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What Are the Metric Units for Volume?

This entry uses the metric system. For the imperial system click here.

Volume measures how much can fit inside of something. How much water is in your bathtub? How much milk is in a carton? How big is the trunk of your car?

Volume is measured in cubic meters or in liters. One cubic meter is a cube in which each side is one meter long. We use the units we learned from length to create smaller cubes. Then, we get cubic decimeters (dm³), cubic centimeters (cm²) and cubic millimeters (mm³).

One cubic decimeter is a cube where each side is one tenth of a meter, or one decimeter. A cubic decimeter is the same as one liter (L). Imagine that you have a box which is as large as one cubic decimeter. If you grab your liter measure from the kitchen and fill it with water, you’ll see that you can fit exactly one liter in the box. Therefore, we say that the box has a volume of $1$ L or 1 cubic decimeter.

A measuring cup of water and cube with side lengths of one decimeter

Below, you see the connection between different cubic meters and measures of liters. It is expected of you to be able to convert one unit into another, and between cubic meters and liters. The link is as follows: $1 {dm}^{3} = 1 L$ and $1 {cm}^{3} = 1 mL$ .

Conversion between different units of volume

Example 1

Liter to centiliter:

\begin{array}{l} 8 L & = (8 \cdot 10) dL \\ = 80 dL \\ = (80 \cdot 10) cL \\ = 800 cL \end{array}

Centiliter to liter:

\begin{array}{l} 800 cL & = (800 \div 10) dL \\ = 80 dL \\ = (80 \div 10) L \\ = 8 L \end{array}

Liter to milliliter:

\begin{array}{l} 0.0049 L & = (0.0049 \cdot 10) dL \\ = 0.049 dL \\ = (0.049 \cdot 10) cL \\ = 0.49 cL \\ = (0.49 \cdot 10) mL \\ = 4.9 mL \end{array}

Milliliter to liter:

\begin{array}{l} 4.9 mL & = (4.9 \div 10) cL \\ = 0.49 cL \\ = (0.49 \div 10) dL \\ = 0.049 dL \\ = (0.049 \div 10) L \\ = 0.0049 L \end{array}

Example 2

Cubic meters to cubic decimeters:

4 m^{3} = (4 \cdot 1000) {dm}^{3} = 4000 {dm}^{3}

Cubic millimeters to cubic centimeters:

4000 {mm}^{3} = (4000 \div 1000) {cm}^{3} = 4 {cm}^{3}

Cubic decimeters to cubic centimeters:

40 {dm}^{3} = (40 \cdot 1000) {cm}^{3} = 40 000 {cm}^{3}

Cubic centimeters to cubic decimeters:

\begin{array}{l} 40 000 {cm}^{3} & = (40 000 \div 1000) {dm}^{3} \\ = 40 {dm}^{3} \end{array}

40 000 {cm}^{3} = (40 000 \div 1000) {dm}^{3} = 40 {dm}^{3}

Cubic centimeters to cubic millimeters:

\begin{array}{l} 400 {cm}^{3} & = (400 \cdot 1000) {mm}^{3} \\ = 400 000 {mm}^{3} \end{array}

400 {cm}^{3} = (400 \cdot 1000) {mm}^{3} = 400 000 {mm}^{3}

Cubic decimeters to cubic meters:

40 000 {dm}^{3} = (40 000 \div 1000) m^{3} = 40 m^{3}

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