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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.

 

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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

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A new publication from the National Coordination System Committee (NCSC) is now available. The NWCG Aircraft Flight Schedule Form, PMS 249, will be used for aviation crews and dispatch to share flight information that is needed for resource tracking, and if needed, for emergency procedures.

For further details, please contact your NCSC representative. 

References:

NCSC Memo 26-01: Implementation of NWCG Aircraft Flight Schedule Form, PMS 249

NWCG Aircraft Flight Schedule Form, PMS 249

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Date:  April 15, 2026
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The Data Standards and Terminology Board is requesting feedback on a new glossary term: Resource Protection Measure (RPM).

The proposed definition is: Practical guidance provided for incident personnel in a manner in which incident objectives can be achieved while reducing impacts to identified resources across the landscape. RPMs are informed by, but not restricted to, Minimum Impact Strategies and Tactics (MIST).

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NWCG is excited to announce that Quarter Three materials for the 2025/2026 Wildland Fire Leadership Campaign are now available. This annual initiative offers all students of leadership and wildland fire management an opportunity to engage with essential leadership skills and knowledge needed to lead effectively in dynamic environments.

Quarter Three materials focus on Leadership Level 3: Leader of People (Develop Intent). Leadership Level 3 is where your values, your team, and your influence come together. Leaders of People put their teams first, build trust, and lead with authenticity. They mentor future leaders and shape decisions up and down the chain.

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2025/2026 NWCG Leadership Campaign - Leadership Levels

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