The formulation of the mixtures of materials is sometimes puzzling. The simplest illustration of this observation is the concrete formula: to pour a reinforced concrete beam in the rules of the art, DTU 21, dealing with concrete structures, recommends a dosage of **350 kg / m3**, wet at **175 liters**. 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 the 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 measure** without having to resort to multiple manipulations of precision instruments. To measure concrete, for example, it is easier and faster to convert, once and for all, the weight of each ingredient (gravel, sand, water, cement), into volume equivalents, which we will know how to implement, quickly with some **tared containers** familiar (buckets, shovels, buckets, skips …)

## Some useful basics for converting tonnes cubic meters

The international system (**IF**), in force in Europe, implies a variation of the unit of measurement in decimal multiples and submultiples (in ^{10}). The only exception is the unit of time.

The **cubic meter **(m3), is the reference unit of **IF** for volumes. IL corresponds to the volume of a cube of 1 meter side and height. Note the remarkable analogy of **cubic decimetre** (dm^{3}) and **liter **(l), units of volume, 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 bodies whose density we know or vice versa.

## Density and density of aggregates

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

**Sands 0/2**and**0/4**: 1,400 kg / m3 (1.6),**Filter sands 0/5**: 1500 kg / m3 (1.5),**Gravel 5/16**and**5/20**: 1700 kg / m3 (1.7),**Chippings 2/63**: 1700 kg / m3 (1.7),**0/20 crushed concrete mix:**1,600 kg / m3 (1.9),**Crushed 0/30:**1700 kg / m3 (1.7),**Crushed 0/80**: 1,800 kg / m3 (1.8),**Ballasts****40/80**: 1900 kg / m3 (1.9),**All comers**: 2000 kg / m3 (2.0),**Topsoil**: 1,500 kg / m3 (1.5).

**Note** : depending on the humidity level, these data can 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 supply, because this data depends on the primary rock used to manufacture the aggregates, crushed or rolled.

## Convert cubic meters to liters and vice versa

We use 2 formulas to convert m3 into dm3 or liters.

1^{e} method: **multiply** number of **m3** per 1000:

- 1 m3 x 1000 =
**1000 l**, - 0.336 m3 x 1000 =
**336**l, - 1.336 m3 x 1000 =
**1336**

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

**number of liters**. Assume that the comma is directly after the whole numbers and add as many zeros as necessary:

- 1 m3 = 1,000 m3 = 1,000.00 dm3 =
**1000**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, it suffices to divide the number of liters by 1000, to convert into cubic meters:

- 1000 l ÷ 1000 =
**1 m3**, - 1230 l ÷ 1000 =
**1.23**m3, - 336 l ÷ 1000 =
**0.336**

## Method of dosing the ingredients of a batch

Objective: to coat a wall of 20 m², with a layer of gobetis in 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 mixing shrinkage),
- 150 l of pure water.

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

- 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’s buckets,
- 1200 ÷ 10 = 120 l = 12 buckets of sand 0/4.

As the useful capacity of the concrete mixer is limited to 100 liters (only the aggregates are counted), you will need to make 2 balanced mixes of 60 l of dry products, namely:

- ¼ 35 kg bag 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 into volume the necessary ingredients according to the proportions adapted to each use.

## Converting cubic meters to tonnes

Aggregates are sold by the ton, so you have to convert the volume of the material to weight (m3 to tons). The conversion can be carried out according to 2 formulas:

1^{e} method: **volume x density **/ **1000**

That is to say, for the sand 0/4 of the preceding plaster:

- 1,200 x (1,400/1000) = 1,680 kg =
**1.68 t**

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

Is :

- 1,200 x 1.4 = 1,680 kg =
**1.68 t**

## Converting tonnes to cubic meters

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

To define, for example, the volume of sand transportable in a trailer of 1080 kg payload (CU), you will need to convert the weight of the sand to 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.