Skip to main content

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

2025/2026 Leadership Campaign Quarter 2 Now Available!

Date: February 13, 2026
Questions? 
Please contact: Leadership Committee

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

This quarter focuses on Leadership Level 2: New Leader (Conveying Intent). Conveying intent is a crucial leadership competency in the high-risk, dynamic environment of wildland firefighting. Months 4 - 6 will concentrate on how successfully conveying intent enhances situational awareness, promotes shared understanding, and empowers firefighters to exercise initiative and adapt to changing conditions.

References:

2025/2026 NWCG Leadership Campaign - Leadership Levels

Wildland Fire Leadership Development Program

Leadership Committee

Opportunity to Serve the Wildland Fire Community as an IPTM SME!

Date: February 10, 2026
Questions? 
Please contact: NWCG SME Specialist

NWCG is seeking experienced wildland firefighters and support personnel to serve as Subject Matter Experts (SMEs) for the Incident Performance and Training Modernization (IPTM) initiative. The intent of IPTM is to transition NWCG’s training and qualification system to a performance-based model through updated position descriptions, Incident Position Standards, Next Generation Position Task Books (Next Gen PTBs), and updates to training where needed.

NWCG is currently recruiting SMEs for the following positions:

  • Aircraft Timekeeper (ATIM)
  • Compensation/Claims Unit Leader (COMP)
  • Cost Unit Leader (COST)
  • Crew Representative (CREP)
  • Deck Coordinator (DECK)
  • Fire Effects Monitor (FEMO)
  • Field Observer (FOBS)
  • Geographic Information System Specialist (GISS)
  • Ordering Manager (ORDM)
  • Receiving/Distribution Manager (RCDM)
  • Staging Area Manager (STAM)

Projects begin April/May 2026 and require 15–20 hours per month for 6–8 months, including a five-day workshop in Boise, Idaho this May. Apply by February 27, 2026, at the link below and review the attached document for details.

References:

NWCG SME Interest Sign-up

IPTM Subject Matter Expert Duties and Expectations Document

Incident Performance and Training Modernization (IPTM)

NEW! M-280, Resource Advisor, Fireline (Instructor-Led) Course Available Now

Date: January 29, 2026
Questions? 
Please contact: Resource Advisor Subcommittee

NWCG is pleased to announce the new M-280, Resource Advisor, Fireline (Instructor-Led) course is now available. This training supports individuals working towards Resource Advisor, Fireline (REAF) incident qualifications.

M-280, Resource Advisor, Fireline (Instructor-Led) training prepares students to serve as a Resource Advisor, Fireline (REAF) as defined in NWCG Incident Position Standards for Resource Advisor, Fireline, PMS 350-112. This course presents scenarios that reflect the diverse challenges a REAF may encounter during an incident. Through these scenarios, participants gain hands-on experience and an understanding of REAF responsibilities in a controlled learning environment.

References:

Resource Advisor, Fireline Position Page

NWCG Position Standards for Resource Advisor, Fireline, PMS 350-112

M-280, Resource Advisor, Fireline (Instructor-Led)

Wildland Fire Learning Portal

2026 Updates to the NWCG Standards for Wildland Fire Position Qualifications, PMS 310-1

Date: January 23, 2026
Questions? 
Please contact: Incident and Position Standards Committee

The Incident and Position Standards Committee has updated the NWCG Standards for Wildland Fire Position Qualifications, PMS 310-1.

These updates address changes to incident position names and requirements for qualification, training, and experience. Updates related to the implementation of Complex Incident Management (CIM) and Incident Performance Training Modernization (IPTM) are also included.

The NWCG Wildland Fire Position Qualification Flowchart, PMS 308 has also been updated to reflect the recent changes.

References:

NWCG Standards for Wildland Fire Position Qualifications, PMS 310-1

NWCG Wildland Fire Position Qualification Flowchart, PMS 308

IPSC Memo 26-01: January 2026 Updates to the NWCG Standards for Wildland Fire Positions Qualifications, PMS 310-1