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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

New! Ransom Road WFSTAR Module

Date: December 16, 2025
Questions about RT-130? 
Please contact: NWCG Audiovisual Specialist

NWCG is excited to announce the release of the new Ransom Road Fire Module to RT-130, Wildland Fire Safety Training Annual Refresher (WFSTAR).

This module features a firsthand account from Rob Lee, official reports, and animated maps of the Ransom Road Fire which occurred on June 8, 1981, in Florida's Merritt Island National Wildlife Refuge.

The module is available now in NWCG's RT-130, WFSTAR Catalog.

References:

WFSTAR Catalog

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Call for Nominations: Paul Gleason Lead by Example Award

Date: December 11, 2025
Questions? Please contact:
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Do you know someone working in wildland fire who strives to make positive change and is undeterred by obstacles or setbacks? Now is your chance to give that person the acknowledgment they deserve by nominating them for a Paul Gleason Lead by Example Award.

This award, is presented by the NWCG Leadership Committee to remember Paul Gleason's contributions to the wildland fire community and to recognize individuals or groups that exhibit the same spirit and dedication to leadership – those who lead by example.

Nominations can be submitted via email with an attached Lead by Example Form to BLM_FA_Leadership_Feedback@blm.gov or through the online form. 

Tips for successful nominations and more information can be found on the Lead by Example webpage. All nominations must be submitted by December 31, 2025.

References:

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Leadership Committee 

Coming Soon! Ransom Road WFSTAR Module

Date: December 9, 2025
Questions about RT-130? 
Please contact: NWCG Audiovisual Specialist

On June 8, 1981, the Ransom Road Fire swept across Merritt Island National Wildlife Refuge in Florida, marking a defining moment in wildland fire management. This event led directly to the creation of the U.S. Fish and Wildlife Service's professional fire program.

Later this month, NWCG will release a compelling video that brings the Ransom Road Fire to life through firsthand accounts, official reports, and animated maps. Rob Lee, second on site during the deployment, shares his powerful recollections of that day. 

This video will be going live later this month in NWCG's RT-130, Wildland Fire Safety Training Annual Refresher (WFSTAR) Catalogue.

References:

WFSTAR Catalogue 

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2025-2026 Wildland Fire Leadership Campaign: "Leadership Levels" Now Available

Date: October 15, 2025
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NWCG is excited to announce the release of the Leadership Committee’s 2025–2026 Leadership Campaign, themed “Leadership Levels.” 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.

The campaign is structured into four quarters and may be completed at any time between October 1, 2025 -December 31, 2026. Leadership levels will be released quarterly.

Quarter One materials are now available on the Wildland Fire Leadership Development Program website and focus on Leadership Level 1, Follower (Self-Leadership).

References:

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