Skip to main content

Firefighter Math: 3.1 Volume or Capacity

Volume is used to indicate the capacity of a tank or container. It is used by firefighters to answer questions like "How much water is left in the tank?" and "At 15 gallons per minute (gpm), how many more minutes before the tank is empty?" 

VOLUME OF A RECTANGULAR OBJECT

The volume of a rectangular container is determined by multiplying the length (l) by the width (w) by the height (h).

volume

Volume = length × width × height
V = l × w × h

Example 1 - Determine the volume of the tank in gallons.

Example 1 Image

Step 1. Use the equation for determining the volume of a rectangle. V = l × w × h

Step 2. Identify the length, width, and height. l = 5 ft, w = 6 ft, h = 8 ft

Step 3. Set up the problem and solve. V = 5ft × 6ft × 8ft = (5 × 6 × 8) (ft × ft × ft) = 240 ft3

Step 4. Determine the appropriate conversion factor. 1 cubic foot = 7.4805 gallons

Step 5. Set up the cancellation table so all units will cancel except gallons (see Section 2.1).

Cancellation Table

The volume of the tank of water is 240 cubic feet or 1,795 gallons.

Example 2 - The water tank on a newly designed engine is 34 inches wide, 5 feet high, and 12 feet long. What is the capacity of the water tank in cubic feet? In gallons?

Example 2 image

Step 1. Use the equation for determining the volume of a rectangle. V = l × w × h

Step 2. Identify the length, width, and height. l = 12 ft, w = 34 in, h = 5 ft

Step 3. Convert all the measurements to the same units, feet.

Inches to Feet
Step 4. Set up the problem, and solve for volume. V = 2.83 ft × 5 ft × 12 ft = 170 ft3

Step 5. Set up the cancellation table so all units will cancel, except the desired unit, gallons.

Ft3 to Gallons

The volume of the tank is 170 cubic feet or 1272 gallons.

VOLUME OF A CYLINDER

The volume of a cylinder is found by multiplying the area of the base times the height, h. The base of a cylinder is a circle, A = π × r2, where π = 3.14. 

Volume Example

Example 3 - A cylindrical tank of foam concentrate is 5 feet tall. The tank diameter is 2.5 feet. What is the capacity, in gallons, of the tank?

Step 1. Use the equation for determining the volume of a cylinder.
V = π r2 × h

Step 2. Draw a sketch. Label the height and diameter.

Height and Diameter

π = 3.14, r = 1/2 d = 1/2 × 2.5 ft = 1.25 ft, h = 5 ft

Step 3. Set up the problem and solve. V = 3.14 × (1.25 ft)2 × 5 ft = 24.5 ft3

Step 4. Set up the cancellation table so all units will cancel, except the desired unit, gallons.

Ft3 to Gallons

The tank capacity is 183.3 gallons.

 

NWCG Latest Announcements

NEW! D-110, Expanded Dispatch Recorder Course Available Now

Date:  May 15, 2026
Questions? 
Please contact: Dispatch Position and Curriculum Management Subcommittee

NWCG is pleased to announce the new D-110, Expanded Dispatch Recorder (Instructor-led) course is now available on the Wildland Fire Learning Portal (WFLP). Developed through the National Coordination System Committee, this course introduces the structure and function of expanded dispatch, the qualities of an effective dispatcher, and provides hands-on experience with the Interagency Resource Ordering Capability (IROC) system. 

The D-110, Expanded Dispatch Recorder course aligns with the competencies and duties outlined in the NWCG Incident Position Standards for Expanded Dispatch Recorder, PMS 350-59, and is designed for individuals with no prior experience who may be called upon to support dispatch operations.

References:

D-110, Expanded Dispatch Recorder (Instructor-Led)

Expanded Dispatch Recorder (EDRC), Position Page

NWCG Incident Position Standards for Expanded Dispatch Recorder, PMS 350-59

Wildland Fire Learning Portal

Leadership Committee IAP Flyer Now Available

Date:  May 8, 2026
Questions? 
Please contact: Leadership Committee

The NWCG Leadership Committee promotes and enables leadership development across the wildland fire service. The committee provides education, training opportunities, and support for leadership innovation and best practices throughout the community.

A new IAP flyer is now available on the committee website, offering an overview of the products, curriculum, and learning opportunities the Leadership Committee develops. This resource is ideal for posting in your office, sharing with new employees, or distributing through your incident management teams to engage new voices in the leadership journey and reinforce a culture of self‑reflection, development, and growth.

References:

Leadership Committee 2026 IAP Flyer

Incident Operations Subcommittee Updates the Next Generation Position Task Book for FFT1

Date:  May 7, 2026
Questions? 
Please contact: Incident Operations Subcommittee

The NWCG Incident Operations Subcommittee (IOSC) has updated the NWCG Position Task Book for Firefighter Type 1 (Squad Boss) (FFT1), PMS 311‑14. The FFT1 Position Task Book transitioned to the Next Generation (Next Gen PTB) format in June 2025 through the Incident Performance and Training Modernization effort. Since then, IOSC has received feedback from the wildland fire community regarding coding for one of the tasks. Task #13 has been updated to include the option of evaluation in a simulation.

See IOSC Memorandum 26‑01: Transition Plan for Implementation of Updates to the NWCG Position Task Book for Firefighter Type 1 (Squad Boss) (FFT1), PMS 311‑14 for more information.

References:

IOSC Memorandum 26-01: Transition Plan for Implementation of Updates to the NWCG Position Task Book for Firefighter Type 1

NWCG Firefighter Type 1 Squad Boss Position Page 

NEW! S-212, Intermediate Faller (Online) Course Available Now 

Date:  April 23, 2026
Questions? 
Please contact: Hazard Tree and Tree Felling Subcommittee

NWCG is pleased to announce that the new S‑212, Intermediate Faller (Online), course is now available on the Wildland Fire Learning Portal (WFLP). This second course in the series provides students with the knowledge and skills required to perform the duties of an Intermediate Faller (FAL2), as described in the FAL2 Incident Position Description. This course is intended for individuals seeking to advance from Basic Faller (FAL3) to FAL2.

S‑212, Intermediate Faller is a fully online, self‑paced training program consisting of 13 units. Learners will engage with interactive, scenario‑based content designed to progressively build foundational skills and knowledge essential for the FAL2 role.

Students must be qualified as a Basic Faller (FAL3) prior to enrolling in S‑212, Intermediate Faller course.

Any changes to qualification pathways will take effect with the next update of the NWCG Standards for Wildland Fire Position Qualifications, PMS 310-1, scheduled for January 2027.

References:

S-212 Intermediate Faller (Online)

RMC Memo 26-01: Transition Plan for Implementing Updates to Intermediate Faller (FAL2) Position Qualifications

Intermediate Faller (FAL2) Position Page

NWCG Standards for Wildland Fire Chainsaw Operations, PMS 212