Do Firefighters Need to Know Math? (6 examples) 

  The National Fire Protection Association (NFPA) estimates there are roughly 1,115,000 career and volunteer firefighters in the United States. Thus, it is safe to say that it is one of the most popular civil service positions. But, this does not mean it is an easy job! 

Becoming a firefighter is a great achievement on both a professional and personal level. Firefighters go through a well-rounded and strict hiring process, and once they are in the station, a lot is expected from them. As a result, a firefighter is usually an individual with extensive knowledge in different fields, including chemistry, math, medicine, biology, and more.   

Although it might seem odd, firefighters need to be well versed in mathematics. Almost everything they do, from planning to tactical actions, are directly related to math.  

Hence, basic math skills (e.g., subtraction, addition, multiplication, division) and a good understanding of formula usage are essential for anyone considering a career in firefighting.  

Situations Where Firefighters Use Math 

Do Firefighters Need to Know Math? (6 examples) 

Below six examples of scenarios where math is applied within firefighting: 

  • Calculating Pump Pressure

One of the most common situations where a member of the fire department might need to use math is when trying to figure out a pump’s pressure. In essence, this is done to determine the “pounds per inch” (PSI) at the end of a nozzle.  

  • Determining the Amount of Water Needed to Extinguish a Fire

It comes as no surprise that a firefighter does not merely turn on a hose and point it to fire until it extinguishes. There is a lot of planning and expertise needed to confront these types of situations, especially when there are civilians involved.  

Therefore, a firefighter usually uses math to determine how much water will be needed in any given situation. Many things go into play. However, one of the most crucial factors involves the size of the structure that has been compromised.  

As a rule of thumb, the fireman must first calculate the area of the building to then be able to determine the gallons per minute (GPM) and “fire flow” needed to suffocate the fire.  

  • Calculating Gallons Per Minute (GPM) 

As we mentioned before, once the area of the structure is available, fire engineers would also need to use a simple formula to calculate the GPM required to extinguish the fire.  

The method to find the GPM is 60 divided by the seconds it takes to fill a one-gallon container. The formula reads:  

60 / seconds = GPM 

So, if the one-gallon container fills in 10 seconds, you would have to divide 60 by 10. As a result, you will have that the GPM equals 6.  

  • Determining the “Fire Flow” 

Up until now, we learned that a firefighter must know the area of a building and the GPM to be able to successfully extinguish a fire. Nonetheless, as we explained before, the department also needs to consider the required “fire flow.” 

To do so, they must learn to apply the “fire flow” formula:  

Fire Flow = length x width / 3 

This formula is most easily applied by using the structure’s area and dividing it by three. In some cases, depending on the scenario, the result can be reduced accordingly to various percentages of fire involvement.  

Note that determining the “fire flow” can turn out to be one of the most complicated mathematical operations that a firefighter can encounter. Depending on the situation, percentages vary, and additional calculations might be involved. For instance, if the fire includes a multi-story building, a firefighter must know that the “fire flow” should be based only on the area represented by the number of floors burning. But, he/she must also calculate the area that could be affected if the fire is not contained in a specific period.  

  • Selecting a Hose Line

Selecting a hose line does not include a mathematical operation per se. But, it does require that the firefighter in charge understands the use and application of fractions.  

A fireman must know, for example, that a 1 1/2-inch hose line flows at 100 -125 GPM, and a 21/2-inch hose line flows approximately at 250 GPM. Based on that knowledge, he/she can select the appropriate re 

resource(s) needed to control the fire. 

  • Hydraulic Calculations

Hydraulic calculations are employed by firefighters to determine the flow of liquids through a medium (usually a piping network or sprinkling system.) This is done to ensure that fires can be adequately controlled or avoided.  

These types of calculations usually take into account three key factors: 

1) The water delivery requirements to suppress a fire 

2) The available water supply 

3) The system or piping network that delivers the water 

Hydraulic Calculations involve different variables that are compared to tables and values expressed on model codes. They also include geometry and the use of basic physics formulas.  

  • Providing Medical Care

Lastly, given that firefighters are also first responders, in some instances, they need to provide medical care. Thus, they also need to know how to calculate the correct dosage for medications in case they need to administer drugs or anesthesia.  

As you know, most medications are calculated in mg/kg and depending on the person’s weight, some drugs are given in a higher or lower dosage. So, to determine the adequate doses, a firefighter must divide the number of kilos by the recommended milligrams.  


The Firefighter Exam 

Note that math is part of the firefighting life even before you officially become a firefighter. As part of the selection process, candidates must take a civil service examination (commonly referred to as the firefighter exam.) And, contrary to popular belief, the exam does not require any specialized knowledge on firefighting or the fire department.  

The firefighter exam usually takes two to three hours to complete and includes 100-150 multiple-choice and true/false questions. The evaluation covers a broad range of subjects such as: 

  • Mathematical Reasoning  Do Firefighters Need to Know Math? (6 examples) 
  • Mechanical Reasoning 
  • Reading Comprehension  
  • Spatial Orientation 
  • Situational Judgment  
  • Observation and Memory  

Moreover, in some cases, the test may also include a personality test, a psychological evaluation, and other supplemental questionnaires. 

Mathematical Reasoning: The Hardest Section on the Firefighter Exam  

Given the importance of math within the firefighting career, this portion of the test is (according to most candidates), one of the hardest sections in the evaluation.  

The mathematical reasoning or numerical reasoning portion of the test evaluates a person’s ability to understand and work with numeric operations, logic, and formulas. Thus, you can expect basic math operations (e.g., sums, subtractions, multiplications, and divisions) and more complex questions (e.g., fractions, potentials, roots, percentages, equations, and word problems.) 

Know that there is no calculator allowed. Hence, here are seven useful tips and tricks that will help you prepare for the day of the test: 

  1. Read the question until you fully understand what is being asked.
  2. Work from the answer, remember the right answer is always there. 
  3. Apply shortcuts whenever possible.
  4. Write down your math, avoid doing all the operations in your head. 
  5. When dealing with sequences and series, try to find the relationship of the given numbers before selecting an answer. 
  6. If you have trouble facing divisibility questions, study the rules. There is no need to waste time dividing large, complicated numbers.
  7. Memorize all formulas and their usage— this will allow you to apply the correct one for any given question. 

 Curious about the firefighter exam? Check out this article:

Other Must-Know Subjects for Firefighters 

Math is not the only subject that firefighters must understand and know. Many different disciplines are related to their day-to-day activities and tasks. In fact, just like in any regular college, the fire academy often requires candidates to take classes devoted to the sciences like chemistry and physics.  

For instance, chemistry studies what substances are made of (based on composition and structure) and how these react/interact with each other. Fire is a chemical reaction produced by combustion. Hence, knowledge of how substances react can help a firefighter understand:  

– Flammability 

– Extinguishing properties 

– How different matters react to water 

– Miscibility with water and density 

– Toxicity and corrosiveness  

– Radioactivity 

Do Firefighters Need to Know Math? (6 examples) 

By knowing these basic principles, firemen can work more efficiently and effectively— especially when controlling fires that are considered high-risk.  

Firefighting also offers several examples of physics applications in the real world. One of the most relevant is when selecting the adequate fire hose nozzle pressure. As you may know, fire hose nozzles need to operate at a certain pressure (usually about 90-100 lbs. per square inch.) So, if the nozzle is too low, water is not properly broken into droplets. But, if the nozzle pressure is too high, the firefighter will not be able to control the hose. Hence, the member of the fire department operating the pump must take into consideration two principles of physics: friction and pressure.  

Additionally, there are other least obvious applications of physics. For example, when determining how many fire victims can be safely allowed on an extended ladder. Or when you need to predict how long a given material will burn or to determine how much energy an object will release.  


Wrapping it up! 

As you can see, firefighters need to be well-rounded individuals capable of understanding different disciplines and applying them to their daily tasks. Mathematics and other sciences, such as chemistry and physics, are an intrinsic part of being a firefighter. And although the job requirements do not usually state “must be proficient at math” or “comprehensive knowledge on chemistry needed,” candidates must have a basic understanding of these disciplines.  

However, do not get discouraged if you do not have all the necessary skills or if you were not the best at math in high school. The fire academy, like any other school, will give you the tools and resources necessary to become the best firefighter you can be. And this extends to learning how to apply math, physics, chemistry, and even biology to your profession.  

Lastly, remember that practice will help you better understand the applications of math and other topics. In fact, most firefighters never stop to think about how they are also mathematicians, physicists, and chemists in one way or another!  


Related Questions

What qualifications do you need to become a firefighter?

From an educational standpoint, you need to have achieved 9-4 grades in General Certificate of Secondary Education (GCSE) math and English language, or a level two equivalent (like a vocational qualification) to sign up for the fire academy.  

Know that when applying for the academy, you will need to provide proof of your educational qualification, including certificates and diplomas.  

 Are all firefighters paramedics?

As first responders, firefighters receive a copious amount of calls involving medical emergencies. As a result, most jurisdictions require firemen to obtain an Emergency Medical Technician (EMT) certificate as an addition to their basic first-aid training.  

Furthermore, in the United States, most public hospitals do not own ambulances. Meaning, that ambulances across the country are mostly owned either by fire departments or private businesses. Consequently, many firefighters are also trained paramedics. 

What are the fitness requirements for a firefighter?

As you know, there are different requirements when applying to the fire academy, including age, nationality, education, and personality. However, there are many other more important requisites related to a person’s physical and psychological conditions.  


Being a firefighter is a very stressful and demanding job. Thus, the department needs to make sure that new (and existing) firefighters have what it takes. As a result, the NFPA conducts a periodical physical evaluation that assesses a person’s ability to run up a flight of stairs, climb ladders, lift weights, and more. This evaluation will test, amongst other things, a person’s heart rate, recovery, and oxygen consumption, body mass, strength, and endurance.   

If a person does not pass the test, he/she would need to get in shape or will not be able to continue in the force as it represents a risk for him/her, the squad, and civilians.  


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Please note: This blog post is for educational purposes only and does not constitute legal advice. Please consult a legal expert to address your specific needs.