A&P Math: The Formulas Every Aviation Maintenance Student Should Know

Math can make a lot of A&P students nervous, but aviation maintenance math is usually very practical. You are not doing math just to do math. You are using it to solve real aircraft maintenance problems.

As an A&P student, math shows up when you are working with:

• Electrical circuits
• Weight and balance
• Torque values
• Sheet metal layout
• Hydraulic pressure
• Fluid quantities
• Temperature conversions
• Measurements
• Engine calculations
• Aircraft drawings and dimensions

The good news is that most A&P math uses the same basic skills over and over: fractions, decimals, ratios, percentages, formulas, and unit conversions.

Once you get comfortable with those, the rest becomes much easier.

Why Math Matters in Aviation Maintenance

Aircraft maintenance has to be accurate. A small math mistake can lead to a wrong torque value, incorrect wire size, poor weight and balance calculation, bad sheet metal layout, or an incorrect electrical troubleshooting result.

A&P math matters because it helps you:

• Measure accurately
• Convert units correctly
• Calculate electrical values
• Understand pressure and force
• Determine aircraft center of gravity
• Follow maintenance manual limits
• Interpret charts, graphs, and tables
• Avoid guessing

In aviation, guessing is not maintenance. You need to calculate, verify, and follow the approved data.

1. Fractions and Decimals

Fractions and decimals are everywhere in aviation maintenance.

You will see measurements like:

1/8 inch
3/16 inch
1/4 inch
5/16 inch
3/8 inch
7/16 inch
1/2 inch

You will also see decimal measurements like:

0.125 inch
0.1875 inch
0.250 inch
0.3125 inch
0.375 inch
0.4375 inch
0.500 inch

Being able to move between fractions and decimals is important when using rulers, calipers, micrometers, drill charts, and maintenance manuals.

Common Fraction to Decimal Conversions

A simple way to convert a fraction to a decimal is:

Decimal = Numerator ÷ Denominator

Example:

3/8 = 3 ÷ 8 = 0.375

2. Adding and Subtracting Fractions

To add or subtract fractions, they need a common denominator.

Example:

1/4 + 1/8

Convert 1/4 to eighths:

1/4 = 2/8

Then add:

2/8 + 1/8 = 3/8

So:

1/4 + 1/8 = 3/8

This matters in aircraft maintenance when measuring, laying out sheet metal, spacing rivets, or reading drawings.

3. Multiplying Fractions

To multiply fractions, multiply the top numbers and multiply the bottom numbers.

Example:

1/2 × 3/4 = 3/8

Work:

1 × 3 = 3
2 × 4 = 8

Answer:

3/8

4. Dividing Fractions

To divide fractions, flip the second fraction and multiply.

Example:

1/2 ÷ 1/4

Flip the second fraction:

1/4 becomes 4/1

Then multiply:

1/2 × 4/1 = 4/2 = 2

Answer:

1/2 ÷ 1/4 = 2

This means there are two 1/4-inch sections in 1/2 inch.

5. Percentages

Percent means “per hundred.”

The basic formula is:

Percent = Part ÷ Whole × 100

Example:

If a battery has 18 volts available out of a possible 24 volts:

Percent = 18 ÷ 24 × 100
Percent = 0.75 × 100
Percent = 75%

Percentages are useful for:

• Battery charge estimates
• Efficiency
• Error calculations
• Mixture ratios
• Inspection limits
• Weight comparisons

6. Ratios

A ratio compares two quantities.

Example:

4:1

This means one value is four times another value.

Ratios are used in:

• Gear ratios
• Compression ratios
• Mixture ratios
• Pulley systems
• Scale drawings

Example:

If an engine has a compression ratio of 8:1, that means the cylinder volume is compressed to one-eighth of its original volume.

7. Unit Conversions

A&P students need to be comfortable converting units.

Common conversions include:

Always check the units before solving a problem. A correct formula with the wrong units can still give you the wrong answer.

8. Temperature Conversions

Temperature conversions are common in aircraft maintenance, especially when working with weather, engine operation, oils, fluids, and performance data.

Fahrenheit to Celsius

C = (F - 32) × 5/9

Example:

F = 68°F
C = (68 - 32) × 5/9
C = 36 × 5/9
C = 20°C

Celsius to Fahrenheit

F = (C × 9/5) + 32

Example:

C = 20°C
F = (20 × 9/5) + 32
F = 36 + 32
F = 68°F

Quick memory tip:

C to F: multiply by 9/5, then add 32
F to C: subtract 32, then multiply by 5/9

9. Area

Area is the amount of surface inside a shape.

Area matters in aircraft maintenance because it is used in:

• Sheet metal layout
• Hydraulic pressure calculations
• Piston area
• Surface repairs
• Inspection areas

Rectangle Area

Area = Length × Width

Example:

A panel is 12 inches long and 6 inches wide.

Area = 12 × 6
Area = 72 square inches

Circle Area

Area = π × Radius²

Or:

A = πr²

Example:

A circular piston has a radius of 2 inches.

A = 3.14 × 2²
A = 3.14 × 4
A = 12.56 square inches

Remember:

Radius = half the diameter
Diameter = distance across the circle

10. Volume

Volume is the amount of space inside an object.

Volume may be used when working with:

• Fluid containers
• Cylinders
• Fuel tanks
• Engine displacement
• Hydraulic systems

Rectangular Volume

Volume = Length × Width × Height

Example:

A box is 10 inches long, 5 inches wide, and 4 inches high.

Volume = 10 × 5 × 4
Volume = 200 cubic inches

Cylinder Volume

Volume = π × Radius² × Height

Example:

A cylinder has a radius of 2 inches and a height of 6 inches.

Volume = 3.14 × 2² × 6
Volume = 3.14 × 4 × 6
Volume = 75.36 cubic inches

11. Torque Math

Torque is a twisting force.

The basic formula is:

Torque = Force × Distance

Or:

T = F × D

Where:

• T = torque
• F = force
• D = distance from the pivot point

Example:

If you apply 50 pounds of force to a wrench that is 1 foot long:

Torque = 50 lb × 1 ft
Torque = 50 ft-lb

If the wrench is 2 feet long:

Torque = 50 lb × 2 ft
Torque = 100 ft-lb

That is why a longer wrench gives you more leverage.

12. Inch-Pounds and Foot-Pounds

Aircraft maintenance often uses inch-pounds and foot-pounds.

The conversion is:

1 ft-lb = 12 in-lb

To convert foot-pounds to inch-pounds:

in-lb = ft-lb × 12

Example:

20 ft-lb × 12 = 240 in-lb

To convert inch-pounds to foot-pounds:

ft-lb = in-lb ÷ 12

Example:

240 in-lb ÷ 12 = 20 ft-lb

This is important because using the wrong torque unit can seriously over-tighten or under-tighten a fastener.

13. Torque Wrench Extension Formula

Sometimes a torque wrench is used with an extension. When the extension changes the effective length of the wrench, the torque setting may need to be corrected.

A common formula is:

TW = T × L ÷ (L + E)

Where:

• TW = torque wrench setting
• T = desired torque
• L = length of torque wrench
• E = length of extension

Example:

Desired torque is 100 ft-lb. The torque wrench is 12 inches long. The extension adds 3 inches.

TW = 100 × 12 ÷ (12 + 3)
TW = 1200 ÷ 15
TW = 80 ft-lb

So the torque wrench should be set to 80 ft-lb to apply 100 ft-lb at the fastener.

Important: Always follow the aircraft maintenance manual or tool manufacturer instructions when using extensions.

14. Weight and Balance Math

Weight and balance is one of the most important math areas for A&P students.

Three key terms are:

• Weight
• Arm
• Moment

Weight

Weight is how heavy the item is.

Example:

Pilot = 180 lb
Fuel = 240 lb
Baggage = 50 lb

Arm

Arm is the distance from the datum to the item.

The datum is a reference point chosen by the aircraft manufacturer.

Example:

Pilot arm = 37 inches
Fuel arm = 48 inches
Baggage arm = 95 inches

Moment

Moment is the turning effect produced by a weight at a distance from the datum.

The formula is:

Moment = Weight × Arm

Example:

Weight = 180 lb
Arm = 37 in
Moment = 180 × 37
Moment = 6,660 lb-in

15. Center of Gravity Formula

The center of gravity, or CG, is found with:

CG = Total Moment ÷ Total Weight

Example:

Total weight:

1,500 + 180 + 240 + 50 = 1,970 lb

Total moment:

60,000 + 6,660 + 11,520 + 4,750 = 82,930

CG:

CG = 82,930 ÷ 1,970
CG = 42.1 inches

The aircraft CG is 42.1 inches aft of the datum.

The final step is always to check whether that CG is within the approved limits.

16. Electrical Math: Ohm’s Law

Basic electricity is a major part of A&P training.

The main Ohm’s Law formula is:

E = I × R

Where:

• E = voltage
• I = current
• R = resistance

You may also see voltage represented as V:

V = I × R

The three main Ohm’s Law formulas are:

E = I × R
I = E ÷ R
R = E ÷ I

17. Ohm’s Law Examples

Solving for Voltage

A circuit has 3 amps of current and 4 ohms of resistance.

E = I × R
E = 3 × 4
E = 12 volts

Solving for Current

A circuit has 24 volts and 6 ohms of resistance.

I = E ÷ R
I = 24 ÷ 6
I = 4 amps

Solving for Resistance

A circuit has 12 volts and 2 amps of current.

R = E ÷ I
R = 12 ÷ 2
R = 6 ohms

18. Electrical Power

Electrical power is measured in watts.

The basic power formula is:

P = E × I

Where:

• P = power in watts
• E = voltage
• I = current

Example:

A 12-volt circuit has 5 amps of current.

P = E × I
P = 12 × 5
P = 60 watts

Other useful power formulas are:

P = I² × R
P = E² ÷ R

19. Series Circuit Math

In a series circuit:

Current is the same through each component.
Voltage drops add up to source voltage.
Resistance adds together.

Total resistance in series:

RT = R1 + R2 + R3

Example:

R1 = 2 ohms
R2 = 4 ohms
R3 = 6 ohms

RT = 2 + 4 + 6
RT = 12 ohms

If the source voltage is 24 volts:

I = E ÷ R
I = 24 ÷ 12
I = 2 amps

Since it is a series circuit, the same 2 amps flows through each resistor.

20. Parallel Circuit Math

In a parallel circuit:

Voltage is the same across each branch.
Current divides between branches.
Total resistance is less than the smallest branch resistance.

For two resistors in parallel:

RT = (R1 × R2) ÷ (R1 + R2)

Example:

R1 = 6 ohms
R2 = 3 ohms

RT = (6 × 3) ÷ (6 + 3)
RT = 18 ÷ 9
RT = 2 ohms

For more than two resistors:

1/RT = 1/R1 + 1/R2 + 1/R3

21. Hydraulic Math

Hydraulic systems use pressure, force, and area.

The main formula is:

Pressure = Force ÷ Area

Or:

P = F ÷ A

The formula can also be rearranged:

Force = Pressure × Area

Or:

F = P × A

And:

Area = Force ÷ Pressure

22. Hydraulic Force Example

A hydraulic system has 1,000 psi acting on a piston with an area of 5 square inches.

Force = Pressure × Area
Force = 1,000 × 5
Force = 5,000 lb

The actuator can produce 5,000 pounds of force.

This is why hydraulic systems are so useful for landing gear, brakes, flaps, and flight controls.

23. Engine Displacement Math

Engine displacement is the total volume displaced by all pistons in the engine.

For one cylinder:

Cylinder Volume = π × Radius² × Stroke

Total engine displacement:

Total Displacement = Cylinder Volume × Number of Cylinders

Example:

An engine has a bore of 5 inches and a stroke of 4 inches.

First, find radius:

Radius = Bore ÷ 2
Radius = 5 ÷ 2
Radius = 2.5 inches

Find cylinder volume:

Volume = π × Radius² × Stroke
Volume = 3.14 × 2.5² × 4
Volume = 3.14 × 6.25 × 4
Volume = 78.5 cubic inches

If the engine has 4 cylinders:

Total Displacement = 78.5 × 4
Total Displacement = 314 cubic inches

24. Compression Ratio

Compression ratio compares the cylinder volume when the piston is at bottom dead center to the volume when the piston is at top dead center.

A compression ratio of 8:1 means:

The original volume is compressed into 1/8 of the space.

A higher compression ratio usually means the fuel-air mixture is compressed more before ignition.

25. Scientific Notation

Scientific notation is a way to write very large or very small numbers.

Example:

1,000 = 1 × 10³

Example:

0.001 = 1 × 10⁻³

This can show up in electrical math, especially with very small or very large values.

Common prefixes:

Examples:

1 kΩ = 1,000 ohms
1 mA = 0.001 amp
1 µF = 0.000001 farad

26. Reading Measurements

A&P students need to read measuring tools accurately.

Common tools include:

• Ruler
• Tape measure
• Caliper
• Micrometer
• Dial indicator
• Feeler gauge
• Torque wrench
• Multimeter

Measurement mistakes can cause incorrect fits, improper clearances, poor electrical readings, or rejected work.

A good habit is to always check:

What unit am I reading?
What scale am I using?
Is this inches, millimeters, volts, amps, ohms, or psi?

27. Rounding Answers

Sometimes A&P math requires rounding.

For example:

42.137 inches

Rounded to one decimal place:

42.1 inches

Rounded to two decimal places:

42.14 inches

Be careful when rounding. Do not round too early in a multi-step problem because it can affect the final answer.

A good habit is:

Do the full calculation first, then round at the end.

28. Common A&P Math Mistakes

Here are some common mistakes to avoid:

• Mixing up inches and feet
• Using inch-pounds when the manual says foot-pounds
• Forgetting to convert units
• Using diameter instead of radius
• Rounding too early
• Adding resistors incorrectly in parallel circuits
• Forgetting that current is the same in a series circuit
• Forgetting that voltage is the same in a parallel circuit
• Using the wrong hydraulic fluid pressure unit
• Forgetting to check CG limits after calculating center of gravity

The math itself may be simple, but the details matter.

Quick Formula Reference

Fractions

Decimal = Numerator ÷ Denominator

Percent

Percent = Part ÷ Whole × 100

Temperature

C = (F - 32) × 5/9
F = (C × 9/5) + 32

Rectangle Area

Area = Length × Width

Circle Area

Area = π × Radius²

Rectangular Volume

Volume = Length × Width × Height

Cylinder Volume

Volume = π × Radius² × Height

Torque

Torque = Force × Distance

Torque Unit Conversion

1 ft-lb = 12 in-lb

Weight and Balance Moment

Moment = Weight × Arm

Center of Gravity

CG = Total Moment ÷ Total Weight

Ohm’s Law

E = I × R
I = E ÷ R
R = E ÷ I

Electrical Power

P = E × I
P = I² × R
P = E² ÷ R

Series Resistance

RT = R1 + R2 + R3

Parallel Resistance for Two Resistors

RT = (R1 × R2) ÷ (R1 + R2)

Parallel Resistance for Multiple Resistors

1/RT = 1/R1 + 1/R2 + 1/R3

Hydraulic Pressure

P = F ÷ A

Hydraulic Force

F = P × A

Engine Displacement

Cylinder Volume = π × Radius² × Stroke
Total Displacement = Cylinder Volume × Number of Cylinders

A&P Student Study Tips

The best way to get better at A&P math is to work practice problems slowly and carefully.

When solving a problem, ask yourself:

What am I solving for?
What formula do I need?
What units are given?
Do I need to convert anything?
Does my answer make sense?

For electrical problems, write down:

E = voltage
I = current
R = resistance
P = power

For weight and balance problems, write down:

Weight
Arm
Moment

For hydraulic problems, write down:

Pressure
Force
Area

Once the known values are organized, the problem usually becomes much easier.

Final Thoughts

A&P math is not about being a mathematician. It is about being accurate, careful, and practical.

Most aviation maintenance math comes down to knowing which formula to use, putting the numbers in the right place, and keeping the units straight.

As an A&P student, the more comfortable you become with fractions, decimals, conversions, torque, electricity, hydraulics, and weight and balance, the more confident you will be in the shop, in class, and during testing.

Math is part of the job because accuracy is part of the job.

Learn the formulas, practice the problems, and always check your work.