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Firefighter Math

This online course provides knowledge of basic math concepts and tools necessary for making math calculations in the field. Topics include calculating tank volumes and flow rates, determining pump pressure and friction loss, understanding maps and location coordinates, and estimating slope. Additionally, the course presents information on calculating flame length, flame height, midflame windspeed, and other variables related to wildland firefighting efforts. This course is designed for wildland firefighters.

Instructions: 

  1. Complete the online course by selecting the "Click to start the online course." link below.
    Note: Some browsers, when "IE Compatibility View" is selected, may not display the course correctly; try removing  compatibility view setting in the browser or switch to a modern browser.
  2. There is no NWCG certificate of completion associated with this online course.
Firefighter Math: Self-Paced Math Course

WELCOME

This self-paced math course refreshers firefighters' knowledge of basic math concepts and tools necessary for making math calculations in the field. Topics include calculating tank volumes and flow rates, determining pump pressure and friction loss, understanding maps and location coordinates, and estimating slope. Additionally, the course presents information on calculating flame length, flame height, midflame windspeed, and other variables related to wildland firefighting efforts.
 

Technical Notes

This site is best viewed using Firefox® 3.0 or greater or Microsoft® Internet Explorer 7.0 or greater. An Adobe® Flash player is required to display some multimedia elements.

HOW DOES IT WORK?

The site contains three types of content to help you learn.

First, Read through an overview of the concepts you want to understand. Second, Follow the examples to see how equations are set up and problems are solved. Third, try some exercises to put your knowledge into practice.
 

As you work through the content, especially in more advanced chapters, you might choose to click on the "Calculator" tab above to open a calculator to a separate window. The calculator can be a useful tool in following the examples and helping solve practice problems.

About the material

Information contained in this document has been developed for the guidance of employees of the Forest Service, USDA, its contractors, and cooperating Federal and State agencies. The Department of Agriculture assumes no responsibility for the interpretation or use of this information by other than its own employees. The use of trade, firm, or corporation names is for the information and convenience of the reader. Such use does not constitute an official evaluation, conclusion, recommendation, endorsement, or approval of any product or service to the exclusion of others that may be suitable. The United States Department of Agriculture (USDA) prohibits discrimination in all its programs and activities on the basis of race, color, national origin, sex, religion, age, disability, political beliefs, sexual orientation, or marital or family status. (Not all prohibited bases apply to all programs.) Persons with disabilities who require alternative means for communication of program information (Braille, large print, audiotape, etc.) should contact USDA's TARGET Center at 202-720-2600 (voice and TDD). To file a complaint of discrimination, write USDA, Director, Office of Civil Rights, Room 326-W, Whitten Building, 1400 Independence Avenue, SW,Washington, D.C. 20250-9410 or call 202-720-5964 (voice and TDD). USDA is an equal opportunity provider and employer.
 

Contact

Additional questions or comments about this course and its content can be directed to Dan Jimenez, USFS.

Click to start the online course

NWCG Latest Announcements

NEW! Incident Performance and Training Modernization Story Map Now Available

Date: Aug 26, 2025
Questions? Please contact:
National Wildfire Coordinating Group

NWCG is excited to announce the launch of the Incident Performance and Training Modernization (IPTM) Story Map, a new interactive resource that showcases how NWCG is transforming wildland fire training and qualifications through a performance-based system.

Since its launch in 2023, IPTM has made major strides in updating how we manage incident positions:

  • 36 incident positions now have new Incident Position Standards and Next Generation Position Task Books available for field use
  • 6 more incident positions are nearing completion
  • 111 total incident positions are being analyzed through the IPTM initiative

The Story Map guides you through the IPTM process, highlights key accomplishments, and outlines what’s ahead. Whether you are a trainer or a trainee, this tool offers valuable insight into the modernization effort shaping the future of wildland fire training and qualifications.

This effort would not be possible without the contributions of NWCG staff, NWCG committees, and hundreds of subject matter experts across the wildland fire community.

References:

IPTM Story Map

Incident Performance and Training Modernization Webpage

NEW! S-290, Intermediate Wildland Fire Behavior (Blended) Available Now

Date: Aug 15, 2025
Questions? Please contact:
Fire Behavior Subcommittee

NWCG is excited to announce that the S-290, Intermediate Wildland Fire Behavior (Blended) training is now available on the Wildland Fire Learning Portal. S-290 (Blended) training combines online training and instructor-led training components that support individuals working towards any Single Resource Boss or Fire Effects Monitor incident qualifications.

This second course in the series collectively serves to develop fire behavior prediction knowledge and skills, and provides more detailed information on fuels, weather, and topography that affect wildland fire behavior for safety purposes.

Students are required to finish the prerequisite S-190, Introduction to Wildland Fire Behavior, before enrolling in S-290, Intermediate Wildland Fire Behavior (Blended).

References:

S-290, Intermediate Wildland Fire Behavior (Blended)

S-190, Introduction to Wildland Fire Behavior

Wildland Fire Learning Portal

NEW! S-271, Helicopter Crewmember (Blended) Now Available

Date: Aug 14, 2025
Questions? Please contact:
Interagency Helicopter Operations Subcommittee

The S-271, Helicopter Crewmember (Blended) is now available. Developed through the Incident Performance and Training Modernization (IPTM) effort, this training supports individuals working towards Helicopter Crewmember (HECM) incident qualifications. 

S-271, Helicopter Crewmember (Blended) training combines online training and instructor-led training components. This course is designed to provide students with the knowledge and skills necessary to perform the duties of the HECM position, as described in the NWCG Incident Position Standards for Helicopter Crewmember, PMS 350-22.

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 2026.

References:

S-271, Helicopter Crewmember (Blended)

NWCG Helicopter Crewmember (HECM) Position Page

Wildland Fire Learning Portal

Incident Position Standards and Next Generation Position Task Books Now Available for FBAN and LTAN

Date: Aug 13, 2025
Questions? Please contact:
Fire Behavior Subcommittee

NWCG is excited to announce that Incident Position Standards and Next Generation Position Task Books are now available for Fire Behavior Analyst (FBAN) and Long Term Fire Analyst (LTAN).

The Performance Support Packages for these positions were developed as part of the Incident Performance and Training Modernization (IPTM) effort. These resources support trainees, qualified personnel, and evaluators in their respective roles.

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 2026.

References:

NWCG Fire Behavior Analyst Position Page

NWCG Long Term Fire Analyst Page