Math for A&P Students: The Formulas You Actually Need to Know

A lot of A&P students get nervous when they hear the word math.

That is understandable. Aviation maintenance math can show up in several different areas: weight and balance, electrical circuits, torque, measurement, area, volume, ratios, percentages, and unit conversions.

The good news is that A&P math is not advanced math. You do not need calculus. You do not need complicated algebra. What you need is a solid understanding of the basic formulas that aircraft mechanics actually use.

This post is written as both a blog article and a study guide. The goal is to explain the math that shows up on the A&P written exams, oral questions, and real maintenance tasks.

Why A&P Mechanics Need Math

Math is part of aircraft maintenance because mechanics deal with exact measurements.

A mechanic may need to calculate:

• Aircraft weight and balance
• Center of gravity
• Electrical current, voltage, resistance, and power
• Torque conversions
• Sheet metal bend allowance
• Area and volume
• Compression ratios
• Gear ratios
• Fuel quantity
• Unit conversions
• Decimal and fraction measurements

In aviation, guessing is not good enough. A small math mistake can affect airworthiness, safety, or the accuracy of a maintenance record.

A good way to think about A&P math is this:

Math is another maintenance tool.

Just like a torque wrench, multimeter, or micrometer, math helps you do the job correctly.

1. Basic Arithmetic

Before getting into aviation formulas, make sure you are comfortable with basic arithmetic:

• Addition
• Subtraction
• Multiplication
• Division
• Fractions
• Decimals
• Percentages
• Rounding

Most A&P math problems are built from these basics.

For example, if you can multiply weight by arm, divide total moment by total weight, and convert fractions to decimals, you can solve many weight and balance problems.

Fractions and Decimals

Aircraft maintenance often uses both fractions and decimals.

For example:

• Drill sizes
• Sheet metal thickness
• Measurements
• Torque values
• Clearance limits
• Wear limits

Common fraction-to-decimal conversions:

Study Tip

Know how to convert a fraction to a decimal:

Divide the top number by the bottom number.

Example:

3/8 = 3 ÷ 8 = 0.375

Percentages

Percent means “per hundred.”

A&P math may use percentages for:

• Efficiency
• Weight changes
• Mixture ratios
• Error calculations
• Compression or leakage comparisons
• Material elongation

Formula:

Percent = Part ÷ Whole × 100

Example:

An aircraft battery has 18 volts available out of a normal 24 volts.

18 ÷ 24 × 100 = 75%

The battery is at 75 percent of nominal voltage.

2. Unit Conversions

Unit conversions are common in aviation maintenance.

A mechanic may need to convert:

• Inches to feet
• Feet to inches
• Pounds to ounces
• Gallons to pounds
• Fahrenheit to Celsius
• Foot-pounds to inch-pounds
• Decimal inches to fractions

Inches and Feet

Basic conversion:

1 foot = 12 inches

Examples:

3 feet = 3 × 12 = 36 inches

48 inches = 48 ÷ 12 = 4 feet

Inch-Pounds and Foot-Pounds

Torque conversions are very common.

Basic conversion:

1 foot-pound = 12 inch-pounds

To convert foot-pounds to inch-pounds:

ft-lb × 12 = in-lb

Example:

20 ft-lb × 12 = 240 in-lb

To convert inch-pounds to foot-pounds:

in-lb ÷ 12 = ft-lb

Example:

180 in-lb ÷ 12 = 15 ft-lb

Study Tip

Be careful with torque units. Inch-pounds and foot-pounds are not the same thing.

Fahrenheit and Celsius

Temperature conversions may appear in aircraft maintenance, especially with weather, engine operation, materials, and servicing.

Formulas:

°C = (°F - 32) × 5/9

°F = (°C × 9/5) + 32

Example:

Convert 68°F to Celsius:

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

So:

68°F = 20°C

3. Ratios and Proportions

Ratios compare one quantity to another.

Aviation maintenance uses ratios in:

• Gear ratios
• Compression ratios
• Mixture ratios
• Scale drawings
• Fuel/oil mixtures
• Pulley and belt relationships

Example ratio:

4:1

This means one quantity is four times another.

Proportion Example

If 2 gallons of oil are needed for 10 gallons of mixture, how much oil is needed for 25 gallons?

Set it up:

2 / 10 = x / 25

Cross multiply:

10x = 50
x = 5

Answer:

5 gallons of oil

Study Tip

When you see a ratio problem, set up the known relationship first, then solve for the missing value.

4. Area and Volume

Area and volume show up in aircraft maintenance because mechanics work with surfaces, tanks, cylinders, materials, and fluid capacity.

Area of a Rectangle

Formula:

Area = Length × Width

Example:

A rectangular inspection panel is 12 inches long and 8 inches wide.

Area = 12 × 8 = 96 square inches

Area of a Triangle

Formula:

Area = 1/2 × Base × Height

Example:

A triangular gusset has a base of 10 inches and height of 6 inches.

Area = 1/2 × 10 × 6
Area = 30 square inches

Area of a Circle

Formula:

Area = πr²

Where:

π ≈ 3.1416
r = radius

Example:

A circular plate has a radius of 4 inches.

Area = 3.1416 × 4²
Area = 3.1416 × 16
Area = 50.27 square inches

Volume of a Rectangular Tank

Formula:

Volume = Length × Width × Height

Example:

A tank is 20 inches long, 10 inches wide, and 8 inches high.

Volume = 20 × 10 × 8
Volume = 1,600 cubic inches

5. Weight and Balance Math

Weight and balance is one of the most important A&P math topics.

The basic idea is simple:

Weight tells how heavy the aircraft is. Balance tells where that weight acts.

The main terms are:

• Weight
• Arm
• Moment
• Center of gravity

Weight

Weight is the force caused by gravity. In aircraft weight and balance problems, weight is usually measured in pounds.

Examples:

• Empty aircraft weight
• Fuel weight
• Passenger weight
• Baggage weight
• Equipment weight

Arm

Arm is the distance from the datum to the item’s location.

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

Arm is usually measured in inches.

Moment

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

Formula:

Moment = Weight × Arm

Example:

A 50-pound battery is installed at an arm of 80 inches.

Moment = 50 × 80
Moment = 4,000 lb-in

Center of Gravity

Center of gravity, or CG, is the point where the aircraft would balance.

Formula:

CG = Total Moment ÷ Total Weight

Example:

Total weight:

1,500 + 240 + 80 = 1,820 lb

Total moment:

60,000 + 11,520 + 5,600 = 77,120

CG:

77,120 ÷ 1,820 = 42.37 in

Answer:

CG = 42.37 inches aft of datum

Weight Shift Formula

Sometimes a weight is moved from one location to another.

Formula:

Weight Shifted ÷ Total Weight = Change in CG ÷ Distance Weight Shifted

Or:

Change in CG = Weight Shifted × Distance Shifted ÷ Total Weight

Example:

A 100-pound item is moved 30 inches aft in a 2,000-pound aircraft.

Change in CG = 100 × 30 ÷ 2,000
Change in CG = 3,000 ÷ 2,000
Change in CG = 1.5 inches

The CG moves 1.5 inches aft.

Study Tip

If weight moves aft, CG moves aft. If weight moves forward, CG moves forward.

Adding or Removing Weight

When adding weight:

New Total Weight = Old Weight + Added Weight
New Total Moment = Old Moment + Added Moment
New CG = New Total Moment ÷ New Total Weight

When removing weight:

New Total Weight = Old Weight - Removed Weight
New Total Moment = Old Moment - Removed Moment
New CG = New Total Moment ÷ New Total Weight

Example:

An aircraft weighs 1,800 pounds with a moment of 72,000. A 20-pound radio is removed from station 60.

Removed moment:

20 × 60 = 1,200

New weight:

1,800 - 20 = 1,780

New moment:

72,000 - 1,200 = 70,800

New CG:

70,800 ÷ 1,780 = 39.78 in

6. Electrical Math

Electrical math is another major A&P area.

The most important formula is Ohm’s Law.

Ohm’s Law

Ohm’s Law relates voltage, current, and resistance.

Formula:

E = I × R

Where:

E = Voltage
I = Current in amps
R = Resistance in ohms

You may also see voltage written as V instead of E:

V = I × R

Ohm’s Law Variations

If you know any two values, you can solve for the third.

Voltage:

E = I × R

Current:

I = E ÷ R

Resistance:

R = E ÷ I

Example:

A circuit has 24 volts and 6 ohms of resistance. What is the current?

I = E ÷ R
I = 24 ÷ 6
I = 4 amps

Electrical Power

Power is measured in watts.

Formula:

P = E × I

Where:

P = Power in watts
E = Voltage
I = Current

Example:

A 12-volt landing light draws 5 amps.

P = 12 × 5
P = 60 watts

Series Circuits

In a series circuit:

• Current is the same through all components.
• Total resistance is the sum of all resistances.
• Voltage drops divide across the loads.

Formula:

Rt = R1 + R2 + R3

Example:

Three resistors are in series:

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

Total resistance:

Rt = 2 + 4 + 6
Rt = 12 ohms

Memory Aid

Series = same current.

Parallel Circuits

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:

Two resistors are in parallel:

R1 = 6 ohms
R2 = 3 ohms

Total resistance:

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

Memory Aid

Parallel = same voltage, current divides, resistance gets smaller.

7. Torque Math

Torque is twisting force.

In aircraft maintenance, torque is used when tightening hardware, fittings, spark plugs, engine components, and many other parts.

Formula:

Torque = Force × Distance

Example:

A force of 30 pounds is applied to a wrench 1 foot long.

Torque = 30 × 1
Torque = 30 ft-lb

If the wrench is 6 inches long:

6 inches = 0.5 feet
Torque = 30 × 0.5
Torque = 15 ft-lb

Torque Wrench Extension Formula

If you use an extension on a torque wrench, the actual torque may be higher than the torque wrench reading.

A common formula is:

TW = Desired Torque × Wrench Length ÷ (Wrench Length + Extension Length)

Where:

TW = torque wrench setting

Example:

Desired torque is 120 in-lb. Torque wrench length is 10 inches. Extension length is 2 inches.

TW = 120 × 10 ÷ (10 + 2)
TW = 1,200 ÷ 12
TW = 100 in-lb

Set the torque wrench to:

100 in-lb

This produces approximately 120 in-lb at the fastener.

Study Tip

If the extension is inline with the wrench, it changes the effective length. If the extension is at 90 degrees, it usually does not change the torque setting.

8. Measurement Math

A&P students must be comfortable reading measurements.

This includes:

• Rulers
• Micrometers
• Dial calipers
• Vernier calipers
• Torque wrenches
• Multimeters
• Pressure gauges

Micrometer Basics

Most inch micrometers read in thousandths of an inch.

Common terms:

0.001 inch = one thousandth
0.010 inch = ten thousandths
0.100 inch = one hundred thousandths

Example:

A micrometer reads:

0.250 inch

That is one quarter inch.

Another reading:

0.375 inch

That is three eighths inch.

Study Tip

Be careful with decimal places.

0.1 = one tenth
0.01 = one hundredth
0.001 = one thousandth

These are not the same.

9. Density and Fluid Weight

Aircraft maintenance often involves fuel, oil, hydraulic fluid, and other liquids.

You may need to calculate fluid weight.

Formula:

Weight = Volume × Weight per Unit

For aviation gasoline, a common approximation is:

1 gallon of avgas ≈ 6 lb

Example:

An aircraft has 40 gallons of avgas.

40 × 6 = 240 lb

Fuel weight:

240 lb

Study Tip

Always use the value given in the test question if one is provided.

10. Formulas to Memorize

Here are the formulas I would memorize first for A&P math.

Weight and Balance

Moment = Weight × Arm

CG = Total Moment ÷ Total Weight

Change in CG = Weight Shifted × Distance Shifted ÷ Total Weight

Electrical

E = I × R

I = E ÷ R

R = E ÷ I

P = E × I

Series Resistance

Rt = R1 + R2 + R3

Parallel Resistance, Two Resistors

Rt = (R1 × R2) ÷ (R1 + R2)

Torque

Torque = Force × Distance

Area

Rectangle Area = Length × Width

Triangle Area = 1/2 × Base × Height

Circle Area = πr²

Volume

Rectangular Volume = Length × Width × Height

Temperature

°C = (°F - 32) × 5/9

°F = (°C × 9/5) + 32

11. Common A&P Math Mistakes

Mistake 1: Mixing Units

Do not mix inches and feet, or inch-pounds and foot-pounds.

Convert first, then calculate.

Mistake 2: Forgetting Total Moment

In weight and balance problems, do not average the arms directly.

Use:

Total Moment ÷ Total Weight

Mistake 3: Thinking Parallel Resistance Gets Bigger

In a parallel circuit, total resistance is less than the smallest branch resistance.

If your answer is larger than the smallest resistor, check your work.

Mistake 4: Rounding Too Early

Carry the numbers through the problem, then round at the end.

Rounding early can change the final answer.

Mistake 5: Ignoring Direction

In weight and balance:

• Weight added aft usually moves CG aft.
• Weight added forward usually moves CG forward.
• Weight removed aft usually moves CG forward.
• Weight removed forward usually moves CG aft.

Think about whether the answer makes physical sense.

12. Quick Practice Problems

Problem 1: Weight and Balance

An aircraft has a total weight of 2,400 lb and a total moment of 96,000 lb-in.

What is the CG?

CG = Total Moment ÷ Total Weight
CG = 96,000 ÷ 2,400
CG = 40 in

Answer:

40 inches aft of datum

Problem 2: Ohm’s Law

A 24-volt circuit has 8 ohms of resistance.

What is the current?

I = E ÷ R
I = 24 ÷ 8
I = 3 amps

Answer:

3 amps

Problem 3: Torque Conversion

Convert 25 ft-lb to inch-pounds.

25 × 12 = 300 in-lb

Answer:

300 in-lb

Problem 4: Parallel Resistance

Two resistors are in parallel. One is 4 ohms and one is 6 ohms.

Rt = (R1 × R2) ÷ (R1 + R2)
Rt = (4 × 6) ÷ (4 + 6)
Rt = 24 ÷ 10
Rt = 2.4 ohms

Answer:

2.4 ohms

Problem 5: Fuel Weight

An aircraft has 32 gallons of avgas. Use 6 lb per gallon.

32 × 6 = 192 lb

Answer:

192 lb

Final Study Summary

A&P math is not about being a mathematician. It is about using the right formula, keeping units straight, and checking whether the answer makes sense.

For the A&P written, oral, and practical exams, focus on these areas first:

• Fractions and decimals
• Unit conversions
• Percentages
• Ratios
• Area and volume
• Weight and balance
• Ohm’s Law
• Electrical power
• Series and parallel circuits
• Torque
• Measurement reading

The best advice is simple:

Write the formula first, plug in the numbers second, and check the units last.

If you do that consistently, A&P math becomes much less intimidating.