The formulation of material mixtures is sometimes perplexing. The simplest illustration of this finding is the concrete formula: to cast a reinforced concrete beam according to the rules of the art, DTU 21, dealing with concrete structures, recommends a dosage of **350 kg/m3**wet at **175 l**. We understand that we must mix 350 kg of cement and 175 l of water, with a sufficient quantity of sand and gravel, to obtain, **after mixing**, 1 m3 of finished product. Cement is sold by weight and water is easy to dose (1 mason’s bucket = 10 l). On the other hand, the **aggregates **are sold **by weight**each characterized by a **density** specific.

The conversion of **weight in volumes** or some **volumes by weight**is a convenient way to define a **common unit of measurement** without resorting to multiple manipulations of precision instruments. To dose concrete, for example, it is simpler and faster to convert, once and for all, the weight of each ingredient (gravel, sand, water, cement), into volume equivalences, which we will be able to implement quickly. with some **tared containers** familiar (buckets, shovels, buckets, dumpsters, etc.)

## Some useful basics for converting tons to cubic meters

The international system (**AND**), in force in Europe, implies a declination of the unit of measurement in decimal multiples and sub-multiples (in steps ^{10}). The only exception is the time unit.

The **cubic meter **(m3), is the reference unit of the **AND** for volumes. It corresponds to the volume of a cube of 1 meter side and height. Note the remarkable analogy of **cubic decimeter** (dm^{3}) a you **litre **(l), volume units, with the **Kilogram **(kg), unit of weight, defined by the density of **1 dm3 **(or 10 cl)** pure water**.

From this triple equivalence, we can extrapolate the conversion into volumes of all the bodies whose density we know or vice versa.

## Density and density of aggregates

Average values of the weights and (densities) of the main aggregates (dry and uncompacted), commonly used in the construction industry:

**Sands 0/2**et**0/4**: 1 400 kg/m3 (1,6),**Filter sands 0/5**: 1500 kg/m3 (1,5),**Gravels 5/16**et**5/20**:1 700 kg/m3 (1,7),**gravel 2/63**: 1 700 kg/m3 (1,7),**Crushed concrete mix 0/20:**1 600 kg/m3 (1,9),**Crushed 0/30:**1 700 kg/m3 (1,7),**Crushed 0/80**: 1 800 kg/m3 (1,8),**Ballasts****40/80**: 1 900 kg/m3 (1,9),**All comers**: 2 000 kg/m3 (2,0),**Topsoil**: 1 500 kg/m3 (1.5).

**Use** : depending on the moisture content, these data may vary from 1 to 8% for sands and mixtures and from 1 to 2% for other aggregates. Do not hesitate to have the supplier specify the density of the material you are supplying, because this data depends on the primary rock used to make the aggregates, crushed or rolled.

## Convert cubic meters to liters and vice versa

We retain 2 formulas to convert m3 into dm3 or litres.

1^{e} method : **multiply** number of **m3** par 1 000 :

- 1 m3 x 1 000 =
**1 000 l**, - 0,336 m3 x 1 000 =
**336**l, - 1,336 m3 x 1 000 =
**1 336**

2^{e} method, empirical, but fast and intuitive: **move** the comma of 3 digits to the right, the **3 ^{e} figure** after the comma directly indicates the

**number of liters**. Consider that the comma is directly after the integers and add as many zeros as necessary:

- 1 m3 = 1,000 m3 = 1 000,00 dm3 =
**1 000**l, - 1,23 m3 = 1, 230 m3 = 1 230 dm3 =
**1 230**l, - 0,336 m3 = 336,00 l = 336 dm3 =
**336**

Converting numbers with more than 3 decimal places implies a new decimal number:

- 0,336687 m3 = 0336,687 l =
**336,687**dm3 or l.

Conversely, simply divide the number of liters by 1,000 to convert to cubic meters:

- 1 000 l ÷ 1 000 =
**1 m3**, - 1 230 l ÷ 1 000 =
**1,23**m3, - 336 l ÷ 1 000 =
**0,336**

## Method of dosing the ingredients of a batch

Objective: to coat a 20 m² wall with a coat of bastard mortar, 0.5 mm thick, dosed at 350 kg/m3. You therefore need 100 liters of mortar to coat the wall.

Dosage for 1 m3 of mortar:

- 175 kg of cement,
- 175 kg of lime,
- 1,200 l of 0/4 sand (1,000 l + 20% for shrinkage during mixing),
- 150 liters of pure water.

The volume of basecoat is 100 liters (1/10 m3). It is therefore sufficient to divide the quantities per m3 by ten, i.e.:

- 175 ÷ 10 = 17.5 kg = ½ 35 kg bag of Portland cement,
- 175 ÷ 10 = 17.5 kg = ½ 35 kg bag of hydraulic lime,
- 150 ÷ 10 = 15 l = 1.5 mason buckets,
- 1200 ÷ 10 = 120 l = 12 buckets of sand 0/4.

The useful capacity of the concrete mixer being limited to 100 liters (only the aggregates are counted), you will have to make 2 balanced mixes of 60 l of dry products, i.e.:

- ¼ bag of 35 kg of binder,
- ¾ mason’s bucket,
- 6 buckets of sand 0/4.

The manufacture of all mortars and concretes is done according to this process, by converting the necessary ingredients into volume according to the proportions adapted to each use.

## Conversion of cubic meters to tons

Aggregates are sold by the tonne, so convert the volume of material to weight (m3 to tonnes). The conversion can be done according to 2 formulas:

1^{e} method : **volume x density **/ **1 000**

Either, for sand 0/4 of the previous coating:

- 1 200 x (1 400/1 000) = 1 680 kg =
**1,68 t**

2^{e} method : **v****olume ** **Density**

That is :

- 1 200 x 1,4 = 1 680 kg =
**1,68 t**

## Convert tons to cubic meters

Conversely, it may be useful to convert the **bulk weight.**

To define, for example, the volume of sand transportable in a trailer of 1080 kg of payload (CU), you will have to convert the weight of the sand into volume. Here again, 2 formulas can be used:

1^{e} method : **weight in tons**/**density x 1000**

That is, volume of sand admissible on the trailer:

- (1,08 / 1 400) x 1 000 =
**0.77142 m3**

2^{e} method : **weight in tons**/**material density **:

These formulas apply to all solid or liquid products.