Capacity vs. Volume

The definitions of volume and capacity are very similar, and the two terms are often used interchangeably. However, there is an important difference:

• Volume is the amount of space an object takes up.
• Capacity is the measure of how much a container can hold.

Volume is measured in cubic units (such as cubic metres or cubic feet), while capacity is usually measured in liquid units (such as litres or gallons). The cubic metre and cubic centimetre are most often used to measure the volume of solid objects, while kilolitres, litres, and millilitres are used to measure fluid (liquid and gas) volumes. In some trade applications, capacity may also be expressed in other units. For example, propane stored in a cylinder or tanks is measured in US gallons or pounds of liquid propane.

For safety, containers are often not filled to their full volume. This reduced amount is called design capacity. For example, a propane cylinder may have an internal volume of 2 ft³, but its design capacity would be 80% of that volume (as specified by codes and standards), or 1.6 ft³. This 20% reduction allows space for thermal expansion of the liquid and for vapour storage for use by the appliance. This concept will be discussed further in later sections.

Converting Volumes to Capacities

When working in the trades, you will often need to convert between volume and capacity. This means converting from cubic units (such as ft³ or m³) to liquid units (such as litres or gallons). The “³” in volume measurements means “cubed,” which tells us the measurement is in three dimensions (length × width × height).

Volume and Capacity Relationships

Some volume and capacity relationships are as follows:

Common Trade Conversions

To convert volumes to capacities, Use the following:

• cubic feet → imperial gallons: multiply by [latex]6.24 \frac{\text{imp. gal.}}{\text{ ft}^3}[/latex]
• cubic feet → US gallons: multiply [latex]7.48 \frac{\text{US gal.}}{\text{ ft}^3}[/latex]
• cubic inches → imperial gallons: divide by [latex]277 \frac{\text{ in.}^3}{\text{imp. gal.}}[/latex]
• cubic inches → US gallons: divide by [latex]231 \frac{\text{ in.}^3}{\text{US gal.}}[/latex]
• cubic metres → litres: multiply by [latex]1,000 \frac{\text{L}}{\text{ m}^3}[/latex]

Additional Useful Relationships

[latex]\quad1 \text{ imperial gallon (water)} = 10 \text{ pounds (lb.)}\\ \quad1 \text{ US gallon (water)} = 8.333 \text{ pounds (lb.)}\\ \quad1 \text{ litre (water)} = 1 \text{ kg}[/latex]

Example 1:

What would be the capacity in imperial gallons of a storage tank with a volume of 29 ft³?

Solution:

[latex]\quad29 \text{ ft}^3 \times 6.24 \frac{\text{imperial gallons}}{\text{ ft}^3} = 180.96 \text{ imp. gallons}[/latex]

Example 2:

What would be the capacity in US gallons of a storm sump with a volume of 84 ft³?

Solution:

[latex]\quad84 \text{ ft}^3 \times 7.48 \frac{\text{US gallons}}{\text{ ft}^3} = 628.32 \text{ US gallons}[/latex]

Example 3:

What is the volume of a tank that has a capacity of 1,700 litres?

Solution:

[latex]\quad\frac{1,700 \text{ litres}}{1,000\frac{\text{litres}}{\text{ m}^3}} = 1.7 \text{ m}^3[/latex]

Self-Test C-1.5: Use Formula to Calculate Capacity

Complete Self-Test C-1.5 and check your answers.

References

BCcampus. (n.d.). Playlist: Tools and equipment videos. BCcampus MediaSpace. https://media.bccampus.ca/playlist/details/0_3g8xp22x/categoryId/175673 Playlist Details – Trades Access Common Core Line C: Tools and Equipment Videos – BCcampus

BC Industry Training Authority. (2019). Piping trades apprenticeship program: Use Tools and Equipment—Level 1 harmonized [Binder]. Crown Publications, Queen’s Printer for British Columbia. https://www.crownpub.bc.ca/Product/Details/7960000261_S

• Plumber: Competency C-1 Use Mathematics and Science
• Steamfitter: Competency C-1 Use Mathematics and Science
• Sprinkler Fitter: Competency C-1 Use Mathematics and Science

Camosun College. (2019). Line C: Tools and Equipment—Competency D-1: Solve Trades Mathematical Problems (Rev. ed.) [Learning guide]. BCcampus.  https://collection.bccampus.ca/textbook/qFKGAJ78/

Camosun College. (2015). Trades Access Common Core Competency D-1: Solve Trades Mathematical Problems. Victoria, B.C.: Crown Publications. Download for free from the B.C. Open Textbook Collection (https://open.bccampus.ca/browse-ourcollection/find-open-textbooks/).

Camosun Innovates. (2022). Tools and Equipment Videos [Video playlist]. Camosun College/BCcampus. https://camosuninnovates.opened.ca/

Flinn, C. (n.d.). OER for Trades: Math for Trades [Video collection]. BCcampus MediaSpace. https://media.bccampus.ca/channel/OER%2Bfor%2BTrades%3A%2BMath%2Bfor%2BTrades/175670
Note: these videos align with the open textbooks Math for Trades: Volume 1 and Math for Trades: Volume 2. All videos are by Chad Flinn and available under a Creative Commons Attribution 4.0 Licence.:

Media Attributions

All figures are sourced from Industry Training Authority (2019) and/or Camosun College (2019) and are used under the Creative Commons Attribution 4.0 (CC BY 4.0) licence unless otherwise noted. Images copyrighted by the BC Industry Training Authority are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 (CC BY-NC-SA 4.0) licence.