031 ATPL subject guide
Mass and Balance
Mass and Balance is compact compared with the biggest ATPL subjects, but it can still cost marks if your calculation method is untidy.
- Subject code
- 031
- Difficulty
- Medium
- Key topics
- 3
Worked example questions
Independently authored revision questions in the same multiple-choice format as the exam. Try each one before opening the answer.
Worked example: shifting the CG between two holds
Not quite. The correct answer is A.
Correct answer: A
- A. Correct: the shift is (800 x 10) / 40000 = 8000 / 40000 = 0.2 m, and since the mass moved aft the CG moves aft too, giving 8.00 + 0.2 = 8.20 m.
- B. This applies the correct 0.2 m shift in the wrong direction. Mass moved aft always moves the CG aft, never forward.
- C. This misplaces a decimal point, treating the shift as 0.02 m instead of 0.2 m, and adds that instead.
- D. This mistakes the raw distance moved between the two arms (10 m) for the new CG itself, ignoring the existing 8.00 m CG entirely and confusing the distance the mass travelled with the much smaller CG shift that distance actually produces.
Step by step
- Find the distance moved: 14 m minus 4 m is 10 m.
- Find the moment change: 800 kg x 10 m = 8000 kg.m.
- Divide by the total aircraft mass to get the shift: 8000 / 40000 = 0.2 m.
- Apply the direction: the mass moved aft, so the CG moves aft too, giving 8.00 + 0.2 = 8.20 m.
- Sanity check: 800 kg is 2 per cent of the 40000 kg total, so a 0.2 m shift on an 8.00 m CG is the right order of magnitude, not an implausible jump.
Worked example: picking the true limit from three candidates
Not quite. The correct answer is C.
Correct answer: C
- A. This quotes the structural figure alone and treats it as the answer because it was the first number in the stem, without ever working out the other two candidate masses.
- B. Built from 64000 + 11000, this is a real candidate mass, but a candidate is not the answer until it has been compared against the other two, and here it is not the smallest.
- C. Correct: 61000 + 8000 = 69000 kg. Set beside 72000 kg and 75000 kg, this landing-mass-based figure is the smallest of the three, so it becomes the binding limit.
- D. This quotes the landing mass limit with no fuel added back for the trip that has to be flown and burned before that landing mass is reached.
Step by step
- Write down the structural ceiling as given: 72000 kg.
- Build the zero-fuel-mass candidate: 64000 kg + 11000 kg take-off fuel = 75000 kg.
- Build the landing-mass candidate: 61000 kg + 8000 kg trip fuel = 69000 kg.
- Compare all three candidates (72000, 75000, 69000) and keep the smallest: 69000 kg is the maximum allowed take-off mass.
- Sanity check: working back from 69000 kg, the zero fuel mass is 69000 - 11000 = 58000 kg, well inside the 64000 kg limit, while the landing mass is 69000 - 8000 = 61000 kg, sitting exactly on its limit, confirming the landing mass is what actually bites.
What this subject asks of you
Clean, repeatable working matters more than speed alone.
What the paper tests
Calculation-focused with repeated patternsWhy it matters
The exam expects you to convert loading information into safe centre-of-gravity decisions, not just plug numbers into formulas without understanding what they mean operationally.Best next step
Use timed practice and spaced recall together so weak areas come back before they decay.
Compare ATPL subject difficulty
Compare ATPL subject difficulty
Key topics
Centre-of-gravity calculations and movement
Load and trim sheet interpretation
Payload, fuel, and envelope limitation trade-offs
How to study it
- Use one standard calculation layout for every practice question so you reduce arithmetic mistakes.
- Practise reading diagrams and envelopes, not just doing the arithmetic.
- Review unit conversions and sign direction carefully when mass shifts forward or aft.
Where Mass and Balance candidates lose marks
Common traps
- Rushing arithmetic because the formulas look simple.
- Ignoring the operational meaning of moving CG forward or aft.
- Losing marks on unit conversions or moment indexing conventions.
The hardest Mass and Balance exam areas
Where candidates actually lose marks in 031, and why.
Picking the limiting take-off mass from three independent limits
Structural, zero-fuel-mass and landing-mass limits are worked out by three unrelated routes, and the exam rewards checking all three every time. Most dropped marks come from stopping at the first plausible figure instead of running the full set and taking the lowest.CG-shift arithmetic under time pressure
The moved-mass formula is short, but a stem often chains a repositioning onto an already-computed CG, so a sign error on the direction of the shift, or reading the mass from the wrong compartment, quietly corrupts an otherwise correct calculation.Telling area load and running load apart in cargo questions
Both checks use the same starting numbers, a mass and one or two compartment dimensions, so it is easy to divide by the wrong one, and the resulting figure still looks like a believable answer even when it checks the wrong limit.
Frequently asked questions
Is ATPL Mass and Balance mostly maths?
Is ATPL Mass and Balance mostly maths?
How do I improve my score in Mass and Balance?
How do I improve my score in Mass and Balance?
Mass and Balance topic deep dives
Mass and Balance topic deep dives
Focused guides to the 031 topics students search for most, each with a fully worked example and the common mistakes.
Topic guide
Centre of Gravity Calculations
Learn how to calculate aircraft centre of gravity for the ATPL exam: moments about a datum, the CG-shift formula, and a fully worked example.
Read the guideTopic guide
CG as Percent MAC
Understand ATPL centre of gravity as a percentage of MAC: the formula, converting an arm to a percentage and back again, and a fully worked example.
Read the guideTopic guide
Floor Loading: Running and Area Load Limits
ATPL floor loading explained: the difference between area load and running load in cargo compartments, how load spreaders help, and a worked pallet check.
Read the guideTopic guide
Operating Masses and Traffic Load
The ATPL mass ladder explained: basic empty mass, dry operating mass, zero fuel mass and take-off mass, plus a worked lowest-of-three take-off mass check.
Read the guideFree tools for this subject
Free tools for this subject
Practise what Mass and Balance tests, free and without an account.
Free tool
Aviation Unit Converter
Drill the conversions Mass and Balance hides inside its numbers: litres and gallons to kilograms through a fuel density, and kilograms to pounds.
Open the toolQuestion bank
Practice Mass and Balance questions
Exam-style 031 Mass and Balance questions with explanations, spaced repetition, and timed mock exams. Free to start.
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