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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

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

Incident Business Committee Memo 26-01: Updated Emergency Equipment Shift Ticket, OF 297

Date: January 22, 2026
Questions? 
Please contact: Incident Business Committee

The Incident Business Committee (IBC) has released Memorandum 26-01: OF 297 and 2026 Fire Use. This memo informs the wildland fire community that the updated Emergency Equipment Shift Ticket, OF 297 is available for download and can be ordered through the Great Basin Cache.

Beginning January 15, 2026 the previous version of the OF 297 form has been discontinued.

For further details, please contact your IBC representative.

References:

Incident Business Committee Memorandum 26-01

Great Basin Cache

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Date: December 22, 2025
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Please contact: Fire Behavior Subcommittee

NWCG is excited to announce that the new S-390, Introduction to Wildland Fire Behavior Calculations (Blended) training is now available on the Wildland Fire Learning Portal.

This third course in the series combines online and instructor-led training components aimed at individuals who are involved in planning, managing, and executing wildland fire and prescribed burn operations; who require a thorough understanding of fire behavior calculations to enhance effectiveness and safety. This includes students who require the knowledge and skill necessary to perform the duties of a Type 3 Incident Commander (ICT3), Division/Group Supervisor (DIVS), or Prescribed Fire Burn Boss Type 2 (RXB2).

Students are required to be qualified as any Single Resource Boss position and complete the prerequisite S-290, Intermediate Wildland Fire behavior (Blended) course, before enrolling in S-390.

References:

S-390, Introduction to Wildland Fire Behavior Calculations (Blended)

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NEW! S-320, Introduction to Incident Management Teams (Blended) Available Now

Date: December 18, 2025
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NWCG is excited to announce that S-320, Introduction to Incident Management Teams (Blended) is now available on the Wildland Fire Learning Portal!

This blended course combines online learning with instructor-led training, designed for individuals seeking to build leadership skills and gain experience in incident management.

Students are required to complete the prerequisite trainings ICS-100, Introduction to Incident Command System (ICS), ICS-200, Basic ICS for Initial Response, and ICS-700, An Introduction to the National Incident Management System (NIMS) prior to attending S-320.

References:

S-320, Introduction to Incident Management Teams (Blended)

Wildland Fire Learning Portal