Flight-Planning Math

You Got 1,180.
The Answer Was 1,240. Now What?

Weight and balance, density altitude, performance, fuel and time-speed-distance, wind triangles and crosswind components — graded step by step, so you find out where your work went wrong rather than just that it did.

Every solution is verified by computation before it reaches you.

Why grading matters here

A Wrong Answer on a Calculation Is Four Different Mistakes

And a multiple-choice bank cannot tell you which one you made, because it never saw your work.

A weight-and-balance problem can go wrong because you used the wrong arm, because you transposed two numbers, because you interpolated the graph badly, or because you did the whole thing correctly and then answered the question about the wrong condition. Those are four separate lessons. A bank that shows you the correct option and moves on teaches you none of them — and if the mistake was the third one, you will make it again next week and not know why.

So the calculation questions here take your work, not just your answer. You get the solution laid out step by step alongside yours, with the line where the two diverge marked. That line is the lesson.

Coverage

The Calculations, and Where They Bite

Every one of these appears on the written, and every one of them appears again on the oral when your examiner asks you to do it in front of them.

Weight and balance

Moments and arms, loading graphs, CG envelopes, shifting and adding weight, and the case that catches people out: an airplane inside limits at takeoff that walks outside them as the fuel burns off.

Density altitude and performance

Pressure altitude and temperature into density altitude, then density altitude into takeoff roll, climb rate and landing distance — with interpolation between chart lines, which is where most of the marks are actually lost.

Wind triangles and crosswind

Wind correction angle, groundspeed, heading and the crosswind and headwind components off a chart or from the trigonometry. Practiced against arbitrary winds and runways rather than the four examples in a textbook.

Fuel, time, speed and distance

Endurance and reserves, fuel to a destination and an alternate, time enroute, and the leg arithmetic that turns into a real decision the moment a headwind is worse than forecast.

Navigation math

True and magnetic course, variation and deviation, wind-corrected headings, and the dead-reckoning legs that a moving map has not made unnecessary, whatever anybody tells you before their checkride.

Transport-category and turbine work

For the airline transport and dispatcher tests: takeoff and landing performance at weight, the V-speeds and the runway analysis, and the dispatch-depth fuel planning that goes with a release.

The mechanics

How a Calculation Gets Graded

Four steps, and the third one is the one that makes the difference.

  1. You get a problem with real numbers in it

    Generated for arbitrary weights, temperatures, altitudes and winds — not one of six problems you will meet again next week and recognize on sight. The parameters move, so the method is what you end up practicing.

  2. You show your work, or just answer

    Enter the intermediate values if you want the fuller feedback, or enter only the final figure if you are drilling for speed. Both are graded; only one of them can tell you where you went wrong.

  3. It marks the line where you diverged

    Your steps sit alongside the worked solution, and the first row where the two stop agreeing is highlighted. If your moment arm was wrong, that is what you see — not a note that your final answer was 60 pounds off.

  4. The answer key was computed, not typed

    Every worked solution is verified by computation before it is ever shown, which matters more here than anywhere else on this site: a study product with an arithmetic error in a weight-and-balance answer key is actively teaching a dangerous habit.

Why we keep saying “verified by computation”: because in this subject a wrong answer key is not a typo, it is a lesson in doing something incorrectly. Values are computed from the problem’s own parameters rather than authored alongside them, so the key and the question cannot drift apart.

Reference and weather

Two Things That Live Next Door to the Math

Both are skills rather than facts, and both are graded as skills.

Finding the rule

Regulation and handbook lookup

A simulated reference browser over the regulations and the aeronautical information manual, in the same format the AccelaStudy AI Safety product uses for the occupational-safety standards. You are given a situation and asked to find the paragraph that governs it — which is what an examiner does on a practical test, and what you will do for the rest of your flying.

  • Practiced as navigation, not as memorization — nobody expects you to recite a section number
  • Every rubric point in the oral practice ties back to the passage it came from, and this is where you go to read it
  • The same skill the standards call for: know where it is, and know how to read it when you get there

Reading the weather

Reports, forecasts and charts, decoded

Observations and forecasts, pilot reports, the advisories for icing, turbulence and convective weather, prognostic and surface charts, and winds and temperatures aloft — read the way a briefing actually presents them rather than as a glossary of codes to recite.

  • Coded reports and forecasts generated with known conditions, so you can decode a hundred of them rather than the four in a chapter
  • Charts and station models read for a decision, not just translated
  • The judgment questions too: what would make you go, what would make you wait, and what would make you turn around

About the Calculations

Do I need a flight computer?
You may use one, and on the real test you may bring an approved calculator or manual flight computer — check the current testing rules, which are the testing provider’s and not ours. The practice here works either way: whether you turn a wheel, use a calculator or work it out on paper, what gets graded is the method and the numbers.
Is this the same as the practice questions?
It overlaps but it is not the same thing. A multiple-choice performance question asks you to pick a number. A graded calculation asks you to produce one and shows you the step where your work diverged. Both are in the subscription; the second is the one that fixes a recurring error.
What if my answer is right but my method was wrong?
That is exactly the case the step-by-step grading exists for, and it happens more than people expect — two errors that cancel, or an interpolation that lands close enough to look right. The comparison shows the divergence even when the final figures agree.
Does it cover the airline transport and dispatcher math?
Yes. Transport-category takeoff and landing performance, the runway analysis, and dispatch-depth fuel and release planning are part of the same graded set, at the depth those tests ask for.
Are the rounding conventions the same as the test?
We follow the conventions the FAA handbooks and charts use, and we show the intermediate values so you can see where any rounding happened. Where a chart is read to the nearest gradation, the tolerance reflects that rather than demanding a decimal nobody could extract from a graph.

Find the Line Where It Went Wrong

Graded flight-planning math with computation-verified solutions, included at $49/mo. Launching Monday, February 8, 2027.

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