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Firefighter Math: 1.15 Ratios & Percentages

RATIOS

A ratio is a proportional relationship of one value to another, e.g., the ratio of gas to oil in chain saw mix. Ratios can be written either as a fraction, 1/2, or in ratio notation, 1:2. The value of a ratio is the division of the first number by the second number. For example, consider the ratio 1:40 . This ratio is read as "1 to 40". Any fraction, for instance, 1/20, can also be written as a ratio: 1:20

Example 1 - The Mara Bella District has 6 engines. The Baldy District has 5 engines. What is the ratio of engines in the Mara Bella versus the Baldy districts? 

The ratio of engines in the Mara Bella versus Baldy districts is 6:5 or 6/5.
 

PERCENTAGES

A percentage is another way of describing a ratio with respect to 100. Percent (%) is a value corresponding to how many out of a hundred (per hundred). For instance, if 92 out of 100 firefighters have completed the FireFighter Math course, the ratio of firefighters completing the course is 92:100, and the percentage is written as 92%.

Example 2 - Write four notations for 56.8%.

56.8% = 56.8 out of 100
56.8% = 56.8/100
56.8% = 56.8:100
56.8% = 0.568 (Note that performing this calculation results in moving the decimal two places to the left because there are two zeros in 100.)
 

PERCENTAGES AND LIVE FUEL MOISTURES

Percentages are useful for a number of fire science applications. One of these applications is estimating live fuel moisture. Live fuel moisture can be measured using oven drying and weighing procedures. Because this process is time-consuming and cannot be completed in the field, fire considerations are usually satisfied with a good estimate. Live fuel moisture can be estimated using the values in the figure below, which provides moisture percentages for fuels at different stages of vegetative development. For instance, from the figure, we observe that completely cured fuels have a live fuel moisture of less than 30%. This value is the result of subtracting the dry weight of the fuel from the total (wet) weight and dividing by the dry weight. 

Live Fuel Moisture %
 

Example 3 - A fuel sample collected in the field weighs 377 grams. After the sample is dried in an oven, it weighs 198 grams. What is the live fuel moisture content?

Step 1. Subtract the dry weight from the wet weight. 377 - 198 = 179.

Step 2.Divide the difference by the dry weight and multiply by 100 to find the value as a percent. 179 / 198 × 100 = 0.904 × 100 = 90.4%. 

The live fuel moisture of your sample is 90.4%. 
 

PROBLEM SOLVING WITH RATIOS

When solving a more complex percentage or ratio problem, write the problem down in words and numbers and work through one step at a time.

 

NWCG Latest Announcements

RMC Safety Bulletin 26-001: Rhabdomyolysis in Wildland Firefighters

Date:  May 28, 2026
Questions? 
Please contact: Risk Management Committee

The Risk Management Committee (RMC) has issued Safety Bulletin 26-001: Rhabdomyolysis in Wildland Firefighters. Research from 2016 to 2025 shows that 88 cases of rhabdomyolysis (rhabdo) were reported. Analysis of reports from eSafety, the Safety Management Information System (SMIS), and the Wildland Fire Lessons Learned Center (LLC) indicates that rhabdo is common during this time of year due to Work Capacity Tests and contributing factors such as weather, hydration, nutrition, and medication or supplement use.

RMC issued this safety bulletin to raise awareness in the Wildland Fire Community, and to provide research findings and educational resources that support reducing future cases of rhabdo.

References:

NWCG Alerts

RMC Safety Bulletin 26-001: Rhabdomyolysis in Wildland Firefighters

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

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Leadership Committee IAP Flyer Now Available

Date:  May 8, 2026
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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
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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