The seemingly complicated calculations of flight make the principle of “pilot math” sound vaguely terrifying. Prospective student pilots wonder, “What kind of math perform pilots use?” and also “Do I have what it takes to handle pilot math?”

Before you obtain discouraged and also give up on the idea, yes, math and physics are crucial subjects the pilots need to be skilled in, but it frequently is not virtually as complicated as you might think. In most cases, there space formulas to guide you v the computations as well as software and devices that deserve to run the numbers because that you. As soon as you understand the principles behind the equations, the actual mathematics itself is not so challenging. Simply select the exactly formula, plugin your numbers, and also arrive in ~ the answer.

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Ready to learn what that takes and conquer your fear of pilot math? below is what you have to know:

What species of math do pilots?

There room several types of math the pilots should familiarize themselves with and also be able to apply. Basic arithmetic, geometry, trigonometry, interpolation, and mental math space all part of being a pilot.

Basic arithmetic

Basic arithmetic is the very first kind of math you learned back in primary school school: addition, subtraction, multiplication, and also division. For many of us, an easy arithmetic comes easily and is not overly intimidating. Because this is the type of pilot math you are most likely to be doing manually or mentally at times and also not constantly with a calculator, be certain to pay fist to detail and also avoid making careless mistakes.


Geometry concentrates on shapes, sizes, and spatial relationships in between objects, making it a very valuable branch of math for aviation. Recipe are common in geometry, so it helps to memorize the many common and also have cheat sheets or reference products for others.


The mathematics branch that trigonometry concentrates on relationships between the sides and angles in ~ a triangle. One of the most usual ways that pilots use trigonometry is as soon as they space making wind correction or crosswind ingredient calculations. The great news is the pilots perform not should be professionals in trigonometry to do these calculations. They simply need to understand just how to perform the calculations, regularly using one E6B or a trip calculator app.



Interpolation is the mathematical term for making an educated estimation based upon surrounding data. This method uses straightforward arithmetic an abilities as well as algebraic skills since the unknown variable you are solving for, “x,” need to be determined based on its relationship to the data you carry out have.

Mental Math

Although pilots usage their physical calculators and calculator apps come do lot of the occupational for them, there room times as soon as you have to perform quick and accurate math in your head. Psychological math is a learned skill and also one that have to be practiced. Start boosting your an abilities by reading mental Math because that Pilots.


What carry out pilots should use math for?

Principles that flight, weight and balance, fuel needs, basic navigation, flight planning and also monitoring, lower planning, crosswind components, and more all need the usage of pilot math. Below are simply a few real-world instances of exactly how pilots use math top top a constant basis:

Weight calculations

Weight calculations usage the basic arithmetic skills of addition and subtraction. For an airplane to fly, it can not weigh much more than the quantity of lift that generates. Each airplane has a known empty weight and everything that is brought onboard consisting of fuel, passengers, luggage, and cargo need to be included to this north weight. The last number should be at or below the preferably takeoff weight developed by the aircraft manufacturer and listed in the pilot’s operating handbook (POH).

For example, a Cessna 180K has actually an empty weight of 1,650 pounds and a maximum takeoff load of 2,810 pounds. To calculation the valuable load, or the amount of weight that deserve to be added to the plane, a pilot will subtract the empty weight from the best takeoff weight:

Maximum takeoff load – empty weight = helpful load

In our instance this comes out to: 2,810-pound takeoff weight – 1,650 empty weight = 1,160 pounds valuable load.

Now that we recognize that a maximum of 1,160 pounds of valuable load can be added to the plane, we will certainly weigh everything that it s okay onboard the aircraft (ourselves included) and subtract those weights native the helpful load to ensure we are still below that max threshold.

Fuel calculations

Fuel calculations additionally use straightforward addition and subtraction skills. Take the very same Cessna 180K and assume we need to understand how plenty of pounds the our easily accessible 1,160-pound useful load should be allocated for fuel. If we mean a fuel burn the 13 gallons per hour and also our destination is 2 hours away, we multiply our per gallon burn through the variety of hours we will certainly be traveling:

Per hour fuel burn x number of hours = Gallons of fuel needed

In this case, 13 gallons per hour x 2 hours = 26 gallons.

Since in aviation, fuel load is calculated in pounds, we will transform our 26 gallons right into pounds again utilizing multiplication and the recognized variable of each gallon the Avgas weighing 6 pounds.

Gallons the fuel necessary x weight per gallon = Fuel weight

Based ~ above this equation us have: 26 gallons x 6 pounds every gallon = 156 pounds.

Our pilot math tells us that us will need a minimum of 156 pounds that fuel to get us come our destination, however we room not excellent yet. The much requirements state that in addition to our minimum fuel budget, us will additionally need to include enough fuel to acquire us come the most distant alternative destination on the trip plan and a 45-minute reserve.

If the alternative destination adds secondary 15 minutes of trip time, we deserve to use our an easy arithmetic an abilities to include up the total amount of added flight time we need to spending plan for.

Additional flight time to alternating destination + fuel to make reservation time = Total additional flight time

For our example this look at like: 15 minute + 45 minute = 60 minutes (or 1 hour)

We understand that ours fuel burn is 13 gallons every hour, so because that an extra hour of flight time, us will have to load an additional 13 gallons the fuel. Again, main point the gallons that fuel by the known weight every gallon to calculate the total weight the the extra fuel.

Gallons of fuel x weight per gallon = Extra fuel weight

Our example plane’s equation reads: 13 gallons x 6 pounds per gallon = 78 pounds.

The last step in our fuel calculation is to add the initial minimum fuel load to ours extra fuel weight so we have actually a total weight because that the amount of fuel we need to take on and also account for in our max weight calculation.

Minimum fuel weight + extra fuel load = complete fuel weight

For ours example plane we have: 156 pounds minimum fuel + 78 pounds extra fuel = 234 total pounds of fuel needed.

Crosswind component calculations

When you room landing or acquisition off, if over there is a wind which is perpendicular to the runway, this is described as a crosswind. A crosswind changes the aerodynamics of your aircraft and makes landings and takeoffs more difficult. Too strong a crosswind deserve to be dangerous, so that is essential to calculation the crosswind and also determine if it is for sure to takeoff or soil under those conditions and with her skillsets. If you continue with the maneuver, friend will additionally be making use of the crosswind ingredient calculation come help adjust and compensate for the crosswind.

Precise crosswind ingredient calculations space done using trigonometric equations, so girlfriend will need your calculator. The straightforward formula is:

Crosswind component = Wind speed x cosine that angle in between the wind and runway

Of course v crosswind components as with many other varieties of pilot math, pilots have developed rules of thumb that deserve to serve together a ballpark calculation if you execute not have actually the calculator to carry out the an exact equation or you want to examine your work.

In this case, pilots remember the if the angle in between the wind and runway is 15 degrees, the crosswind component is about 25% the the wind velocity. At 30 degrees it is 50%, in ~ 45 degrees it is 75%, and at 60+ degrees, the crosswind component is 100% of wind speed.

While rules of thumb like this must not be used where absolute precision is needed, lock can aid augment pilot math and serve together a overcome check. For example, if you were planning your takeoff and knew the there to be a 40 node wind at a 30 level angle to the runway, based on your rule of thumb, friend would suppose your calculator to tell you the the crosswind component is around 20 knots. If the calculator check out 18 knots, you would think it to be accurate since it is close to the dominance of ignorance estimate. If for some reason, her calculated crosswind ingredient read double the calculation at 40 knots, that would be a flag and you would understand to review your calculations.

Descent price calculations

For pilots to land safely, they require to organize to a offered descent angle. To perform this, they need to calculate how much out from the airport they should start the descent and also how rapid that descent must be so the they preserve the ideal descent angle and also stay ~ above the glidepath.

To recognize descent rate math, visualize the ground as the basic of a triangle, with a perpendicular invisible vertical line from the ground to the aircraft as one side of the triangle, and a diagonal heat from the aircraft to the ground together the various other side that the triangle. The angle between the diagonal line line and the ground is the lower angle. For this example, we will say the we need that edge to be 3-degrees.

Now us must determine how fast we require to shed altitude to save that 3-degree glidepath angle as we strategy the runway in ~ a offered speed. To carry out this we have to use the formula:

Tangent that glidepath edge = altitude loss vital per minute / groundspeed every minute

Several data conversions space necessary since groundspeed is measured in nautical miles every hour whereas we desire to settle for our descent rate which is expressed in feet per minute. To start our conversions, we first use the formula:

Groundspeed in nautical miles every hour / 60 = Groundspeed in nautical miles every minute

If our groundspeed is 100 kts and we division that by 60, we gain a rate of about 1.66 nautical miles per minute. Currently we require to convert this to feet per minute.

Groundspeed in nautical miles every minute x 6,080 feet every mile = Groundspeed in feet every minute

For example, 1.67 x 6,080 = 10,134 feet every minute.

Now the our groundspeed is expressed in feet per minute, we are ready to calculation the rate of descent we must stay top top glidepath.

Descent rate = Groundspeed per minute x tangent the glidepath angle

When we multiply 10,134 feet per minute x the tangent of ours 3-degree glidepath, we get a descent rate of 531 feet every minute.

This may sound complicated, however usually if you carry out the equation, friend will use a calculator. Also, due to the fact that 3-degrees is a usual glideslope angle, pilots have cleared up another dominance of ignorance that it s okay you nearby if you carry out not have a calculator come plug her equations into. Simply take your groundspeed in knots and multiply that by 5 to arrive at an almost right descent price of 500 feet every minute i m sorry is really close come the exactly calculated 531 feet every minute you obtain when utilizing the equation.


Pilot math have the right to seem intimidating, however the vital thing to remember is that if you understand the purpose and also theory behind the equations, following the mathematics itself frequently gets easier. Also, in many cases you have the right to simply usage a calculator or apply a rule of ignorance estimation to arrive at a quick ballpark answer come a math question that does not require specificity.

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If gift a pilot is your dream, execute not allow the mathematics scare girlfriend away. Instead invest some time in learning an ext about how pilots use math. To obtain you started, Pilot’s rule of ignorance is fantastic compact reference publication that quickly fits in your trip bag and also contains an easy formulas together with rules the thumb, tips, and also strategies for mathematical success.