Enter the volume you need (after mixing) and the mix. Typical values are already filled in for the yield, water-cement ratio, bulk density and bag weight. Change them if the product specifies other values.
:
:
Cement
Sand
Gravel
The mix ratio is by volume. Choosing a preset fills in the ratio, the yield and the water-cement ratio. With gravel set to 0 it is mortar; with gravel above 0 it is concrete.
Result and figure
Enter the volume you need (or the area and thickness) on the left, choose a mix from the presets and press "Calculate". The breakdown of materials will appear here.
Table of Contents
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What you can do on this page
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What is this calculation used for?
-
How to Use
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Formulas and figures
-
Symbols and terms
-
Good to know before you start
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How to calculate it in Excel
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How to calculate it in Google Sheets
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How to calculate it in Python
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How to write it in LaTeX and other math languages (copy and paste)
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How to have ChatGPT do the calculation
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DataChef Features
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Related Features
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NumberChef Calculators List
What you can do on this page
- From the volume you need (ft³ or yd³, or area × thickness) and a mix ratio (presets such as 1:3 mortar and 1:2:4 concrete, or your own), you get the volume and weight of cement, sand and gravel on the spot
- The number of bags is rounded up for the bag size you choose (94 lb cement, 50 lb sand and so on, all changeable) and shown next to the value before rounding, so you can see where the count comes from
- The water is found from the water-cement ratio (w/c). The formulas also show the yield (the mixed volume is smaller than the dry materials) and the waste factor for spills and material left on tools
- You can also work backward to find how much you can make with the cement bags you have. It is handy for checking how much mortar one bag of cement makes and how many bags of sand go with it
- Enter bag prices to get the estimated cost. A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page
This page finds the breakdown of materials from a mix ratio. To find the volume of concrete from a shape such as a slab or footing, use the "Concrete Calculator" first and enter that volume here. The yield, water-cement ratio and bulk density are rough values that change with the materials and the job; if the bag or the manufacturer gives a mix, follow it. For footings, structures and other concrete where strength matters, do not rely on these volume ratios; follow the design documents, the local building code and the ready-mix supplier's mix design (proportioned by weight).
What is this calculation used for?
Joint mortar for a block wall or a brick flower bed
For a short garden wall of concrete blocks, the mortar for the 3/8 in joints is often well under 1 ft³, which you can find from the joint area × thickness. Enter that volume with a 1:3 mix, and you find that one bag of cement is plenty, and how many 50 lb bags of sand to buy.
The smaller the job, the more useful the backward calculation "how much does one bag of cement make?" becomes. One 94 lb bag in 1:3 mortar makes about 2.8 ft³ (at a 70% yield).
A small concrete slab by the door or under a shed
A 5 ft × 4 ft slab 4 in thick needs \(20 \times 4 \div 12 \approx 6.67\) ft³ (about 0.25 yd³). With a 1:2:4 mix, a 67% yield and 5% waste, the dry materials come to about 10.4 ft³: cement about 1.49 ft³ (about 140 lb, two 94 lb bags), sand about 2.99 ft³ (about 281 lb, six 50 lb bags) and gravel about 5.97 ft³ (about 597 lb, twelve 50 lb bags), with about 77 lb (about 9.3 gal) of water.
Materials and water together weigh more than 1,000 lb, so at this size you should decide whether to mix it yourself, rent a mixer, or use premixed concrete bags. An 80 lb bag of premixed concrete makes about 0.6 ft³, so this slab would take \(\lceil 6.67 \div 0.6 \rceil = 12\) bags. Find the volume from the shape with the "Concrete Calculator" and enter it here to get the breakdown.
A mortar bed under tile or stone
To redo the tile at an entry, spreading a ¾ in mortar bed over 30 ft² takes \(30 \times 0.75 \div 12 = 1.875\) ft³. With a 1:3 mix, a 70% yield and 10% waste, the dry materials come to about 2.95 ft³: cement about 0.74 ft³ (about 69 lb, one bag) and sand about 2.21 ft³ (about 208 lb, five 50 lb bags).
Counting the tiles themselves with the "Tile Calculator" and the mortar bed on this page keeps items from being missed in your estimate.
Premixed mortar bags versus mixing your own
Premixed mortar in bags (sand already included, such as Type N or Type S masonry mortar) only needs water and is convenient, but for larger amounts buying cement and sand separately and mixing them yourself often costs less. Find the bags of cement and sand and the estimated cost on this page, and compare them with the number of premixed bags (the amount one bag makes is printed on the bag) to decide which suits your job.
Prices vary by store and region, so enter the prices at the store where you will buy.
Checking the material breakdown on an estimate
Masonry and landscaping estimates list mixes and quantities such as "1:3 mortar, ... ft²" or "1:2:4 concrete, ... yd³". Enter the same mix and quantity on this page to see the breakdown into cement, sand and gravel (weight and bags), so you can follow where the estimate's materials come from.
In real jobs the yield, waste and water change with site conditions, and labor, delivery and tools cost extra, so the material quantities alone cannot tell you whether the price is fair. Use this as a guide.
Formulas and figures
Volume needed from area and thickness
Standard notation
(the usual math form)
\(V\)
\(=\)
\(A\)
\(\times\)
\(t\)
In words
(symbols replaced with words)
③
\(V\): volume needed
\(=\)
①
\(A\): area
\(\times\)
②
\(t\): thickness
The formula in words
①
Multiply the
\(A\): area (ft²)
②
by the
\(t\): thickness (in feet)
③
to get the
\(V\): volume needed (ft³)
Quick example
To spread mortar ¾ in (= 0.0625 ft) thick over 40 ft² along a flower bed, the volume needed is
\(V\): volume needed
\(=\)
area (40 ft²)
\(\times\)
thickness (0.0625 ft)
\(40 \times 0.0625 = 2.5\ \mathrm{ft^3} \approx 0.0926\ \mathrm{yd^3}\)
Key idea
Area is in square feet, but thickness is usually measured in inches, so turn the thickness into feet before multiplying (¾ in = 0.75 ÷ 12 = 0.0625 ft, 4 in = 4 ÷ 12 ≈ 0.333 ft). For small DIY jobs cubic feet are easy to picture, while concrete for bigger jobs is ordered in cubic yards, so this calculator shows both. 1 yd³ = 27 ft³.
For complex shapes such as slabs, footings and steps, find the volume from the shape with the "Concrete Calculator" and enter it under "Enter the volume directly".
Volume needed with waste
Standard notation
(the usual math form)
\(V'\)
\(=\)
\(V\)
\(\times\)
\((\)
\(1\)
\(+\)
\(r\)
\(\div\)
\(100\)
\()\)
In words
(symbols replaced with words)
③
\(V'\): volume with waste
\(=\)
①
\(V\): volume needed
\(\times\)
\((\)
\(1\)
\(+\)
②
\(r\): waste factor (%)
\(\div\)
\(100\)
\()\)
The formula in words
①
Multiply the
\(V\): volume needed
②
by "1 +
\(r\): waste factor (%)
÷ 100" (the waste multiplier)
③
to get the
\(V'\): volume with waste
Quick example
If you need 2.5 ft³ and allow a 10% waste factor, the volume is
\(V'\): volume with waste
\(=\)
volume needed (2.5 ft³)
\(\times\)
\((\)
\(1\)
\(+\)
waste factor (10%)
\(\div\)
\(100\)
\()\)
\(2.5 \times (1 + 10 \div 100) = 2.5 \times 1.1 = 2.75\ \mathrm{ft^3}\)
Key idea
Some mortar or concrete always stays in the mortar box (mixing tub), on the trowel and shovel, spills while you carry it, or fills dips in the surface, so the exact calculated amount usually falls short. This is the "waste", and a set percentage is added to the net amount for it. 5–10% is common; allow a bit more for rough surfaces or when you mix many small batches.
"10% more" is calculated as "× 1.1": the net amount times 1.1, not the net amount plus the number 10. In the backward mode (how much your cement makes), the amount you can make is divided by this multiplier to give the "usable amount".
Total dry volume before mixing (yield)
Figure
Standard notation
(the usual math form)
\(V_d\)
\(=\)
\(V'\)
\(\div\)
\((\)
\(y\)
\(\div\)
\(100\)
\()\)
In words
(symbols replaced with words)
③
\(V_d\): total dry volume (before mixing)
\(=\)
①
\(V'\): volume with waste
\(\div\)
\((\)
②
\(y\): yield (%)
\(\div\)
\(100\)
\()\)
The formula in words
①
Divide the
\(V'\): volume with waste
②
by "
\(y\): yield (%)
÷ 100"
③
to get the
\(V_d\): total dry volume (before mixing)
Quick example
If you want 2.75 ft³ after mixing and the yield is 70%, the total dry materials to prepare are
\(V_d\): total dry volume
\(=\)
volume with waste (2.75 ft³)
\(\div\)
\((\)
yield (70%)
\(\div\)
\(100\)
\()\)
\(2.75 \div (70 \div 100) = 2.75 \div 0.7 \approx 3.929\ \mathrm{ft^3}\)
Key idea
Mixing 1 ft³ of cement and 3 ft³ of sand with water does not give 4 ft³ of mortar. Dry sand and gravel have air gaps between the grains, and when you mix, the cement paste (cement and water) fills those gaps, so the total volume shrinks. The mixed volume as a share of the total dry materials is called the yield here.
The yield changes with the grain size, moisture and how well it is compacted; it is often about 65–75% for mortar and 60–70% for concrete. This calculator uses the value in the input as is, so if a real batch comes out short, lower the value, and if there is extra, raise it. The defaults (70% for mortar and 67% for concrete) lean slightly toward having a little extra. "Amount needed ÷ yield" is the same as "amount needed × about 1.4–1.5", and estimators often use it in that form, as a dry volume factor.
Splitting the volume by the mix ratio
Figure
Standard notation
(the usual math form)
\(V_c\)
\(=\)
\(V_d\)
\(\times\)
\(\dfrac{c}{c + s + g}\)
In words
(symbols replaced with words)
③
\(V_c\): cement volume
\(=\)
①
\(V_d\): total dry volume
\(\times\)
②
\(\dfrac{\text{cement part } c}{\text{sum of the ratio } c + s + g}\)
The formula in words
①
Multiply the
\(V_d\): total dry volume
②
by "
cement part \(c\) ÷ sum of the ratio \(c + s + g\)
" (the share of cement in the whole)
③
to get the
\(V_c\): cement volume
(sand and gravel work the same way, each with its own part ÷ the sum)
Quick example
Splitting a total dry volume of 3.929 ft³ for 1:3 mortar (1 cement, 3 sand, 0 gravel), the cement volume is
\(V_c\): cement volume
\(=\)
total dry volume (3.929 ft³)
\(\times\)
share of cement (1 ÷ 4)
\(3.929 \times \dfrac{1}{1 + 3} \approx 0.982\ \mathrm{ft^3}\)
\(3.929 \times \dfrac{3}{1 + 3} \approx 2.946\ \mathrm{ft^3}\ \text{(sand)}\)
Key idea
"1:3" is a ratio by volume, "1 part cement to 3 parts sand", meaning 1 bucket of cement to 3 buckets of sand, measured with the same bucket. The total is \(1 + 3 = 4\) parts, so cement is \(\dfrac{1}{4}\) of the whole and sand is \(\dfrac{3}{4}\). For "1:2:4" concrete the total is 7: cement \(\dfrac{1}{7}\), sand \(\dfrac{2}{7}\) and gravel \(\dfrac{4}{7}\).
As a rough guide, 1:3 mortar is a common mix for plastering and block joints, and 1:2 is for a stronger, stickier finish or repairs. For concrete, 1:2:4 is a common mix for slabs and small footings, and 1:3:6 is a lean mix for a mud slab or fill where strength matters little. If the bag or the manufacturer gives a mix, follow it.
Weight and bags of each material
Standard notation
(the usual math form)
\(W\)
\(=\)
\(V\)
\(\times\)
\(\rho\)
\(N\)
\(=\)
\(\lceil\)
\(W\)
\(\div\)
\(b\)
\(\rceil\)
In words
(symbols replaced with words)
③
\(W\): weight (lb)
\(=\)
①
\(V\): volume of the material (ft³)
\(\times\)
②
\(\rho\): bulk density (lb/ft³)
⑤
\(N\): number of bags
\(=\)
\(\lceil\)
\(W\): weight (lb)
\(\div\)
④
\(b\): bag weight (lb)
\(\rceil\)
The formula in words
①
Multiply the
\(V\): volume of the material (ft³)
②
by the
\(\rho\): bulk density (weight per cubic foot, lb/ft³)
③
to get the
\(W\): weight (lb)
. Then divide it by the
④
\(b\): bag weight (lb)
and round up to a whole number (the symbol \(\lceil\ \rceil\) means "round up")
⑤
to get the
\(N\): number of bags
Quick example
For 0.982 ft³ of cement (bulk density 94 lb/ft³) bought in 94 lb bags, the weight and the number of bags are
\(W\): weight
\(=\)
cement volume (0.982 ft³)
\(\times\)
bulk density (94 lb/ft³)
\(0.982 \times 94 \approx 92.3\ \mathrm{lb}\)
\(92.3 \div 94 \approx 0.982 \quad \lceil 0.982 \rceil = 1\ \text{bag}\)
Key idea
The mix is set by volume, but the materials are sold by weight (in bags). Bulk density turns volume into weight: it is the weight of 1 ft³ of loose material poured out of the bag. The grains of sand and gravel themselves weigh about 165 lb/ft³, but loose material has gaps between the grains, so its bulk density is much lower, about 94–100 lb/ft³. In the US, one 94 lb bag of portland cement is traditionally counted as 1 ft³. The values are for dry sand; damp sand bulks up (the water holds the grains apart), so 1 ft³ of it weighs less. Measuring damp sand by the bucket gives too little sand (too much cement), so use bagged dry sand, or add a little more if your sand is damp.
Bags can only be bought whole, so if the division leaves a decimal, always round up. In the same example, sand is \(2.946 \times 94 \approx 277\) lb, and with 50 lb bags \(277 \div 50 \approx 5.54\) → 6 bags. The calculator also shows the value before rounding up, so you can try other bag sizes to reduce the leftover.
Water (water-cement ratio)
Standard notation
(the usual math form)
\(W_w\)
\(=\)
\(W_c\)
\(\times\)
\(\dfrac{W}{C}\)
\(\div\)
\(100\)
In words
(symbols replaced with words)
③
\(W_w\): water (lb)
\(=\)
①
\(W_c\): cement weight (lb)
\(\times\)
②
\(W/C\): water-cement ratio (%)
\(\div\)
\(100\)
The formula in words
①
Multiply the
\(W_c\): cement weight (lb)
②
by the
\(W/C\): water-cement ratio (%)
÷ 100
③
to get the
\(W_w\): water (lb; 1 gal of water ≈ 8.34 lb)
Quick example
The water for mixing 92.3 lb of cement at a water-cement ratio of 60% is
\(W_w\): water
\(=\)
cement weight (92.3 lb)
\(\times\)
water-cement ratio (60%)
\(\div\)
\(100\)
\(92.3 \times 60 \div 100 \approx 55.4\ \mathrm{lb}\)
\(55.4 \div 8.34 \approx 6.64\ \mathrm{gal}\)
Key idea
The water is based on the weight of cement, not of sand or gravel. Cement hardens by reacting with water (hydration), so the strength depends on the ratio of water to cement. This ratio is called the water-cement ratio (w/c) and is given as the weight of water as a percentage of the weight of cement. Mixing water is usually measured in gallons in the US, and 1 gal of water weighs about 8.34 lb, so divide the pounds by 8.34.
More water makes the mix softer and easier to work, but it is weaker after it hardens and cracks more easily. About 55–65% for mortar and 50–60% for concrete is typical, but the water you need changes with how damp the sand is, so in practice add water a little at a time and check the consistency. If the bag gives an amount of water, follow it.
Working backward: how much your cement makes
Standard notation
(the usual math form)
\(V_{mix}\)
\(=\)
\(\dfrac{h \times b_c}{\rho_c}\)
\(\times\)
\(\dfrac{c + s + g}{c}\)
\(\times\)
\(\dfrac{y}{100}\)
In words
(symbols replaced with words)
④
\(V_{mix}\): mixed volume you can make
\(=\)
①
\(\dfrac{\text{cement weight (bags } h \times \text{bag weight } b_c\text{)}}{\text{cement bulk density } \rho_c}\)
\(\times\)
②
\(\dfrac{\text{sum of the ratio } c + s + g}{\text{cement part } c}\)
\(\times\)
③
\(\dfrac{\text{yield } y}{100}\)
The formula in words
①
Take the
cement volume (weight \(h \times b_c\) ÷ bulk density \(\rho_c\))
②
multiply by
the sum of the ratio \(c + s + g\) ÷ the cement part \(c\)
to get the total dry volume,
③
and multiply by
the yield \(y\) ÷ 100
④
to get the
\(V_{mix}\): mixed volume you can make
Quick example
Making 1:3 mortar at a 70% yield with one 94 lb bag of cement (bulk density 94 lb/ft³), the amount you can make is
\(V_{mix}\): amount you can make
\(=\)
cement volume (94 lb ÷ 94)
\(\times\)
sum of the ratio ÷ cement part (4 ÷ 1)
\(\times\)
yield (70%)
\(94 \div 94 = 1\ \mathrm{ft^3}\)
\(1 \times 4 \times 0.7 = 2.8\ \mathrm{ft^3}\)
Key idea
This formula follows the "split by the mix ratio" and "yield" formulas in reverse. Once you know the volume of one bag of cement, the mix ratio tells you how much sand goes with it (in the example \(1 \times 3 = 3\) ft³, about 282 lb, which is 6 bags of 50 lb), and the total dry materials \(1 + 3 = 4\) ft³ times the yield is the amount of mortar you can make.
So one 94 lb bag of cement in 1:3 mortar makes about 2.8 ft³ (at a 70% yield). Use this to judge whether one bag is enough for block joints or a small repair. If you enter a waste factor, the calculator also shows the "usable amount", the amount you can make divided by the waste multiplier.
Estimated cost
Standard notation
(the usual math form)
\(T\)
\(=\)
\(N_c \times u_c\)
\(+\)
\(N_s \times u_s\)
\(+\)
\(N_g \times u_g\)
In words
(symbols replaced with words)
④
\(T\): estimated cost
\(=\)
①
cement bags \(N_c\) × price \(u_c\)
\(+\)
②
sand bags \(N_s\) × price \(u_s\)
\(+\)
③
gravel bags \(N_g\) × price \(u_g\)
The formula in words
①
Add
cement bags \(N_c\) × price per bag \(u_c\)
②
,
sand bags \(N_s\) × price per bag \(u_s\)
③
and
gravel bags \(N_g\) × price per bag \(u_g\)
④
to get the
\(T\): estimated cost
Quick example
The cost of one 94 lb bag of cement (for example, $15 a bag) and six 50 lb bags of sand (for example, $6 a bag) is
\(T\): estimated cost
\(=\)
cement (1 bag × $15)
\(+\)
sand (6 bags × $6)
\(1 \times 15 + 6 \times 6 = 15 + 36 = 51\)
Key idea
You buy materials in whole bags, so the cost is "rounded-up bags × price per bag" added up for each material. Only materials with a price entered are included (for mortar with no gravel, the gravel field is not used). This cost covers only the materials. Tools such as a mortar box, trowel and buckets, water, delivery and labor if you hire someone all cost extra.
The backbone of a mix calculation is "add waste to the volume you need, divide by the yield to get the total dry volume, and split it among the materials by the mix ratio". Each volume is turned into weight with the bulk density and the bags are rounded up, and the water is the cement weight × the water-cement ratio.
Symbols and terms
Symbols
| \(V\) | vee | The volume needed (the amount of mortar or concrete after mixing, in ft³ or yd³). From the first letter of "volume". 1 yd³ = 27 ft³. |
| \(A\) | ay | The area of the surface to cover or pour (ft²). From the first letter of "area". |
| \(t\) | tee | The thickness (ft). From the first letter of "thickness". A thickness measured in inches is divided by 12 to turn it into feet before multiplying. |
| \(r\) | ar | The waste factor (%), the extra for material left in the mortar box and on tools and for spills. From the first letter of "rate". |
| \(V'\) | vee prime | The volume needed with waste. Found with \(V' = V \times (1 + r \div 100)\). The prime mark (′) shows "a slightly changed version of \(V\)". |
| \(y\) | why | The yield (%), the mixed volume as a share of the total dry materials. From the first letter of "yield". |
| \(V_d\) | vee sub dee | The total dry volume of the materials before mixing (ft³). Found with \(V_d = V' \div (y \div 100)\). The subscript d comes from "dry". |
| \(c,\ s,\ g\) | see, ess, gee | The cement, sand and gravel parts of the mix ratio by volume. From the first letters of "cement", "sand" and "gravel". For "1:3", \(c = 1,\ s = 3,\ g = 0\). |
| \(V_c,\ V_s,\ V_g\) | vee sub see, vee sub ess, vee sub gee | The volumes of cement, sand and gravel (ft³). Each is the total dry volume times "that material's part ÷ the sum of the ratio". |
| \(\rho\) | rho | The bulk density (lb/ft³). The Greek letter rho, the usual symbol for density in physics. Cement, sand and gravel each have their own, \(\rho_c,\ \rho_s,\ \rho_g\). |
| \(W\) | double-u | The weight of a material (lb). Found with \(W = V \times \rho\). From the first letter of "weight". The cement weight is written \(W_c\) and the water \(W_w\). |
| \(b\) | bee | The weight of one bag (lb). From the first letter of "bag". In the US, cement is commonly 94 lb and sand and gravel 50 lb. |
| \(N\) | en | The number of bags. Found with \(N = \lceil W \div b \rceil\). From the first letter of "number". |
| \(W/C\) | water-cement ratio | The water-cement ratio (%), the weight of water ÷ the weight of cement. It sets the amount of water. |
| \(h\) | aitch | The number of cement bags on hand (the input for working backward). From the first letter of "have". |
| \(V_{mix}\) | vee sub mix | The mixed volume you can make with the cement on hand (ft³). From "mix". |
| \(u\) | you | The price of one bag ($). From the first letter of "unit price". |
| \(T\) | tee | The estimated cost (materials only). From the first letter of "total". |
| \(\lceil x \rceil\) | ceiling of x | The symbol for rounding up to a whole number. (Example - \(\lceil 5.54 \rceil = 6\), \(\lceil 2 \rceil = 2\)) |
Terms
| mortar | Cement and sand mixed with water. It is used for block and brick joints, as a base coat or finish on walls and floors, and as a bed under tile. It has no gravel, so it can be worked into small spaces. Bagged masonry mortar in the US (such as Type N and Type S) also contains lime. |
| concrete | Cement, sand and gravel mixed with water. The gravel makes it hard and strong, so it is used for slabs, footings, posts and other parts that carry loads. Thinking of it as mortar with gravel added shows why the same formulas work on this page. |
| cement | A gray powder made by heating limestone and other materials. It reacts with water and hardens (hydration), acting as the "glue" that binds sand and gravel. In the US, portland cement is sold in 94 lb bags (one "sack", taken as 1 ft³) and 47 lb bags. |
| mix ratio | The proportions in which cement, sand and gravel are mixed. On this page it is by volume. "1:3" is 1 part cement to 3 parts sand, and "1:2:4" is 1 part cement, 2 parts sand and 4 parts gravel. |
| by volume | A mix measured by volume. You can measure "1 bucket of cement to 3 buckets of sand" with the same bucket, so on job sites and for DIY a mix by volume is more common than a mix by weight. |
| yield | The mixed volume of mortar or concrete as a percentage of the total dry materials. It is below 100% because the cement paste fills the gaps between the grains of sand and gravel (often about 65–75% for mortar and 60–70% for concrete). Estimators often use its reciprocal, a dry volume factor of about 1.4–1.5. |
| water-cement ratio | The weight of water as a percentage of the weight of cement, written w/c. The lower it is, the stronger the result; the higher, the softer and easier to work. About 55–65% for mortar and 50–60% for concrete is typical, but follow the product instructions if there are any. |
| bulk density | The weight of loose material poured out of the bag, per unit volume (lb/ft³). It includes the gaps between the grains, so it is lower than the density of the grains themselves (about 165 lb/ft³ for sand and gravel). Typical values are about 94 lb/ft³ for cement, 94–100 for sand and 100 for gravel. |
| waste factor | The percentage added to the net amount for material left in the mortar box and on the trowel and shovel, spills, and extra used on uneven surfaces. 5–10% is common. |
| rounding up | If there is any decimal part, the number goes up to the next whole number. Materials can only be bought in whole bags, so the number of bags is always rounded up. |
| mortar box | A shallow, wide tub for mixing mortar or concrete (also called a mixing tub). You put the materials in it and mix them with a hoe or shovel. |
| joint | The gap between blocks, bricks or tiles. It is filled with mortar to bond them and seal the gap. For concrete block walls in the US, a 3/8 in joint is standard. |
| mud slab | A thin layer of concrete poured on the ground before building a foundation. It gives a clean, level surface for layout lines and forms and needs little strength, so it is made with a lean mix (little cement), such as 1:3:6. |
| hydration | The chemical reaction in which cement hardens with water. It hardens by reacting with water, not by drying out, so keeping it moist for a while after placing (curing) makes it stronger. |
| curing | Protecting freshly placed concrete or mortar from drying out, freezing and rain while it hardens, for example by covering it with plastic or keeping it wet. |
| plastering | Applying mortar, plaster or stucco to walls and floors with a trowel. A 1:3 mortar is a common mix for base coats and finishes in this kind of work. |
| quantity takeoff | Working out the amounts and costs of materials a job needs from the drawings and specifications. The quantities on an estimate come from it. The formulas on this page turn the idea of mixing by volume used in estimating directly into formulas. |
| ready-mix concrete | Concrete mixed at a plant and delivered by truck. For larger amounts it is faster and more reliable than mixing your own. You can find the amount needed with the "Concrete Calculator". |
Good to know before you start
Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.
| Volume and units (Grades 5–6) |
|
| Ratios (Grade 6) |
|
| Percentages (Grade 6) |
|
| Unit rates (Grade 6) |
|
| Rounding (Grades 3–4) |
|
How to calculate it in Excel
Copy the whole table below and paste it into cell A1 in Excel. It works as is.
Table to find the volume needed from area and thickness
| Area (ft²) | 40 |
| Thickness (in) | 0.75 |
| Volume needed (ft³) | =B1*B2/12 |
Table to find the volume needed with waste
| Volume needed (ft³) | 2.5 |
| Waste factor (%) | 10 |
| Volume with waste (ft³) | =B1*(1+B2/100) |
Table to find the total dry volume before mixing
| Volume with waste (ft³) | 2.75 |
| Yield (%) | 70 |
| Total dry volume (ft³) | =B1/(B2/100) |
Table to split the volume by the mix ratio
| Total dry volume (ft³) | 3.929 |
| Cement part | 1 |
| Sand part | 3 |
| Gravel part | 0 |
| Cement volume (ft³) | =B1*B2/(B2+B3+B4) |
| Sand volume (ft³) | =B1*B3/(B2+B3+B4) |
| Gravel volume (ft³) | =B1*B4/(B2+B3+B4) |
Table to find the weight and bags of a material
| Volume of the material (ft³) | 0.982 |
| Bulk density (lb/ft³) | 94 |
| Bag weight (lb) | 94 |
| Weight (lb) | =B1*B2 |
| Bags | =ROUNDUP(B4/B3,0) |
Table to find the water
| Cement weight (lb) | 92.3 |
| Water-cement ratio (%) | 60 |
| Water (lb) | =B1*B2/100 |
| Water (gal) | =B3/8.34 |
Table for working backward: how much your cement makes
| Cement bags on hand | 1 |
| Bag weight (lb) | 94 |
| Cement bulk density (lb/ft³) | 94 |
| Sum of the ratio | 4 |
| Cement part | 1 |
| Yield (%) | 70 |
| Mixed volume you can make (ft³) | =B1*B2/B3*B4/B5*B6/100 |
Table to find the estimated cost
| Cement bags | 1 |
| Price per bag of cement ($) | 15 |
| Sand bags | 6 |
| Price per bag of sand ($) | 6 |
| Gravel bags | 0 |
| Price per bag of gravel ($) | 0 |
| Estimated cost ($) | =B1*B2+B3*B4+B5*B6 |
After pasting, the upper cells in column B are your inputs, and the last row (or the last few rows) is calculated automatically.
"ROUNDUP(value, 0)" is the function that rounds up to a whole number (it matches ⌈ ⌉ in the formulas).
B3 of the first table is 2.5 (the thickness in inches is divided by 12 to get feet), B3 of the second is 2.75, B3 of the third is about 3.929, B5 to B7 of the fourth are about 0.982, 2.947 and 0, B4 of the fifth is about 92.3 and B5 is 1, B3 of the sixth is about 55.4 lb (B4 about 6.64 gal), B7 of the seventh is 2.8, and B7 of the eighth is 51.
Use the fifth table once for each material by changing B1 to B3 (for sand, 2.946, 94 and 50). Just replace the numbers in column B with your own.
"ROUNDUP(value, 0)" is the function that rounds up to a whole number (it matches ⌈ ⌉ in the formulas).
B3 of the first table is 2.5 (the thickness in inches is divided by 12 to get feet), B3 of the second is 2.75, B3 of the third is about 3.929, B5 to B7 of the fourth are about 0.982, 2.947 and 0, B4 of the fifth is about 92.3 and B5 is 1, B3 of the sixth is about 55.4 lb (B4 about 6.64 gal), B7 of the seventh is 2.8, and B7 of the eighth is 51.
Use the fifth table once for each material by changing B1 to B3 (for sand, 2.946, 94 and 50). Just replace the numbers in column B with your own.
How to calculate it in Google Sheets
Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.
Table to find the volume needed from area and thickness
| Area (ft²) | 40 |
| Thickness (in) | 0.75 |
| Volume needed (ft³) | =B1*B2/12 |
Table to find the volume needed with waste
| Volume needed (ft³) | 2.5 |
| Waste factor (%) | 10 |
| Volume with waste (ft³) | =B1*(1+B2/100) |
Table to find the total dry volume before mixing
| Volume with waste (ft³) | 2.75 |
| Yield (%) | 70 |
| Total dry volume (ft³) | =B1/(B2/100) |
Table to split the volume by the mix ratio
| Total dry volume (ft³) | 3.929 |
| Cement part | 1 |
| Sand part | 3 |
| Gravel part | 0 |
| Cement volume (ft³) | =B1*B2/(B2+B3+B4) |
| Sand volume (ft³) | =B1*B3/(B2+B3+B4) |
| Gravel volume (ft³) | =B1*B4/(B2+B3+B4) |
Table to find the weight and bags of a material
| Volume of the material (ft³) | 0.982 |
| Bulk density (lb/ft³) | 94 |
| Bag weight (lb) | 94 |
| Weight (lb) | =B1*B2 |
| Bags | =ROUNDUP(B4/B3,0) |
Table to find the water
| Cement weight (lb) | 92.3 |
| Water-cement ratio (%) | 60 |
| Water (lb) | =B1*B2/100 |
| Water (gal) | =B3/8.34 |
Table for working backward: how much your cement makes
| Cement bags on hand | 1 |
| Bag weight (lb) | 94 |
| Cement bulk density (lb/ft³) | 94 |
| Sum of the ratio | 4 |
| Cement part | 1 |
| Yield (%) | 70 |
| Mixed volume you can make (ft³) | =B1*B2/B3*B4/B5*B6/100 |
Table to find the estimated cost
| Cement bags | 1 |
| Price per bag of cement ($) | 15 |
| Sand bags | 6 |
| Price per bag of sand ($) | 6 |
| Gravel bags | 0 |
| Price per bag of gravel ($) | 0 |
| Estimated cost ($) | =B1*B2+B3*B4+B5*B6 |
The same formulas as in Excel (including the ROUNDUP function) work as is. Copy the whole table, paste it into cell A1, and replace the numbers in column B with your own.
How to calculate it in Python
import math
area_ft2 = 40 # area (ft²)
thickness_in = 0.75 # thickness (in)
ratio = (1, 3, 0) # mix ratio by volume, cement : sand : gravel. For 1:2:4 concrete use (1, 2, 4)
waste_percent = 10 # waste factor (%)
yield_percent = 70 # yield (%)
wc_percent = 60 # water-cement ratio w/c (%)
density = (94, 94, 100) # bulk density (lb/ft³) of cement, sand, gravel
bag_lb = (94, 50, 50) # bag weight (lb) of cement, sand, gravel
price = (15, 6, 0) # price per bag ($) of cement, sand, gravel (examples; 0 is left out of the cost)
volume_ft3 = area_ft2 * thickness_in / 12 # volume needed (ft³). Thickness changed to feet
volume_with_waste = volume_ft3 * (1 + waste_percent / 100) # volume with waste (ft³)
dry_volume = volume_with_waste / (yield_percent / 100) # total dry volume before mixing (ft³)
ratio_sum = sum(ratio)
names = ("Cement", "Sand", "Gravel")
total_weight = 0
cost = 0
for i in range(3):
volume_i = dry_volume * ratio[i] / ratio_sum # volume of each material (ft³)
weight_i = volume_i * density[i] # weight (lb)
bags_i = math.ceil(weight_i / bag_lb[i]) if weight_i > 0 else 0 # bags (rounded up)
total_weight += weight_i
cost += bags_i * price[i]
if i == 0:
cement_weight = weight_i
print(f"{names[i]}: {volume_i:.3f} ft³, {weight_i:.3f} lb, bags: {bags_i} (before rounding up {weight_i / bag_lb[i]:.3f})")
water_lb = cement_weight * wc_percent / 100 # water (lb)
water_gal = water_lb / 8.34 # water (gal). 1 gal of water is about 8.34 lb
print(f"Volume needed: {volume_ft3} ft³ -> with waste {volume_with_waste:.3f} ft³ -> total dry volume {dry_volume:.3f} ft³")
print(f"Water: {water_lb:.3f} lb ({water_gal:.2f} gal), total weight with water: {total_weight + water_lb:.1f} lb, estimated cost: ${cost:,.2f}")
# Working backward: mixed volume you can make with one bag of cement (ft³)
have_bags = 1
cement_volume = have_bags * bag_lb[0] / density[0]
mix_volume = cement_volume * ratio_sum / ratio[0] * yield_percent / 100
print(f"Mixed volume from {have_bags} bag(s) of cement: {mix_volume:.3f} ft³")
Runs with the standard library only. math.ceil() rounds up (the ⌈ ⌉ in the formulas). Replace the area, thickness, mix ratio and prices at the top with your own numbers and run it. To enter a volume directly, assign it in ft³ to volume_ft3.
How to write it in LaTeX and other math languages (copy and paste)
Volume needed from area and thickness
V = A × t
V = A \times t
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>V</mi>
<mo>=</mo>
<mi>A</mi><mo>×</mo><mi>t</mi>
</mrow>
</math>
V = A xx t
a*t
V := A*t;
V = A*t;
V = A × t
Volume needed with waste
V' = V × (1 + r ÷ 100)
V' = V \left(1 + \frac{r}{100}\right)
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msup><mi>V</mi><mo>′</mo></msup>
<mo>=</mo>
<mi>V</mi>
<mo>⁢</mo>
<mrow><mo>(</mo><mn>1</mn><mo>+</mo><mfrac><mi>r</mi><mn>100</mn></mfrac><mo>)</mo></mrow>
</mrow>
</math>
V' = V (1 + r / 100)
v*(1 + r/100)
V2 := V*(1 + r/100);
V2 = V*(1 + r/100);
V' = V (1 + r/100)
Total dry volume before mixing (yield)
V_d = V' ÷ (y ÷ 100)
V_d = \frac{V'}{y / 100}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>V</mi><mi>d</mi></msub>
<mo>=</mo>
<mfrac>
<msup><mi>V</mi><mo>′</mo></msup>
<mrow><mi>y</mi><mo>/</mo><mn>100</mn></mrow>
</mfrac>
</mrow>
</math>
V_d = V' / (y / 100)
v2/(y/100)
Vd := V2/(y/100);
Vd = V2/(y/100);
V_d = V'/(y/100)
Splitting the volume by the mix ratio
V_c = V_d × c ÷ (c + s + g)
V_c = V_d \times \frac{c}{c + s + g}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>V</mi><mi>c</mi></msub>
<mo>=</mo>
<msub><mi>V</mi><mi>d</mi></msub>
<mo>×</mo>
<mfrac><mi>c</mi><mrow><mi>c</mi><mo>+</mo><mi>s</mi><mo>+</mo><mi>g</mi></mrow></mfrac>
</mrow>
</math>
V_c = V_d xx c / (c + s + g)
vd*c/(c + s + g)
Vc := Vd*c/(c + s + g);
Vc = Vd*c/(c + s + g);
V_c = V_d × c/(c + s + g)
Weight and bags of each material
W = V × ρ, N = ⌈W ÷ b⌉
W = V \times \rho,\quad N = \left\lceil \frac{W}{b} \right\rceil
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>W</mi><mo>=</mo><mi>V</mi><mo>×</mo><mi>ρ</mi>
<mo>,</mo>
<mi>N</mi><mo>=</mo>
<mo>⌈</mo><mfrac><mi>W</mi><mi>b</mi></mfrac><mo>⌉</mo>
</mrow>
</math>
W = V xx rho, N = |~ W / b ~|
{v*rho, Ceiling[v*rho/b]}
W := V*rho; N := ceil(W/b);
W = V*rho; N = ceil(W/b);
W = V × ρ, N = ⌈W/b⌉
Water (water-cement ratio)
W_w = W_c × (W/C) ÷ 100
W_w = W_c \times \frac{W/C}{100}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>W</mi><mi>w</mi></msub>
<mo>=</mo>
<msub><mi>W</mi><mi>c</mi></msub>
<mo>×</mo>
<mfrac><mrow><mi>W</mi><mo>/</mo><mi>C</mi></mrow><mn>100</mn></mfrac>
</mrow>
</math>
W_w = W_c xx (W/C) / 100
wc*ratio/100
Ww := Wc*ratio/100;
Ww = Wc*ratio/100;
W_w = W_c × (W/C)/100
Working backward: how much your cement makes
V_mix = (h × b_c ÷ ρ_c) × (c + s + g) ÷ c × y ÷ 100
V_{mix} = \frac{h \times b_c}{\rho_c} \times \frac{c + s + g}{c} \times \frac{y}{100}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>V</mi><mi>mix</mi></msub>
<mo>=</mo>
<mfrac><mrow><mi>h</mi><mo>×</mo><msub><mi>b</mi><mi>c</mi></msub></mrow><msub><mi>ρ</mi><mi>c</mi></msub></mfrac>
<mo>×</mo>
<mfrac><mrow><mi>c</mi><mo>+</mo><mi>s</mi><mo>+</mo><mi>g</mi></mrow><mi>c</mi></mfrac>
<mo>×</mo>
<mfrac><mi>y</mi><mn>100</mn></mfrac>
</mrow>
</math>
V_(mix) = (h xx b_c) / rho_c xx (c + s + g) / c xx y / 100
h*bc/rhoc*(c + s + g)/c*y/100
Vmix := h*bc/rhoc*(c + s + g)/c*y/100;
Vmix = h*bc/rhoc*(c + s + g)/c*y/100;
V_mix = (h × b_c)/ρ_c × (c + s + g)/c × y/100
Estimated cost
T = N_c × u_c + N_s × u_s + N_g × u_g
T = N_c u_c + N_s u_s + N_g u_g
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>T</mi>
<mo>=</mo>
<msub><mi>N</mi><mi>c</mi></msub><mo>⁢</mo><msub><mi>u</mi><mi>c</mi></msub>
<mo>+</mo>
<msub><mi>N</mi><mi>s</mi></msub><mo>⁢</mo><msub><mi>u</mi><mi>s</mi></msub>
<mo>+</mo>
<msub><mi>N</mi><mi>g</mi></msub><mo>⁢</mo><msub><mi>u</mi><mi>g</mi></msub>
</mrow>
</math>
T = N_c u_c + N_s u_s + N_g u_g
nc*uc + ns*us + ng*ug
T := Nc*uc + Ns*us + Ng*ug;
T = Nc*uc + Ns*us + Ng*ug;
T = N_c u_c + N_s u_s + N_g u_g
How to have ChatGPT do the calculation
You are a quantity calculation assistant for masonry and concrete work. Do the following calculation by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing). I am spreading mortar ¾ in thick over 40 ft² along a flower bed. The mix is 1 part cement to 3 parts sand by volume, the waste factor is 10%, the yield is 70% (the mixed volume as a share of the total dry materials), and the water-cement ratio is 60%. The bulk densities are 94 lb/ft³ for cement and 94 lb/ft³ for sand, and the bags are 94 lb for cement and 50 lb for sand. Find each of the following: 1. The volume needed (area × thickness, in ft³) 2. The volume needed with waste (× (1 + waste factor / 100)) 3. The total dry volume before mixing (÷ (yield / 100)) 4. The volume of cement and of sand (total dry volume × part ÷ sum of the ratio) and their weights (× bulk density) 5. The number of bags of cement and of sand (weight ÷ bag weight, rounded up), and the values before rounding up 6. The water (cement weight × water-cement ratio / 100), in lb and in gallons (1 gal ≈ 8.34 lb) 7. The mixed volume one 94 lb bag of cement makes (94 ÷ 94 × (1 + 3) ÷ 1 × 70 / 100) Show the formulas you used and the numbers from the execution result.
How to Use
-
1Enter your numbersType the numbers you want to calculate with into the input fields
-
2CalculatePress the "Calculate" button
-
3Check the resultThe result appears on the spot. The same page also explains the idea behind the calculation and the formula
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