SI and CGS Units of Volume: Comparison, Conversion & Examples
The unit of volume is a foundational concept in physics, chemistry, and daily life. Volume refers to the three-dimensional space occupied by a substance—be it a solid, liquid, or gas. Recognizing and applying the correct units of volume is essential for measurement accuracy in both academics and practical situations, such as laboratory experiments and solving numerical problems.
What is Volume?
Volume measures the amount of space a material occupies in three dimensions. It is calculated by multiplying an object's length, breadth (width), and height. This property is relevant to all states of matter, allowing us to quantify how much space an object or fluid covers.
For example, a liquid in a container, the space inside a gas cylinder, or the room occupied by a cube—all represent practical applications of volume measurement. Understanding volume helps in comparing capacities, determining solution concentrations, and solving physics problems related to density, pressure, and more.
What is the Unit of Volume?
The cubic metre (m³) is the standard unit of volume in the International System of Units (SI). This is the volume occupied by a cube with sides of one metre. However, several other units are widely used in science and everyday activities, such as:
- Litre (L)
- Millilitre (mL)
- Cubic centimetre (cm³)
- Gallon (gal)
- Cubic foot (ft³)
Each of these units is applicable in contexts like laboratory measurements, industrial usage, and daily life (e.g., measuring milk, fuel, or water).
SI Unit of Volume and Common Conversions
The SI unit—cubic metre (\(m^3\))—is a derived unit based on the metre, the fundamental SI unit of length. Sometimes, particularly in laboratory and chemical contexts, the litre (L) is used for convenience, even though it is not the official SI standard.
Conventional prefixes are applied to accommodate a broad range of measurements. For example, millilitres (mL) are used for small amounts, while kilolitres (kL) are used for large volumes.
| Unit | Symbol | Equivalent in \(m^3\) |
|---|---|---|
| Cubic kilometre | km³ | 1,000,000,000 |
| Cubic hectometre | hm³ | 1,000,000 |
| Cubic decametre | dam³ | 1,000 |
| Cubic metre | m³ | 1 |
| Cubic decimetre (Litre) | dm³ (L) | 0.001 |
| Cubic centimetre | cm³ | 0.000001 |
| Cubic millimetre | mm³ | 0.000000001 |
CGS Unit of Volume
In the CGS (centimetre-gram-second) system, the unit for volume is the litre (L). Importantly, one litre is equivalent to 1000 cubic centimetres (\(1\,L = 1000\,cm³\)). While the CGS system is less common today, litres and cubic centimetres are extensively used in laboratory settings and in measuring small volumes.
| Unit | Symbol | Equivalent in Litre (L) |
|---|---|---|
| Cubic centimetre | cm³ | 0.001 |
| Litre | L | 1 |
Conventional Units of Volume
Apart from SI and CGS, several other units are still used for specific applications. These include gallons, pints, barrels, cubic inches, and cubic feet.
| Unit | Cubic Metres (m³) | Litres (L) |
|---|---|---|
| 1 Cubic metre | 1 | 1000 |
| 1 Barrel | 0.158987294928 | 158.987294928 |
| 1 Cubic inch | 0.000016387064 | 0.016387064 |
| 1 Cubic foot | 0.028316846592 | 28.316846592 |
| 1 Cubic decimetre | 0.001 | 1 |
| 1 Gallon (US) | 0.003785411784 | 3.785411784 |
| 1 Pint (US) | 0.000473176473 | 0.473176473 |
| 1 Cubic centimetre | 0.000001 | 0.001 |
SI Units for Volume of Liquids
When dealing with liquids, the SI unit remains the cubic metre (m³). However, the litre (L) is commonly used and is defined as one cubic decimetre (1 L = 1 dm³). Large and small liquid quantities are often represented in kilolitre (kL), millilitre (mL), and microlitre (μL), enabling precise measurement across a vast range of scales.
Formulas to Calculate Volume
Volume calculation varies with object shape. Below are core equations used in physics:
| Object | Formula | Standard SI Unit |
|---|---|---|
| Cuboid (Box) | V = length × breadth × height | m³ |
| Cylinder | V = π × radius² × height | m³ |
| Sphere | V = (4/3) × π × radius³ | m³ |
| Cone | V = (1/3) × π × radius² × height | m³ |
Step-by-Step Approach: Solving Volume Problems
- Identify the geometric shape of the object or substance.
- Record all necessary dimensions (length, radius, height, etc.) in appropriate units.
- Use the relevant volume formula based on the shape.
- Carry out calculations carefully, ensuring unit consistency.
- Express the final result in standard SI units, unless otherwise required.
Practical Example
Suppose you have a box with a length of 2 m, breadth of 1 m, and height of 0.5 m.
Step 2: Note dimensions—L = 2 m, B = 1 m, H = 0.5 m.
Step 3: Apply V = L × B × H = 2 × 1 × 0.5 = 1 m³.
Thus, the volume is 1 cubic metre.
Quick Conversions: Cubic Metres and Litres
1 cubic metre (m³) is equal to 1000 litres (L). To convert cubic metres to litres, multiply by 1000. For small measurements, remember 1 millilitre (mL) equals 1 cubic centimetre (cm³).
Key Points to Remember
- Always represent answers in SI units unless specified otherwise.
- Review conversion tables before solving numericals.
- Understand context—use litres for liquid volumes and m³ for solids or gases in academic problems.
- Volume is not the same as mass; do not confuse the two.
Continue Learning on Vedantu
To practice more and master concepts on units, measurements, and related physics topics, continue with detailed notes, solved questions, and interactive exercises on Unit of Volume by Vedantu. Find more topic-wise resources and prepare for excellence in exams.
FAQs on Unit of Volume in Physics: Definitions, Units & Formulas
1. What is the SI unit of volume?
The SI unit of volume is the cubic metre (m³). It is the standard unit used in Physics for measuring the space occupied by a three-dimensional object.
• 1 m³ is the volume of a cube with sides of 1 metre each.
• 1 m³ = 1,000 litres (L).
• Always use cubic metres (m³) for SI-based Physics exams unless otherwise specified.
2. Is litre an SI unit of volume?
No, litre (L) is not the SI unit of volume. Litre is a commonly used metric unit, but the official SI unit is cubic metre (m³).
• 1 L = 1 cubic decimetre (dm³)
• 1 m³ = 1,000 L
• Use litres for Chemistry, Biology and lab work, but always adopt m³ in SI Physics numericals unless specified.
3. What are 5 units of volume?
Five common units of volume are:
• Cubic metre (m³)
• Litre (L)
• Cubic centimetre (cm³)
• Millilitre (mL)
• Cubic millimetre (mm³)
All units can be converted to and from the SI unit (m³) as needed in Physics and Chemistry.
4. What is the CGS unit of volume?
The CGS unit of volume is the cubic centimetre (cm³). It is widely used for smaller quantities in laboratory and Chemistry contexts.
• 1 cm³ = 1 millilitre (mL)
• 1 m³ = 1,000,000 cm³
Always convert units correctly between SI (m³) and CGS (cm³) during calculations.
5. How do you convert cubic metre (m³) to litre (L)?
To convert cubic metre to litre, multiply by 1,000.
• 1 m³ = 1,000 L
• Example: 0.5 m³ = 0.5 × 1,000 = 500 L
Moving the decimal three places to the right converts m³ to L easily.
6. Why is it important to use correct units in Physics calculations?
Using correct units ensures accurate answers and prevents mark loss in exams.
• Physics formulas are derived based on SI units.
• Always check and unify units before calculation.
• Results are only correct and comparable when expressed in standard (SI) units.
7. What is the formula for calculating the volume of a cuboid?
The volume (V) of a cuboid is:
V = length × breadth × height
• SI unit: m³
• Example: For a box of 2 m × 0.5 m × 0.1 m, volume = 2 × 0.5 × 0.1 = 0.1 m³
8. What is per unit volume?
Per unit volume refers to a physical quantity expressed for every 1 unit of volume.
• Used in terms like density (mass per unit volume)
• Helps standardize comparisons (e.g., concentration of a substance per litre)
9. How do you convert cm³ to m³?
To convert cm³ to m³, divide by 1,000,000.
• 1 m³ = 1,000,000 cm³
• Conversion: Volume in m³ = (Volume in cm³) ÷ 1,000,000
• Example: 2,500 cm³ = 2,500 ÷ 1,000,000 = 0.0025 m³
10. What are common mistakes students make regarding units of volume?
Common mistakes include:
• Using litre as SI unit (correct is m³)
• Mixing SI and CGS units without conversion
• Forgetting to convert cm³ to m³ or vice versa in density/mass calculations
• Not expressing final answers in the units asked in the problem
• Skipping unit checks in formulas
11. In which situations is it preferable to use litres instead of cubic metres?
Litres are preferable when:
• Measuring small to medium quantities of liquids (e.g., Chemistry labs, medical dosing, beverages)
• Lab work requiring volume readings in mL, L, or cm³ for ease
• SI unit (m³) is more common for large industrial or theoretical Physics cases
12. How do you calculate the volume of a cylinder?
The volume (V) of a cylinder is:
V = πr²h
• r = radius, h = height (use SI units)
• The answer will be in m³ (if r and h in metres) or in cm³ (if r and h in centimetres)
