How Do You Calculate Weight and Balance? A Step-by-Step Pilot’s Guide

To calculate weight and balance, you multiply each item’s weight by its arm (the distance from the reference datum) to get a moment, add up all the weights and all the moments, then divide total moment by total weight to find the center of gravity. Finally, you confirm both the total weight and the CG fall inside the limits published in your aircraft’s POH. That’s the whole formula in one breath. Every step after this is just learning where to find each number and how to keep it organized so you never make an arithmetic mistake that matters at 500 feet.

If you’ve ever stared at a loading graph and felt your stomach drop, stick with me. We’re going to walk it from the reference datum to the final CG, the same way I teach it on the ramp before a student ever touches the yoke.

What is weight and balance and why does it matter?

Weight and balance is the calculation that confirms your airplane is loaded both light enough and balanced correctly before you fly. It answers two questions: is the airplane under its maximum allowable weight, and does the center of gravity — the point the airplane balances around — fall within the forward and aft limits the manufacturer flight-tested? Per the FAA Weight and Balance Handbook (FAA-H-8083-1B), getting both right is a condition of safe, legal flight, and 14 CFR § 91.9 requires you to operate within the limitations in the approved flight manual.

Here’s why it’s not optional paperwork. Too much weight means the wing has to work harder to fly, so your takeoff roll lengthens, your climb flattens, your stall speed rises, and your service ceiling drops. Every performance number in the back of the POH assumes you’re at or below gross weight — go over it and those numbers are fiction.

Balance is the subtler, more dangerous half. Where the weight sits — forward or aft of the CG limits — changes how the airplane handles, how it stalls, and how it recovers. An overweight airplane is sluggish; an out-of-balance airplane can be uncontrollable. That’s why we run both numbers, every flight, before we ever start the engine.

What are the key terms — datum, arm, moment, and CG?

You only need four words to do this whole calculation, so let’s define them cleanly. The datum is an imaginary vertical reference line the manufacturer picks (often the firewall or nose). The arm is the horizontal distance in inches from that datum to an item. The moment is weight multiplied by arm — a measure of the turning effect that weight has around the datum. The center of gravity (CG) is the point where the whole airplane balances, found by dividing total moment by total weight. These definitions come straight from FAA-H-8083-1B.

Think of a seesaw. The datum is one end of the board, and the pivot is the CG. A small child far out on the board can balance a heavier adult sitting close to the pivot — because what matters isn’t just weight, it’s weight times how far out it sits. That “weight times distance” is exactly what a moment is.

So when you load the airplane, two pilots up front, bags in the back, and fuel in the wings, each item sits at its own arm and creates its own moment. Add up every weight and every moment, divide moment by weight, and you’ve located the balance point of the loaded airplane. The arms for your specific model are listed in the POH — you don’t measure them yourself.

How do you calculate weight and balance step by step?

This is the heart of it, and it’s the same five steps every single time. First, list every weight: empty weight, pilot and passengers, baggage, and fuel. Second, find each item’s arm from the POH. Third, multiply weight × arm to get each moment. Fourth, total the weights and total the moments. Fifth, divide total moment by total weight to get the CG, then check both totals against the POH limits. Do it in a table and arithmetic mistakes have nowhere to hide.

Let’s work a realistic Cessna 172-style example so you can see the columns fill in. (Use your own airplane’s numbers in real life — these are illustrative.)

Now divide: 104,880 ÷ 2,460 = 42.6 inches aft of datum. If this airplane’s maximum gross weight is 2,550 lb and its CG envelope runs from roughly 35 to 47.3 inches, you’re under gross and your CG sits comfortably inside the range. You’re legal and you’re safe — and you proved it with five lines of fourth-grade math.

A few cautions. Fuel weighs about 6 pounds per gallon (avgas), so 40 gallons is 240 pounds — never estimate fuel by “tanks look full.” Weigh your baggage, don’t guess. And always start from your airplane’s empty weight and empty-weight CG, which live on the equipment list in the POH and change whenever the airplane is modified.

How do you read a weight and balance graph or table?

Most POHs give you two tools so you don’t have to compute every arm by hand. The loading graph lets you read each item’s moment directly: find the item’s weight on the vertical axis, slide across to the line for that station (front seats, baggage, fuel), and read the moment off the bottom. The CG envelope (or moment envelope) is a second graph where you plot your total weight against your total moment — if the dot lands inside the printed envelope, you’re within limits. This is the diagram PLT092 asks you to interpret.

The loading graph saves you arithmetic. Instead of multiplying weight by arm yourself, each diagonal line already bakes in that station’s arm, so you just read the moment straight off. Tally those moments, add them to the empty-weight moment, and you have your total moment without a calculator.

Then comes the gut-check: the envelope. Plot total weight on one axis and total moment (often shown in thousands, “moment/1000,” to keep the numbers small) on the other. If your point sits inside the shaded box, both your weight and your CG are legal. If it falls outside — too high, too far left, or too far right — you must rearrange the load, shed weight, or burn fuel before you go. The envelope turns a column of numbers into a single yes-or-no you can see.

What happens if the center of gravity is out of limits?

An out-of-limits CG changes how the airplane flies, and the two directions fail in different ways. A forward CG (too nose-heavy) makes the airplane more stable but heavier on the controls — it needs more elevator to flare, raises stall speed, lengthens the takeoff, and can make landing difficult. An aft CG (too tail-heavy) is the dangerous one: it reduces stability, lightens the controls dangerously, and can make recovery from a stall or spin difficult or impossible. This is core PHAK and Weight and Balance Handbook material (FAA-H-8083-1B).

Picture the forward case first. With the CG too far forward, the tail has to push down harder to hold the nose up, which is extra drag and extra control force. You’ll find the airplane reluctant to flare, the nosewheel slamming down, and stall speeds creeping up because the wing is carrying more load. It’s uncomfortable and it eats performance — but the airplane still wants to fly right-side up.

The aft case is the one that hurts people. As the CG moves rearward, the airplane gets twitchy and the natural nose-down tendency that helps you recover from a stall weakens. Too far aft and the airplane may not recover from a stall at all. That’s why, when in doubt, we load slightly forward and treat the aft limit with real respect — it’s the line that bites.

Why do you have to check both takeoff and landing weight?

Because the airplane you take off in is not the airplane you land in. As you burn fuel, you lose weight, and since fuel sits at its own arm, the CG shifts during the flight. A loading that’s perfectly legal at takeoff can drift toward — or past — a CG limit by the time you land, so you must verify the airplane stays inside the envelope for the whole flight, not just the start. The POH expects both a takeoff and a landing (or zero-fuel) computation.

Run the math twice. Compute your CG at full takeoff weight, then recompute it with the fuel you’ll have burned subtracted out. Plot both points on the envelope. If both dots land inside the box, you’re good for the whole trip. If the landing point sneaks outside, you have a problem you’d never catch by checking takeoff alone.

This is exactly where students who want a real, examiner-proof handle on the numbers get a leg up — we drill loading scenarios, fuel-burn shifts, and reading the envelope cold inside the Angle of Attack Private Pilot Ground School, so the checkride W&B problem feels like review, not a pop quiz.

A loaded-airplane lesson from an Alaska gravel bar

I learned to take the aft limit seriously on a backcountry day in Alaska that looked routine on the worksheet. We were loading my 172 to fly out to a gravel bar — two of us up front, a buddy in the back, and a pile of gear we’d been collecting all morning. On paper the total weight was fine. We were under gross. The trap was where the weight wanted to go.

All that gear naturally drifted toward the baggage area, behind the rear seats. And baggage way back there sits at a long arm — every pound back there swings the moment hard and walks the CG aft fast. When I actually ran the numbers instead of eyeballing it, our CG was pressing right up against the rear edge of the envelope. Legal weight, marginal balance.

So we did the unglamorous thing: we pulled the heaviest bags out of the back and tucked them lower and more forward, redistributed the gear, and re-ran the math until the dot sat comfortably inside the box. Took fifteen minutes. The flight out was a non-event, which is exactly what you want — boring is the goal.

The lesson I drill from that day is simple: total weight is only half the question. You can be a hundred pounds under gross and still be loaded into a corner of the envelope where the airplane doesn’t want to recover cleanly. Run the balance, not just the weight, and respect the aft limit like it can bite — because it can.

How is weight and balance tested on the checkride?

Weight and balance shows up in both the knowledge test and the practical, so expect it twice. On the Private Pilot checkride, the Airman Certification Standards (ACS) require you to compute the airplane’s weight and balance for the planned flight, determine whether it’s within limits, and explain how an out-of-limits CG affects performance and controllability. The examiner will hand you a loading scenario and watch you work it. This maps directly to the PLT codes the FAA tags on the written.

In the oral, be ready to define datum, arm, moment, and CG in your own words, and to explain why an aft CG is more hazardous than a forward one. You’ll likely get a “what if” — what happens to your CG as you burn fuel, or what you’d do if a passenger swap pushes you out the back of the envelope. The examiner wants to see that you understand the airplane, not just the arithmetic.

For the practical computation, you’ll typically work a real problem from the POH: load the airplane on paper, find the CG, and confirm it’s legal for both takeoff and landing. Show your work in a clean table, state your limits out loud, and give a clear go/no-go. If you want every one of these reps before exam day — done the way examiners expect — start free with the Total Student Pilot course, the on-ramp we built for brand-new students.

PLT Study Guide

The FAA tags knowledge-test questions with PLT (learning statement) codes. The codes that actually map to weight and balance are below, with the FAA’s own wording translated into plain study points. (Note: the load-factor codes sometimes lumped in here — PLT309/310/311/312 — are about load factor in maneuvers, not weight and balance, so don’t study them for this topic.)

Plain-English study points:

• PLT021 (calculate weight and balance): Memorize the formula chain. Weight times arm equals moment. Total moment divided by total weight equals CG. Then two checks: under max gross, and CG inside the envelope.
• PLT003 (center of gravity): Know that adding weight aft moves the CG aft, adding weight forward moves it forward, and burning fuel shifts it according to where the tanks sit relative to the current CG.
• PLT092 (W&B diagram): Be able to read a loading graph (weight in, moment out) and plot total weight vs. total moment on the envelope to get a clean yes/no.
• PLT313 (loading terminology): Lock in the definitions — datum, arm, moment, CG, max gross, forward/aft limits — because the written loves a vocabulary question.
• PLT121 (loading computations): Practice the “now move 50 lb from the back seat to the baggage area — what’s the new CG?” style problem until it’s automatic.
• PLT328 (performance planning / loading): Connect weight to performance: more weight means longer takeoff, weaker climb, higher stall speed, lower ceiling.

Frequently Asked Questions

FROM CHRIS

Weight and balance isn’t the part of flight planning that gets your heart racing, but it’s the one that quietly decides whether the airplane does what the charts promise. Learn the four words — datum, arm, moment, CG — run the five steps in a clean table, and check both weight and balance for takeoff and landing. Do that every flight and it becomes a thirty-second habit that keeps the numbers honest and the airplane flying the way it was built to.

Throttle On!

Chris Palmer

Founder & Chief CFI, Angle of Attack — Two-Time Master Aviation Educator and Gold Seal CFI