Trade Mathematics for Aviation Maintenance

Why Math Matters in Aviation Maintenance

Every task an aviation mechanic performs relies on accurate numbers. A torque value applied incorrectly can cause a fastener to fail in flight. A fuel calculation error can leave an aircraft short of fuel or dangerously overloaded. A wrong drill size ruins a rivet hole and weakens a structural repair. The FAA A&P General written exam tests your ability to perform these calculations reliably, and the work itself demands the same accuracy every day. This lesson gives you structured practice across the math topics you must master.

Fractions and Mixed Numbers

Aviation hardware specifications are routinely expressed as fractions. A bolt may be 3/8-inch in diameter; a rivet hole may call for a #30 drill or a 3/32-inch bit. When you add, subtract, multiply, or divide fractions, always find a common denominator before adding or subtracting. To multiply fractions, multiply numerators together and denominators together, then reduce. To divide, invert the second fraction and multiply.

Mixed numbers (for example, 2 3/4) must be converted to improper fractions before most operations: multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. A torque specification written as 14 1/2 ft-lb becomes 29/2 ft-lb for calculation purposes.

Decimals and Percentages

Decimals are essential for reading micrometers, calculating fuel quantities, and working with metric values. Align decimal points when adding or subtracting. When multiplying decimals, complete the multiplication and then count the total decimal places in both factors to position the point in the answer. Percentages are decimals expressed per hundred: 12% = 0.12. To find a percentage of a value, multiply the value by the decimal form.

In maintenance, you will use percentages to calculate a fuel load as a fraction of maximum capacity, to express tolerance limits, and to check whether a measured value falls within a manufacturer's allowable range.

Ratio and Proportion

A ratio compares two quantities. A proportion states that two ratios are equal. If a hydraulic actuator moves 2 inches for every 5 inches of input travel, and you need to find the output for 12 inches of input, set up a proportion: 2/5 = x/12. Cross-multiply and solve: x = (2 × 12) / 5 = 4.8 inches. Gear ratios, compression ratios, and mixture ratios all use this same structure.

Basic Algebra and Ohm's Law

Algebra allows you to find an unknown value when you know the relationship between quantities. In a series electrical circuit, Ohm's Law states that voltage (E) equals current (I) multiplied by resistance (R): E = I × R. If you know voltage and current, solve for resistance by dividing both sides by I: R = E / I. Always isolate the unknown on one side by performing the same operation to both sides of the equation.

Area and Volume

When applying sealant, primer, or paint, you need the surface area of the part so you can order the correct amount of material and avoid waste or shortage.

• Rectangle: Area = length × width
• Triangle: Area = 1/2 × base × height
• Circle: Area = π × radius² (use π ≈ 3.1416)

Volume calculations appear when you compute fuel tank capacity or the displacement of a cylinder.

• Rectangular solid: Volume = length × width × height
• Cylinder: Volume = π × radius² × height

Always label units throughout the calculation (in², ft², gallons, liters) so you can catch errors before they matter.

Unit Conversions: US Customary and Metric

The FAA A&P exam and real shop work both require you to move between unit systems. Keep a conversion reference card at your bench until the values are memorized.

| To convert | Multiply by |

|---|---|

| inches → centimeters | 2.54 |

| gallons → liters | 3.785 |

| pounds → kilograms | 0.4536 |

| ft-lb → Newton-meters | 1.3558 |

| psi → kPa | 6.895 |

To reverse any conversion, divide by the same factor (or multiply by its reciprocal).

Safety in the Shop While You Calculate

Math errors have direct safety consequences, so build habits that prevent them:

• Double-check torque values against the maintenance manual before applying any torque. A value in the wrong units (ft-lb versus in-lb) can be a 12:1 error that strips threads or snaps a bolt.
• Verify fuel volumes independently using a second calculation method or a dipstick before releasing an aircraft.
• Wear appropriate PPE (safety glasses, chemical-resistant gloves) when handling sealants and fuels whose quantities you have calculated.
• Use lockout/tagout procedures on any electrical or hydraulic system before measuring components in a live circuit.
• Never estimate a critical measurement. Round only at the final step and only to the precision the specification requires.

Using Your Calculator Correctly

A scientific calculator speeds arithmetic but cannot catch a wrong setup. Enter the problem in the order the formula requires, check the display for reasonableness before recording your answer, and always re-examine unit labels. The FAA General written exam permits an approved calculator; practice now with the same model you will use on test day.