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newSchoolWorks.com › VoTechWorks › Transportation › Commercial Driving (CDL) › Universal Core: Safety, Math, Communication & Career for Commercial Drivers › Lesson 3
TRN-CDL23-01 · Lesson 3 · 24 clock hours · theory

Trade Math for Commercial Drivers: Weights, Measures, Fuel, and Time

Objective. Students will solve CDL-relevant math problems—including gross vehicle weight rating (GVWR) calculations, axle weight distribution, fuel consumption and cost, unit conversion between US customary and metric, and hours-of-service time math—with at least 80% accuracy on a timed test.

⚠ 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.

VoTechWorks program approval and accreditation are still in progress. Credentials are issued only by the certifying bodies named in each program, after their own exams.

Why Math Matters Behind the Wheel

Commercial driving is not just a physical skill—it is an applied math job. Every trip requires you to verify that the load is legal, that you have enough fuel, and that you are within your hours-of-service (HOS) limits before you turn the key. An overweight truck can destroy a bridge, void your insurance, and cost your employer thousands in fines. Running out of hours midway through a delivery puts your CDL at risk. Mastering trade math is a safety and compliance requirement, not just a test hurdle.

Gross Vehicle Weight Rating and Payload

The Gross Vehicle Weight Rating (GVWR) is the maximum allowable total weight of a vehicle as set by the manufacturer—the truck itself plus everything in or on it. It is stamped on the vehicle's certification label.

Payload capacity is the weight you are actually allowed to carry:

> Payload = GVWR − Curb Weight

The curb weight is the weight of the truck with all fluids but no cargo or driver. If a truck has a GVWR of 80,000 lb and a curb weight of 32,000 lb, the legal payload is 48,000 lb. Add the driver, fuel load, and all cargo—if the total exceeds GVWR, the load is illegal before it reaches the scale.

For combination vehicles, the federal maximum gross vehicle weight on the Interstate System is 80,000 lb unless a state issues an oversize/overweight permit. Always check the spec sheet and the manifest together.

Axle Weight Distribution

Even if the total weight is within GVWR, each individual axle group has its own legal limit. Typical federal limits are:

The bridge formula (published by FHWA) limits the weight that any group of axles may carry based on the distance between the outermost axles in that group. The intent is to protect bridge structures from concentrated loads. You do not need to memorize the formula equation for the CDL knowledge test, but you must understand that sliding the tandems forward or backward shifts weight between axles—moving the rear trailer tandems toward the rear axle increases weight on the drives and reduces weight on the tandems, and vice versa.

Always check each axle group separately, not just the gross total.

Fuel Consumption and Cost Math

Two essential fuel calculations appear regularly on manifests, trip plans, and CDL practice tests.

Miles per gallon (MPG):

> MPG = Miles Driven ÷ Gallons Used

Cost per mile:

> Cost per mile = Total Fuel Cost ÷ Miles Driven

Diesel Exhaust Fluid (DEF) is required by most modern diesel engines equipped with Selective Catalytic Reduction (SCR) emissions systems. DEF consumption is roughly proportional to fuel use—consult the vehicle's operator manual for the specific ratio, as it varies by engine. Running out of DEF will put the engine into reduced-power mode, which is a safety and scheduling hazard. Always check the DEF tank on the pre-trip inspection.

Unit Conversion: US Customary and Metric

International cargo, Canadian border crossings, and some federal documents use metric units. Key conversions to know:

To convert pounds to kilograms, divide by 2.205. To convert kilograms to pounds, multiply by 2.205. Rounding to three significant figures is standard for commercial work.

Hours-of-Service Time Math

FMCSA HOS rules govern how many hours a property-carrying driver may drive and be on duty. The core limits for property-carrying drivers (under the standard rules) are:

When calculating HOS on a log grid, work in 15-minute increments. Add each duty-status line across the grid, then total the columns. A common test error is forgetting to count all on-duty-not-driving time (fueling, inspections, loading) against both the 14-hour window and the 60/70-hour total.

Safety Points

Key terms9

Gross Vehicle Weight Rating (GVWR)The maximum total weight a vehicle is designed to carry, including the vehicle itself, all fluids, cargo, and occupants, as specified by the manufacturer.
Curb WeightThe weight of a vehicle with all standard fluids but no cargo, passengers, or driver.
Payload CapacityThe maximum weight of cargo (and driver) a vehicle can legally carry, calculated as GVWR minus curb weight.
Bridge FormulaAn FHWA formula that limits the weight allowed on any group of axles based on the distance between the outermost axles, designed to protect road and bridge structures.
Hours of Service (HOS)FMCSA regulations that limit the number of hours a commercial driver may drive and be on duty within defined time windows to prevent fatigue-related crashes.
34-Hour RestartA provision in FMCSA HOS rules that allows a driver to reset the weekly on-duty hour accumulation by taking at least 34 consecutive hours off duty.
Diesel Exhaust Fluid (DEF)A urea-water solution injected into the exhaust stream of SCR-equipped diesel engines to reduce nitrogen oxide emissions; running low causes reduced engine power.
Tandem Axle GroupTwo axles close together that are treated as a single unit for weight-limit purposes; the federal limit for a tandem axle group is 34,000 lb.
14-Hour On-Duty WindowThe maximum span of time from when a driver comes on duty (after 10 consecutive hours off) during which all driving must be completed, regardless of how much of that time was spent off duty.

Worked examples4

1. A tractor-trailer has a GVWR of 80,000 lb and a curb weight of 31,500 lb. The fuel load adds 1,200 lb and the driver weighs 220 lb. What is the maximum legal cargo weight?
  1. Write the formula: Payload = GVWR − Curb Weight.
  2. Payload = 80,000 − 31,500 = 48,500 lb (this is the room for everything that is not the empty truck).
  3. Subtract non-cargo items already on the truck: fuel load 1,200 lb + driver 220 lb = 1,420 lb.
  4. Maximum legal cargo = 48,500 − 1,420 = 47,080 lb.
Answer: The maximum legal cargo weight is 47,080 lb.
2. A driver travels 624 miles and uses 96 gallons of diesel at $3.85 per gallon. What is the truck's fuel economy in MPG and the fuel cost per mile?
  1. MPG = Miles ÷ Gallons = 624 ÷ 96 = 6.5 MPG.
  2. Total fuel cost = 96 gallons × $3.85 = $369.60.
  3. Cost per mile = Total Fuel Cost ÷ Miles = $369.60 ÷ 624 = $0.5923, rounded to $0.59 per mile.
Answer: Fuel economy is 6.5 MPG; fuel cost per mile is approximately $0.59.
3. A driver came on duty at 6:00 a.m. after 10 consecutive hours off. She drove 3 hours, took a 30-minute fuel stop (on-duty not driving), drove 4 more hours, and then went off duty. How many driving hours and total on-duty hours did she use, and how many driving hours remain in her 11-hour limit?
  1. Total driving time = 3 hours + 4 hours = 7 hours.
  2. Total on-duty time = 7 hours driving + 0.5 hours on-duty not driving = 7.5 hours.
  3. The 14-hour window started at 6:00 a.m.; 7.5 on-duty hours used means the window is not yet closed.
  4. Remaining driving hours = 11-hour limit − 7 hours used = 4 hours remaining.
  5. However, the 14-hour window closes at 8:00 p.m. (6:00 a.m. + 14 hours). She must complete all driving before 8:00 p.m. regardless of hours remaining.
Answer: She has used 7 driving hours and 7.5 on-duty hours; 4 driving hours remain under the 11-hour rule, but all driving must end by 8:00 p.m.
4. A shipment manifest lists cargo in metric: 4 pallets at 950 kg each and 2 pallets at 680 kg each. Convert the total cargo weight to pounds. (Use 1 kg = 2.205 lb.)
  1. Total kilograms = (4 × 950) + (2 × 680) = 3,800 + 1,360 = 5,160 kg.
  2. Convert to pounds: 5,160 kg × 2.205 lb/kg = 11,377.8 lb.
  3. Round to the nearest pound: 11,378 lb.
Answer: The total cargo weight is approximately 11,378 lb.

The math in this lesson2

Learners compute 6.5 MPG and $0.59 fuel cost per mile from 624 miles on 96 gallons.
6.RP.3A-SSE.1
Brush up in the math halls at newSchoolWorks.com:
In class: Instructor-led direct instruction and guided practice: work through a structured problem set covering (a) GVWR and payload math using example truck spec sheets, (b) axle weight limits using a simplified bridge-formula concept and sample state permit tables, and (c) fuel consumption word problems (miles per gallon, cost per mile, DEF usage), with students solving problems individually on whiteboards and comparing answers. · HOS time-math workshop: using printed blank paper log grids (the same format as the CDL knowledge-test exhibits), students calculate duty-status hours, on-duty totals, and 34-hour restart windows for five sample driver scenarios of increasing complexity, then check answers against an instructor key. · Small-group applied challenge: each group receives a load manifest listing cargo weights by pallet, a truck spec sheet with axle ratings, and a fuel receipt; groups calculate whether the load is legal, the cost per mile for the trip, and how many HOS hours the driver has remaining, then present findings to the class in a two-minute verbal summary.
Materials: Calculators, dry-erase boards and markers, printed truck spec sheets (from publicly available manufacturer literature), blank paper log grids, sample load manifests created by instructor, federal bridge formula reference card (FHWA public document), HOS summary reference card
Check: 30-item timed math quiz (45 minutes) covering all four topic areas; minimum passing score is 80% (24/30). Partial credit is awarded for correct setup with arithmetic error. Students scoring below 80% complete a targeted remediation worksheet and retest once.

Practice check8

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

Vehicle Inspection / Weight and Balance
1. A straight truck has a GVWR of 26,000 lb and a curb weight of 14,800 lb. The driver and personal items weigh 250 lb. What is the maximum cargo weight the truck can legally carry?
Hours of Service
2. Under FMCSA rules for property-carrying drivers, what is the maximum number of hours a driver may drive after 10 consecutive hours off duty?
Hours of Service
3. A driver came on duty at 7:00 a.m. She drove 5 hours, spent 1 hour on-duty not driving for a delivery, then drove 2 more hours. What is the latest time she may continue driving under the 14-hour on-duty window rule?
Fuel and Trip Planning
4. A truck travels 480 miles and uses 75 gallons of diesel. What is the fuel economy?
Vehicle Weight and Axle Limits
5. The federal tandem axle weight limit on the Interstate System is:
Unit Conversion
6. A cargo manifest lists items weighing 4,500 kg. Approximately how many pounds is this? (1 kg ≈ 2.205 lb)
Hours of Service
7. A driver has accumulated 58 on-duty hours over the past 7 days on a carrier operating under the 60-hour/7-day rule. How many on-duty hours remain before the driver must stop and take a 34-hour restart or go off duty?
Fuel and Trip Planning
8. Fuel costs $4.10 per gallon and a truck gets 6.5 MPG. What is the approximate fuel cost per mile?
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