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newSchoolWorks.com › VoTechWorks › Transportation › Diesel & Heavy Truck › Universal Core: Safety, Math, Communication & Career for Diesel & Heavy Truck › Lesson 4
TRN-DIES20-01 · Lesson 4 · 18 clock hours · theory

Trade Math II: Formulas, Ratios & Basic Electrical/Hydraulic Calculations

Objective. Students will apply Ohm's Law (V=IR, P=IV) and basic hydraulic pressure–force–area relationships to solve shop-realistic problems, and correctly interpret gear ratio, compression ratio, and displacement calculations found in diesel service documentation.

⚠ Pending professional review

This lesson, its worked examples and its practice questions has not yet been verified by a certified examiner or master technician in the trade or by a certification or approval body. It is a study draft and may contain errors. Do not use it as instructions for work on a job site or on live equipment. Always follow your instructor, your supervising professional, and current official references and regulations.

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Trade Math II: Formulas, Ratios & Basic Electrical/Hydraulic Calculations

Diesel technicians work with numbers every day—reading wiring schematics, sizing hydraulic circuits, and verifying engine specifications. Mastering a handful of formulas lets you diagnose problems faster, order correct parts, and catch specification errors before they become expensive failures.

Ohm's Law and Power in Diesel Electrical Systems

Three variables describe any simple DC circuit: voltage (V, volts), current (I, amperes), and resistance (R, ohms). Ohm's Law ties them together:

V = I × R

Rearrange to solve for any one variable:

Power (P, watts) measures how much work a circuit does per second:

P = I × V

Alternately, P = I² × R or P = V² ÷ R when only two of the three variables are known.

In a diesel truck, the 12-volt or 24-volt system powers everything from the starter motor to the ECM. A fully charged 12 V battery bank that shows only 10.5 V under load has excessive internal resistance or a bad cell—Ohm's Law explains exactly why voltage drops when current demand rises. Starter motors draw hundreds of amperes; a marginal cable connection adds resistance, drops voltage at the starter, and causes hard-start complaints that look like a weak battery.

Safety note: High-current battery circuits can deliver enough energy to vaporize tools and cause severe arc burns. Before working on battery cables or starter circuits, follow lockout/tagout (LOTO) procedures per your shop's written program. Wear safety glasses and insulated gloves rated for the voltage level. Never lay metal tools across battery terminals.

Hydraulic Pressure, Force, and Area

Shop presses, lift cylinders, and brake boosters all rely on Pascal's principle: pressure applied to a confined fluid transmits equally in all directions. The working formula is:

P = F ÷ A

Where:

To find cylinder bore area, use the circle area formula:

A = π × r² (r = radius = bore diameter ÷ 2)

Unit conversions you will need: 1 bar ≈ 14.504 PSI; 1 square inch = 6.452 square centimeters.

When operating a shop press, never exceed the rated capacity shown on the press's data plate. Exceeding rated pressure can fracture fittings or burst hoses, sending fluid or metal fragments at high velocity. Wear a face shield (not just safety glasses) when operating any hydraulic press. Keep bystanders clear of the work envelope. Inspect hoses and fittings for cracks or chafing before every use.

Gear Ratio and Final Drive

A gear ratio compares the rotational speed of the driving gear to the driven gear:

Gear Ratio = Number of teeth on driven gear ÷ Number of teeth on driving gear

A ratio of 4:1 means the output shaft turns once for every four turns of the input shaft, multiplying torque by four (before friction losses). In a drivetrain, the overall final drive ratio is the product of the transmission ratio in a selected gear multiplied by the rear axle ratio:

Overall Ratio = Transmission Ratio × Axle Ratio

Transmission and axle specification sheets list these values; always verify against the manufacturer's published data rather than relying on memory.

Engine Displacement

Displacement is the total volume swept by all pistons moving from bottom dead center (BDC) to top dead center (TDC):

Displacement = (π ÷ 4) × Bore² × Stroke × Number of cylinders

Result is in cubic inches if bore and stroke are in inches, or in cubic centimeters if bore and stroke are in millimeters. Divide cubic centimeters by 1,000 to convert to liters; divide cubic inches by 61.024 to convert to liters.

Compression Ratio

Compression ratio compares the total cylinder volume at BDC to the clearance volume at TDC:

Compression Ratio = (Displacement Volume + Clearance Volume) ÷ Clearance Volume

Diesel engines typically run very high compression ratios to achieve the heat needed for autoignition. Published engine spec sheets list this value; calculating it from bore, stroke, and head data lets you verify whether a rebuilt engine meets factory specs.

Putting It Together

Every formula in this lesson follows the same discipline: write the formula, identify your known values with units, substitute, calculate, and label your answer with the correct unit. If your unit does not match what the problem asked for, convert before recording the answer. Showing full work is not just a grading requirement—it is a professional habit that lets a co-worker or service manager verify your reasoning and catch errors before a repair goes wrong.

Key terms8

Ohm's LawThe relationship V = I × R, stating that voltage across a conductor equals current through it multiplied by its resistance.
Ampere (A)The SI unit of electrical current; the rate at which electric charge flows through a circuit.
Pascal's PrincipleThe principle that pressure applied to an enclosed fluid is transmitted equally and undiminished in all directions throughout the fluid.
PSI (pounds per square inch)A US customary unit of pressure; the force in pounds applied over one square inch of area.
Gear RatioThe ratio of the number of teeth on the driven gear to the number of teeth on the driving gear; indicates the mechanical advantage or speed change provided.
DisplacementThe total swept volume of all engine cylinders as pistons travel from bottom dead center to top dead center; expressed in liters or cubic inches.
Compression RatioThe ratio of the total cylinder volume at BDC to the clearance volume at TDC; determines how much the air–fuel mixture (or air alone in a diesel) is compressed.
Power (Watts)The rate of electrical energy transfer, calculated as P = I × V; the product of current in amperes and voltage in volts.

Worked examples4

1. A diesel starter circuit operates on a 12 V system. The starter motor has an internal resistance of 0.04 ohms. What current does the starter draw, and what is the power consumed?
  1. Write Ohm's Law and identify knowns: V = 12 V, R = 0.04 Ω, solve for I.
  2. I = V ÷ R = 12 ÷ 0.04 = 300 A
  3. Write power formula: P = I × V
  4. P = 300 A × 12 V = 3,600 W (3.6 kW)
Answer: The starter draws 300 amperes and consumes 3,600 watts (3.6 kW).
2. A shop hydraulic press has a ram cylinder with a bore diameter of 4 inches. A technician needs to apply 8,000 pounds of force to a bearing. What hydraulic pressure (in PSI) is required?
  1. Find the radius: r = 4 ÷ 2 = 2 inches
  2. Calculate cylinder area: A = π × r² = 3.1416 × (2)² = 3.1416 × 4 = 12.566 square inches
  3. Apply P = F ÷ A: P = 8,000 lbf ÷ 12.566 in² = 636.6 PSI
  4. Convert to bar for reference: 636.6 PSI ÷ 14.504 = 43.9 bar
Answer: Approximately 637 PSI (43.9 bar) of hydraulic pressure is required.
3. A 6-cylinder diesel engine has a bore of 4.02 inches and a stroke of 4.72 inches. Calculate the engine displacement in cubic inches and in liters.
  1. Write displacement formula: D = (π ÷ 4) × Bore² × Stroke × Number of cylinders
  2. Calculate bore squared: 4.02² = 16.1604 in²
  3. Multiply: (π ÷ 4) × 16.1604 = 0.7854 × 16.1604 = 12.691 in² (area of one bore)
  4. Multiply by stroke: 12.691 × 4.72 = 59.902 in³ per cylinder
  5. Multiply by 6 cylinders: 59.902 × 6 = 359.4 cubic inches
  6. Convert to liters: 359.4 ÷ 61.024 = 5.89 liters
Answer: Engine displacement is approximately 359 cubic inches (5.9 liters).
4. A manual transmission has a first-gear ratio of 6.29:1. The rear axle ratio is 3.73:1. What is the overall final drive ratio in first gear?
  1. Write the formula: Overall Ratio = Transmission Ratio × Axle Ratio
  2. Substitute: Overall Ratio = 6.29 × 3.73
  3. Calculate: 6.29 × 3.73 = 23.46
Answer: The overall final drive ratio in first gear is approximately 23.46:1.

The math in this lesson3

Learners multiply a 6.29:1 gear ratio by a 3.73:1 axle ratio for overall reduction.
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Brush up in the math halls at newSchoolWorks.com:
In class: Ohm's Law problem set: students solve 15 problems drawn from diesel electrical system scenarios (battery voltage drop, starter draw, circuit resistance), showing full work and circling the variable solved—peer-graded, then instructor-reviewed for misconceptions. · Hydraulic lift scenario: given a shop press with a known cylinder bore and desired force, students calculate required hydraulic pressure using P = F/A, convert to PSI and bar, then verify their answer by checking the press's rated capacity plate. · Gear ratio and displacement worksheet: using a sample transmission specification sheet and engine displacement formula (bore, stroke, number of cylinders), students calculate final drive ratio, engine displacement in liters and cubic inches, and compression ratio—results checked against manufacturer published values.
Materials: Student math workbook (Ohm's Law and hydraulic sections); scientific calculator; sample diesel wiring schematic (Cummins or PACCAR); shop hydraulic press with rating plate; sample automatic and manual transmission specification sheets; diesel engine displacement data sheet.
Check: Combined Ohm's Law and hydraulic/ratio problem set: 90% or better on 20 problems; each student must show formula setup, substitution, and correct unit labeling—partial credit not awarded for answers without correct units.

Practice check8

Answer each question, then check it. Nothing is recorded; this is your own practice.

Electrical/Electronic Systems
1. A 24-volt truck electrical system powers an auxiliary circuit with a resistance of 6 ohms. Using Ohm's Law, what is the current flowing through that circuit?
Electrical/Electronic Systems
2. A technician measures only 9 volts at a starter motor while the battery reads 12.5 volts at rest. Which conclusion is best supported by Ohm's Law?
Hydraulics
3. A hydraulic cylinder has a piston area of 10 square inches. A hydraulic pressure of 1,500 PSI is applied. What force does the cylinder exert?
Hydraulics
4. A shop press ram has a 3-inch diameter bore. What is the piston area used in a pressure–force–area calculation?
Engine Performance
5. An engine specification sheet lists a compression ratio of 17.3:1. What does this value mean?
Drive Train
6. A drivetrain has a transmission top-gear ratio of 0.73:1 and a rear axle ratio of 3.55:1. What is the overall final drive ratio in top gear?
Electrical/Electronic Systems
7. Which safety measure is most critical before testing resistance in a high-current starter circuit?
Engine Performance
8. A 6-cylinder diesel engine has a bore of 4.50 inches and a stroke of 5.00 inches. Which calculation correctly sets up the total engine displacement in cubic inches?
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