# How To Calculate Quantities Of Cement, Sand, and Aggregate

Mix design is a process of determining the quality of the correct materials and their relative proportions to prepare the concrete for the desired properties such as workability, strength, set time, and durability. The quantity of concrete materials, such as cement, sand and aggregate, used to produce the required quantity of concrete with a given mixing ratio, such as 1:2:4 (M15), 1:1.5: 3 (M20), 1:1: 2 (M25)) The absolute volume method can be used to calculate. This method is based on the principle that the volume of fully compacted concrete is equal to the absolute volume of all concrete materials, namely cement, sand, coarse aggregate and water.

### Cement, Sand And Aggregate Requirement For Different Grade Concrete

Grade of Concrete | Nominal Mix Proportion | Cement Required (bag)/cum | Sand Required (in cft) | Aggregate Required (in cft) |
---|---|---|---|---|

M15 | 1:3:6 | 4.5 | 16.04 | 32.07 |

M20 | 1:2:4 | 6 | 14.98 | 29.96 |

M25 | 1:1.75:3.5 | 6.75 | 14.75 | 29.14 |

M30 | 1:1.5:3 | 7.5 | 14.06 | 28.11 |

Depending on the type of structure, concrete structures may include beams, slabs, columns, and foundations. The volume of concrete required for a concrete structure can be calculated by adding up the volume of each structural member or each part of the member.

The volume of a rectangular cross-section member can be calculated as length x width x height (or depth or thickness). Appropriate formulas should be used for components with different cross-sectional shapes.

The material calculation formula for the required concrete volume is

Where, V_{c} = Absolute volume of fully compacted fresh concrete W =Mass of water C = Mass of cement Fa = Mass of fine aggregates Ca = Mass of coarse aggregates S_{c}, S_{fa} and S_{ca} are the specific gravities of cement, fine aggregates and coarse aggregates respectively. The air content is ignored in this calculation. This method of calculating the number of concrete materials takes into account the design mix ratio or the nominal mix ratio required for structural strength and durability.

**Consider a concrete with a mix ratio of 1:1.5:3**, where 1 is a part of cement, 1.5 is a part of fine aggregate, and 3 is a part of coarse aggregate with a maximum size of 20mm. The water-cement ratio required for concrete mixing is 0.45.

Suppose the bulk density of the material per cubic meter, cubic foot and cubic yard is as follows:

- Cement = 1500 kg/m
^{3}= 93.642 lb/ft^{3}= 2528.332 lb/cubic yards, Sand = 1700 kg/m^{3}= 105 lb/ft^{3}= 2865 lb/cu. Yard coarse aggregate = 1650 kg/m^{3 }= 103 lb/ft^{3 }= 2781.166 lb/cubic yard. - The specific gravity of concrete material is as follows: cement = 3.15, sand = 2.6, coarse aggregate = 2.6.
- The assumed percentage of entrained air is 2%. 1:1.5:3 The mixing ratio of the dry volume of the material can be expressed by mass:- cement = 1 x 1500 = 1500 sand = 1.5 x 1700 = 2550 coarse aggregate = 3 x 1650 = 4950.

Therefore, the ratio of masses of these materials w.r.t. cement will as follows =

= 1 : 1.7 : 3.3

The water cement ratio = 0.45 Now we will **calculate the volume of concrete** that can be produced with one bag of cement (i.e. 50 kg cement) for the mass proportions of concrete materials. Thus, the **absolute volume of concrete** for 50 kg of cement =

Therefore, considering the mix ratio, a bag of 50 kilograms of cement can produce 0.1345 cubic meters of concrete. We have considered 2% of entrained air. Therefore, the actual concrete volume of 1 cubic meter of compacted concrete structure is = 1 -0.02 = 0.98 m3. Therefore, the amount of cement required for 1 cubic meter of concrete = 0.98/0.1345 = 7.29 bags of cement. The amount of material produced by 1 m3 concrete can be calculated as follows: Required cement weight = 7.29 x 50 = 364.5 kg. The weight of fine aggregate (sand) = 1.5 x 364.5 = 546.75 kg. Coarse aggregate weight = 3 x 364.5 = 1093.5 kg.

## Methods to Calculate:

**Method 1:**Calculating cement sand and coarse aggregate in volume and weight from**Nominal Concrete Mix Ratio****Method 2:**Calculating the weight of sand and aggregate needed per bag of cement (50kg bag) using**Total weight of aggregate****value**given in IS codebook

## Method:1 Calculation of Cement, Sand, and Aggregate from Nominal mix ratio

While the ingredients are being mixed, the cement and sand (fine aggregate) must fill the gaps between the coarse aggregate before taking up their own space. Therefore, to prepare 1 cubic meter of M20, M15, and M10 concrete, you need 1.57 cubic meters of “total dry volume:” of cement, sand, and aggregates, and in case of M7.5 and M5 concrete, you need 1.52 cubic meters of total dry volume cement sand and aggregates.

### Cement, Sand and Coarse aggregate requirement for M20 Grade concrete

Prescribed Concrete Mix Ratio of M20 grade concrete is 1:1.5:3 as per codebook.

- Cement = 1 Part
- Sand = 1.5 Part
- Aggregate = 3 Part
- Total dry volume of Material Required = 1.57 cu.m

Volume of cement needed | = Ratio of cement x 1.57/(1+1.5+3) |

= 1 x 1.57/5 .5 | |

= 0.285 cu.m | |

Volume of sand needed | = Ratio of Sand x 1.57/(1+1.5+3) |

= 1.5 x 1.57/5 .5 | |

= 0.427 cu.m | |

Volume of aggregate needed | = Ratio of agg x 1.57/( 1+1.5+3) |

= 0.427 x 32 | |

= 0.854 cu.m |

### Weight of Cement required for 1 cubic meter of M20 Grade concrete

Weight of cement required can be calculated from multiplying the volume of cement with the bulk density of cement. The bulk density of frequently used cement varieties (both PPC and OPC) is 1440 kg/cu.m.

Weight of cement needed | = volume of cement x bulk density of cement |

= 0.285 cu.m x 1440 kg/cu.m | |

Weight of cement needed | = 410 kg |

No of cement bags required | = 410/50 |

= 8.2 bags |

Therefore, 8 bags of cement are required to prepare one cubic meter of M20 grade concrete.

**Alternative method:- **1 cu.m of cement is approximately 28.8 bags.

Weight of cement needed | = volume of cement x 28.8 |

= 8.2 bags |

### Volume of Sand and Aggregate required for 1 cubic meter of M20 grade concrete

Suppliers sell sand and coarse aggregates in the measure of Cubic Feet (CFT), UNITS, and in truck or dump truck LOADS. A UNIT measurement equals 100 cubic feet. A cubic meter is 35.32 cubic feet.

Volume of sand needed | = Volume of sand x 35.32 |

=0.427 x 35.32 | |

= 15.08 cft | |

Volume of aggregate needed | = Volume of agg x 35.32 |

= 30.16 cft |

Therefore, 15.08 cubic feet of sand and 30.16 cubic feet of aggregate are required to prepare one cubic meter of M20 grade concrete.

### Number of Cement bags, Sand and Aggregate required for different Concrete Grades

GRADE | CEMENT | SAND | AGG |

M20 | 8.2 bags | 15.01cft | 30.16cft |

M15 | 6.4 bags | 15.82cft | 31.65cft |

M10 | 4.5 bags | 16.64cft | 33.27cft |

M7.5* | 3.38 bags | 16.64cft | 33.27cft |

M5* | 2.7 bags | 16.64cft | 33.27cft |

## Method:2 Calculation of Weight of Sand and Coarse aggregate needed per bag of cement

IS456 Codebook recommends the following quantities of total aggregate per 50kg bag of cement to produce nominal mix concrete.

CONCRETE GRADE | TOTAL AGGREGATE( FINE + COARSE ) |

M 5 | 800 kg |

M 7.5 | 625 kg |

M 10 | 480 kg |

M 15 | 330 kg |

M 20 | 250 kg |

### Weight of Sand and Aggregate required per 50kg cement bag for M20 Grade Concrete

Let’s find out the quantity needed to prepare M20 grade by the codal procedure. Sand is confirmed to Zone II – average grading. The ratio of fine to coarse aggregate is chosen as usual as 1:2. From the above table we know we need 250kg of total dry aggregate for our concrete.

The general ratio of fine aggregate to coarse aggregate is 1:2, but it can be adjusted between 1:1.5 to 1:2.5 based on the grading of fine aggregate and size of coarse aggregate.

- Sand = 1 Part
- Aggregate = 2 Part
- Total aggregate required = 250 kg

Sand needed per bag of cement | = Ratio of sand x 250 /(1+2) |

= 1 x 250 /(1+2) | |

= 83 kg ~ 85 kg | |

Aggregate needed per bag of cement | = Ratio of agg x 250 /(1+2) |

= 170 kg |

### Weight of Sand and Aggregate required per 50kg cement bag for different Concrete Grades

GRADE | CEMENT | SAND | AGG |

M20 | 1 bag | 85 kg | 170 kg |

M15 | 1 bag | 110 kg | 220 kg |

M10 | 1 bag | 160 kg | 320 kg |

M7.5 | 1 bag | 210 kg | 415 kg |

M5 | 1 bag | 265 kg | 535 kg |

## WATER REQUIREMENT FOR DIFFERENT CONCRETE GRADES AS PER IS456 CODE

For the design mix, the water content of the concrete is calculated from the water/cement ratio, which depends on various factors such as the weight of the cement, the workability, etc. But for the nominal concrete mix, the IS456 codebook suggests the following amounts per bag of cement.

CONCRETE GRADE | WATER PER 50KG BAG OFCEMENT |

M5 | 60 Liters |

M7.5 | 45 Liters |

M10 | 34 Liters |

M15 | 32 Liters |

M20 | 30 Liters |

**References**:

- IS456 -“Plain and Reinforced Cement Concrete – Code of Practice”
- IS20262 – ” Concrete Mix Design Proportioning -Guidelines ” – to design different types of concrete.

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