Yes, but we missed a bar at 0 (imagine holding the tape measure to measure where to put these bars). You need a bar at 0 as well, which is what the + 1 is for. Also its better to have too many than not enough.

Single Unit Products

Single Unit Products (SUPs) are products that can’t be calculated using an existing Job Element. Examples of SUPs are corner bars and re-entrant bars.

SUPs have attributes of their own but we can’t simply apply them to a calculation of a Job Element to determine the quantity needed. Consider re-entrant bars as an example: 

Re-Entrant Bars Cut from 3 Bar Trench Mesh

The engineer may ask for re-entrant bars which can be either 3 x N12 bars at 2.0m long, or a piece of 3 bar trench mesh (3-L11TM) that is 2.0m long.

It is often quicker to look at the plan and count up what you need for items like this, but if you want to use a formula in a spreadsheet you need a way to mathematically calculate these items. If we decide to use 3-L11TM as our re-entrant bars we can calculate using this formula: 

RoundUp(Number or Re-Entrant Corners x (Re-Entrant Length / 6))
= Total Number of Stock 3-L11TM Needed

The 6 in the formula represents a stock length of trench mesh, which is 6.0m long. Re-Entrant Length is the length the engineer wants the re-entrant bars to be, the number of re-entrant corners is how many internal corners on the job require re-entrant bars (you need to count this up looking at the plan). Let’s add some example values. Say we have 5 corners that need re-entrant bars, and the re-entrant bars have to be 1.8m minimum length:

RoundUp(5 x (1.8 / 6))
= RoundUp(1.5)
= 2 x Stock 3-L11TM Needed

This means that 2 stock lengths of 3-L11TM trench mesh will be enough for 5 re-entrant corners where the bars are 1.8m. Check it manually: 3 x 1.8 = 5.4m (600mm off cut) + 2 x 1.8m = 3.6m (2.4m off cut).

Corner Bars

Corner bars are a SUP that is just quicker and easier to count off plan and add into the quote or estimate figures. There’s no real way to calculate how many you need, so in a spreadsheet or program you’d just have to have an option to manually add items like this.

Check the engineer’s details to see how many corner bars are needed per right angle corner and T-intersection and then count the number of each corner type on the plan. Multiply out how many individual corner bars are needed.

Delivery

Delivery is another SUP that should be added to quotes or estimates. It’s just 1 unit of delivery at whatever the charge rate is for delivery of the goods to the job address.

Discuss

Let me know if something I have here is not correct. I know that the trench mesh formula doesn’t always calculate out correctly, and I’m not sure why. I’d guess it’s because it is calculating for continuous bar use but we will end up with off-cuts that can’t be used in a lot of situations.

If you have any other handy formulas for concreting quantities, let us know in the comments below!