Every time an AMT reads a gear ratio, mixes a corrosion-inhibiting compound, converts a fuel quantity, or determines a mechanical advantage, ratio and proportion are doing the heavy lifting behind the scenes. These concepts might sound like middle-school math, but in aviation maintenance they carry real safety weight. A fluid mixed at the wrong ratio can corrode aluminum instead of protecting it; a misread gear ratio can mean a control surface moves too fast or too slow; an incorrect torque scaling calculation can leave a fastener dangerously under- or over-tightened. Understanding the mechanics of ratio and proportion—not just the formulas—is therefore a core competency for every certificated aviation maintenance technician (AMT).
This article walks through the definitions, the arithmetic mechanics, and the hands-on applications you will encounter both on the FAA General Knowledge exam and on the shop floor. Concrete examples are worked out step by step so you can see exactly how the math flows from problem to answer.
What Is a Ratio?
A ratio is a comparison of two quantities expressed as a fraction or with a colon. If a gearbox has 40 teeth on the driven gear and 10 teeth on the driving gear, the gear ratio is 40:10, which simplifies to 4:1. That single expression tells you the output shaft turns once for every four turns of the input shaft—an enormous amount of information packed into two numbers.
Ratios can compare any two like or unlike quantities: teeth to teeth, parts of oil to parts of solvent, inches of travel to degrees of rotation, or even events over time (cycles per flight hour). The key rule is that both numbers must be in the same units before you write the ratio, unless the ratio is explicitly comparing unlike things (such as miles per gallon, which is a rate, a special kind of ratio). Always simplify a ratio to its lowest whole-number terms so that relationships are instantly readable.
What Is a Proportion?
A proportion is a statement that two ratios are equal. Written algebraically: a/b = c/d, or equivalently, a:b = c:d. The practical power of a proportion is that if you know three of the four values, you can always solve for the fourth. This is the engine behind an enormous range of maintenance calculations.
The fundamental rule of proportions is the cross-multiplication property: if a/b = c/d, then a × d = b × c. The products of the diagonal pairs (called the means and extremes) are always equal. This rule lets you isolate any unknown with simple algebra.
Worked Example — Solving for an Unknown
Suppose a hydraulic actuator produces 600 pounds of force when system pressure is 1,500 psi. You need to know what force it will produce at 2,000 psi, assuming the piston area is unchanged. Set up the proportion:
600 lb / 1,500 psi = X lb / 2,000 psi
Cross-multiply: 600 × 2,000 = 1,500 × X, so 1,200,000 = 1,500X. Divide both sides by 1,500: X = 800 lb. At 2,000 psi the actuator exerts 800 pounds of force. This kind of scaling is used constantly when evaluating system upgrades, troubleshooting actuator performance, or checking whether a component is within spec under varying pressures.
Gear Ratios and Mechanical Advantage
Gear ratios are among the most frequently tested ratio topics in the FAA General Knowledge exam for AMTs. The ratio is always expressed as driven gear teeth : driving gear teeth (or driven rpm to driving rpm, which is the inverse).
- Speed reduction (torque multiplication): When the driven gear is larger than the driving gear, output speed decreases and output torque increases by the same factor. A 3:1 gear ratio means the output shaft turns at one-third the input speed but with three times the torque.
- Speed increase (torque reduction): When the driven gear is smaller, output speed increases and torque decreases proportionally. A 1:3 ratio triples output speed but reduces torque to one-third.
- Idler gears: An idler gear inserted between driver and driven gear changes rotation direction but does NOT change the overall gear ratio between the first and last gear in the train.
For belt- and chain-driven systems, the same ratio logic applies but uses pulley or sprocket diameters (or circumferences) rather than tooth counts. Larger driving pulley relative to the driven pulley increases output speed; smaller driving pulley reduces it.
Compression Ratio
The compression ratio of a reciprocating aircraft engine compares the total cylinder volume at bottom dead center (BDC) to the clearance volume at top dead center (TDC). It is written as total volume : clearance volume. For example, if total cylinder volume is 96 cubic inches and clearance volume is 12 cubic inches, the compression ratio is 96:12, simplified to 8:1. This value directly influences the fuel grade required and the power output potential of the engine, so precise measurement and correct ratio calculation are maintenance-critical tasks during overhaul inspections.
Mixture Ratios for Fluids and Compounds
Many aviation maintenance materials—battery electrolytes, corrosion inhibitors, cleaning solutions, hydraulic fluid concentrates, and certain adhesives—must be mixed at precise ratios specified in the manufacturer's instructions or the aircraft maintenance manual (AMM). Getting these wrong can cause immediate or latent damage.
- Parts-based mixing: A ratio of 1:4 (concentrate to water) means for every 1 unit of concentrate you add 4 units of water, yielding 5 total units of solution. Always add concentrate to water (or as directed), not the reverse, to prevent violent reactions with some chemicals.
- Percentage concentration: Some specs express concentration as a percentage by volume or by weight. A 20% solution means 20 parts solute per 100 parts total solution, which is equivalent to a 20:80 (or 1:4) ratio of solute to solvent.
- Scaling up: If you need 10 gallons of a 1:4 mixture, use a proportion. 1/5 = X/10, so X = 2 gallons concentrate and 8 gallons water. Proportional scaling ensures the ratio is maintained regardless of batch size.
Torque and Force Proportions
When a torque wrench extension or adapter changes the effective wrench length, the indicated torque reading is no longer equal to the torque applied at the fastener. The relationship between indicated and actual torque is proportional to the ratio of effective lengths. The AMM and FAA handbook formulae for this correction are ratio-based: actual torque at the fastener equals the desired torque multiplied by the ratio of the wrench length to the extended wrench length. Technicians must calculate this proportion every time an extension is used so that critical fasteners receive exactly the torque the engineer specified—not more, not less.
Scale Drawings and Blueprint Reading
Aircraft structural drawings routinely use scale ratios such as 1:20 or 1:50. A scale of 1:20 means every 1 inch on the drawing represents 20 inches on the actual aircraft. To find a real dimension from a drawing measurement, set up a proportion: (drawing measurement) / 1 = (actual dimension) / 20. If a rib spacing measures 0.75 inch on a 1:20 drawing, the actual spacing is 0.75 × 20 = 15 inches. Misreading or ignoring the scale ratio can result in parts fabricated to the wrong dimension—a costly or even catastrophic error on structural repairs.
Key Numbers and Rules
- Cross-multiplication: if a/b = c/d, then a × d = b × c. Isolate the unknown by dividing both sides.
- Gear ratio = driven teeth ÷ driving teeth. Higher ratio = more torque, less speed at output.
- Compression ratio = total cylinder volume ÷ clearance volume.
- Mixture ratio parts must be in the same unit (volume or weight as specified). Always confirm which unit the spec uses.
- A proportion requires three known values to solve for the fourth—identify what is given before writing the equation.
- Simplify all ratios to lowest whole-number terms for readability and to catch arithmetic errors early.
Common Test Traps
- Confusing driver and driven gear: The FAA exam often presents gear problems where students must identify which gear is the driver and which is driven. The ratio is always expressed as driven:driving; reversing the two gives a reciprocal answer that may appear plausible but is wrong.
- Forgetting to include all parts in a mixture: A 1:4 ratio is 5 total parts, not 4. If a question asks how much of each component is needed for a specific total volume, divide the total by 5 (or whatever the sum of parts is), not by 4.
- Unit mismatch in proportions: Both ratios in a proportion must use consistent units on each side. Mixing inches with feet, or psi with bar, gives a wrong answer even if the algebra is perfect.
- Idler gear trap: Adding an idler gear between driver and driven gears changes rotation direction but leaves the overall speed ratio unchanged. Exam distractors often imply the ratio changes.
- Scale drawing arithmetic direction: Students sometimes divide instead of multiply (or vice versa) when converting drawing measurements to real dimensions. Always ask: is the actual part bigger or smaller than the drawing? The answer tells you which direction to scale.
Mastering ratio and proportion gives an AMT a reliable mental framework for dozens of everyday tasks—and a solid foundation for the more advanced mathematics (such as area, volume, and weight-and-balance calculations) that build on these same principles. Practice setting up the proportion first, labeling every value with its units, and solving methodically. That habit will serve you accurately and safely throughout your maintenance career.