Calculating Aircraft Weight and Balance

Calculating Aircraft Weight and Balance Calculator | Aviation Safety Tool :root { –primary: #004a99; –primary-dark: #003366; –success: #28a745; –danger: #dc3545; –light: #f8f9fa; –border: #dee2e6; –text: #333; –shadow: 0 4px 6px rgba(0,0,0,0.1); } body { font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, "Helvetica Neue", Arial, sans-serif; line-height: 1.6; color: var(–text); background-color: var(–light); margin: 0; padding: 0; } .container { max-width: 960px; margin: 0 auto; padding: 20px; background: #fff; box-shadow: 0 0 20px rgba(0,0,0,0.05); } header { text-align: center; padding: 40px 0 20px; border-bottom: 3px solid var(–primary); margin-bottom: 30px; } h1 { color: var(–primary); margin: 0; font-size: 2.5rem; } h2, h3 { color: var(–primary-dark); margin-top: 1.5em; } /* Calculator Styles */ .loan-calc-container { background: #fff; padding: 30px; border-radius: 8px; border: 1px solid var(–border); box-shadow: var(–shadow); margin-bottom: 50px; } .input-group { margin-bottom: 20px; } .input-row { display: flex; flex-wrap: wrap; gap: 15px; align-items: flex-end; border-bottom: 1px solid #eee; padding-bottom: 15px; margin-bottom: 15px; } .input-col { flex: 1; min-width: 150px; } label { display: block; font-weight: 600; margin-bottom: 8px; color: var(–primary-dark); } input[type="number"] { width: 100%; padding: 10px; border: 1px solid var(–border); border-radius: 4px; font-size: 16px; box-sizing: border-box; } input[type="number"]:focus { border-color: var(–primary); outline: none; box-shadow: 0 0 0 3px rgba(0,74,153,0.1); } .helper-text { font-size: 0.85rem; color: #666; margin-top: 5px; } .error-msg { color: var(–danger); font-size: 0.85rem; display: none; margin-top: 5px; } .calc-controls { display: flex; gap: 15px; margin-top: 30px; flex-wrap: wrap; } button { padding: 12px 24px; border: none; border-radius: 4px; cursor: pointer; font-weight: 600; font-size: 16px; transition: background 0.2s; } .btn-primary { background-color: var(–primary); color: white; } .btn-primary:hover { background-color: var(–primary-dark); } .btn-outline { background-color: transparent; border: 2px solid var(–border); color: #666; } .btn-outline:hover { border-color: var(–primary); color: var(–primary); } /* Results Section */ #results-area { margin-top: 40px; padding-top: 30px; border-top: 2px dashed var(–border); } .main-result-box { background: #e8f0fe; padding: 25px; border-radius: 8px; text-align: center; margin-bottom: 30px; border: 1px solid #b3d7ff; } .result-value { font-size: 2.5rem; font-weight: 700; color: var(–primary); display: block; } .result-label { font-size: 1.1rem; color: var(–primary-dark); font-weight: 600; } .status-badge { display: inline-block; padding: 5px 15px; border-radius: 20px; font-weight: bold; margin-top: 10px; color: white; } .status-safe { background-color: var(–success); } .status-unsafe { background-color: var(–danger); } .metrics-grid { display: flex; flex-wrap: wrap; gap: 20px; margin-bottom: 30px; } .metric-card { flex: 1; min-width: 200px; background: #fff; padding: 15px; border: 1px solid var(–border); border-radius: 6px; text-align: center; } .metric-val { font-size: 1.5rem; font-weight: 700; color: #333; } /* Table Styles */ .data-table-wrapper { overflow-x: auto; margin-bottom: 30px; } table { width: 100%; border-collapse: collapse; margin-bottom: 20px; } th, td { padding: 12px; text-align: right; border-bottom: 1px solid var(–border); } th:first-child, td:first-child { text-align: left; } th { background-color: #f1f3f5; color: var(–primary-dark); font-weight: 600; } /* Chart */ .chart-container { width: 100%; height: 400px; border: 1px solid var(–border); background: white; position: relative; margin-bottom: 20px; border-radius: 8px; padding: 10px; box-sizing: border-box; } canvas { width: 100%; height: 100%; } /* Article Content */ .content-section { background: white; padding: 0 10px; } .variable-table td { text-align: left; } .faq-item { margin-bottom: 20px; border-bottom: 1px solid #eee; padding-bottom: 20px; } .faq-question { font-weight: 700; color: var(–primary); display: block; margin-bottom: 10px; } .internal-links-list { list-style: none; padding: 0; display: grid; grid-template-columns: repeat(auto-fill, minmax(250px, 1fr)); gap: 15px; } .internal-links-list li a { display: block; padding: 15px; background: #f8f9fa; border: 1px solid var(–border); border-radius: 6px; text-decoration: none; color: var(–primary); font-weight: 600; transition: all 0.2s; } .internal-links-list li a:hover { background: #e8f0fe; border-color: var(–primary); } footer { text-align: center; padding: 40px 0; color: #666; font-size: 0.9rem; border-top: 1px solid var(–border); margin-top: 50px; } @media (max-width: 600px) { h1 { font-size: 1.8rem; } .metric-card { min-width: 100%; } }

Calculating Aircraft Weight and Balance

Ensure flight safety by accurately determining Center of Gravity (CG) and total weight limits.

Aircraft Configuration & Loading

Enter the limitations from your Pilot Operating Handbook (POH).

Item Description
Weight (lbs)
Arm (in)
Standard aircraft weight
Combined weight
Combined weight
Approx. 6 lbs/gal
Weight: 240 lbs
Cargo / Bags
Calculated Center of Gravity (CG)
Within Limits
Total Weight
— lbs
— under max
Total Moment
lb-in
CG Status
Inches aft of datum

Loading Manifest

Station Weight (lbs) Arm (in) Moment (lb-in)
TOTALS 0 0

Center of Gravity Envelope

Chart displays Weight vs. CG. The box represents the safe operating envelope based on input limits.

What is Calculating Aircraft Weight and Balance?

Calculating aircraft weight and balance is a fundamental flight safety process used by pilots and dispatchers to ensure an aircraft is loaded within the specific engineering limits set by the manufacturer. It involves determining two critical values: the total weight of the loaded aircraft and the location of its Center of Gravity (CG).

Every aircraft, from a small Cessna 172 to a massive Boeing 747, has a maximum certified takeoff weight and a specific range within which the aircraft must balance. If the nose is too heavy (forward CG) or the tail is too heavy (aft CG), the aircraft may become uncontrollable. This calculator helps pilots visualize where their aircraft sits within the "safe envelope" before engine start.

This process is essential for:

  • Student Pilots: Learning flight planning and safety regulations.
  • Private Pilots: Planning trips with passengers and baggage.
  • Fleet Operators: Ensuring compliance with FAA or EASA regulations.

Weight and Balance Formula and Explanation

The math behind calculating aircraft weight and balance relies on the principle of moments. In physics, a moment is the turning effect of a force around a pivot point (the datum line).

The core formula is: Weight × Arm = Moment

To find the Center of Gravity (CG) for the entire aircraft, you divide the Total Moment by the Total Weight:

CG = Total Moment ÷ Total Weight

Variable Definitions

Variable Meaning Typical Unit
Weight The mass of the object (aircraft, passenger, fuel). Lbs or Kg
Arm Horizontal distance from the reference Datum line. Inches (in)
Moment The rotational force created by the weight at that distance. lb-in
Datum An imaginary vertical plane from which all measurements are taken (often the firewall or propeller tip). N/A

Practical Examples: Safe vs. Unsafe Loading

Example 1: The Standard Family Trip (Safe)

A pilot flies a PA-28 with a spouse and two children.

  • Empty Weight: 1500 lbs @ 85.0″ arm = 127,500 moment
  • Front Occupants: 340 lbs @ 80.5″ arm = 27,370 moment
  • Rear Occupants: 150 lbs @ 118.1″ arm = 17,715 moment
  • Fuel: 300 lbs (50 gal) @ 95.0″ arm = 28,500 moment

Total Weight: 2,290 lbs
Total Moment: 201,085 lb-in
CG Calculation: 201,085 / 2,290 = 87.8 inches.
Result: Since the limit range is usually 82″ to 93″, this flight is safe and legal.

Example 2: The Tail-Heavy Cargo (Unsafe)

A pilot loads heavy equipment in the rear baggage compartment without passengers.

  • Baggage: 200 lbs @ 142.8″ arm (far aft).
  • Pilot: 170 lbs (front).
  • Fuel: Low fuel (100 lbs).

The heavy weight at the long arm (142.8″) creates a massive moment. This pushes the CG beyond the Aft Limit. If the pilot attempts takeoff, the aircraft may rotate prematurely or be impossible to recover from a stall (spin recovery becomes impossible with an aft CG).

How to Use This Weight and Balance Calculator

  1. Enter Aircraft Limits: Input the Maximum Gross Weight and the Forward/Aft CG limits found in Section 2 (Limitations) of your Pilot Operating Handbook (POH).
  2. Input Basic Empty Weight: Enter the specific empty weight and arm from your aircraft's actual weight and balance sheet (Form 337). Do not use generic manual numbers.
  3. Add Load: Enter the weights for Pilot, Passengers, and Baggage. Ensure the "Arm" matches your specific aircraft stations.
  4. Add Fuel: Enter gallons of fuel. The calculator converts this to pounds (using standard AvGas density of 6 lbs/gal).
  5. Analyze Results: Check the "Results Area." If the Safety Status is green, you are within the envelope. If red, you must reduce weight or shift cargo.

Key Factors That Affect Aircraft Loading

Several variables impact the outcome of calculating aircraft weight and balance:

1. Fuel Burn

As you fly, you burn fuel. This reduces total weight, but importantly, it changes the CG. In some aircraft, burning fuel moves the CG backward. You must calculate weight and balance for both Takeoff and Landing.

2. Temperature and Density Altitude

While density altitude doesn't change the scale weight, it affects performance. A heavy aircraft on a hot day may not generate enough lift to take off, even if it is technically under Max Gross Weight.

3. Gear Retraction

On retractable gear aircraft, the movement of the landing gear shifts the moment arm. The CG may move slightly as the gear swings up or down.

4. Zero Fuel Weight

Some larger aircraft have a "Zero Fuel Weight" limit to prevent excessive structural bending loads on the wing roots caused by heavy fuselage payloads.

5. Baggage Placement

Placing heavy items in the rear baggage area has a much greater effect on CG than placing them in the front seat due to the longer "arm" (leverage).

6. Installed Equipment

Modifications like new avionics, air conditioning, or floats change the Basic Empty Weight and arm. Always use the most current maintenance logs.

Frequently Asked Questions (FAQ)

What happens if the CG is too far forward?

A forward CG increases longitudinal stability but decreases performance. The aircraft will be heavier on the controls, have a higher stall speed, and may not have enough elevator authority to flare during landing, risking a nose-wheel strike.

What happens if the CG is too far aft?

An aft CG is dangerous. It reduces longitudinal stability, making the aircraft difficult to control. Crucially, it makes stall recovery difficult or impossible. It generally provides faster cruise speeds due to less tail downforce required.

Is standard passenger weight (170 lbs) legal?

For small Part 91 operations, you should use actual weights or asked weights plus 10 lbs. Standard weights are typically used for Part 121/135 operators with an approved program. Always aim for accuracy.

Does fuel have a constant arm?

In most small aircraft, yes. However, in swept-wing jets or aircraft with complex tank shapes, the fuel arm varies as the tank level changes. This calculator assumes a constant arm for simplicity.

How do I calculate Moment?

Multiply the Weight (lbs) by the Arm (inches). Example: 100 lbs at 50 inches = 5,000 lb-in moment.

What is the "Datum"?

The datum is the imaginary reference line (Station 0) fixed by the manufacturer. All arm measurements are taken from this point. It is often the firewall, the tip of the propeller spinner, or a point ahead of the nose.

Can I be under Max Gross Weight but still be illegal?

Yes. Even if you are light, if your load is too far back (aft of the limit) or too far forward, the aircraft is not airworthy.

Why is the calculator result red?

If the result is red, either your Total Weight exceeds Max Gross Weight, or your Center of Gravity (CG) is outside the Forward or Aft limits. You must adjust the load.

© 2023 Aviation Safety Tools. All rights reserved.
Disclaimer: This calculator is for educational purposes only. Always consult your official Pilot Operating Handbook before flight.

// Global variable for chart instance simulation var canvas = document.getElementById('cgChart'); var ctx = canvas.getContext('2d'); function updateFuelWeight() { var gals = parseFloat(document.getElementById('fuelGallons').value) || 0; var weight = gals * 6; // Standard AvGas 6lb/gal document.getElementById('fuelWeightDisplay').innerText = "Weight: " + weight.toFixed(1) + " lbs"; } function getNum(id) { var val = parseFloat(document.getElementById(id).value); return isNaN(val) ? 0 : val; } function calculateWB() { // 1. Get Inputs var maxGross = getNum('maxGrossWeight'); var fwdLimit = getNum('cgLimitFwd'); var aftLimit = getNum('cgLimitAft'); // Items var emptyWt = getNum('emptyWeight'); var emptyArm = getNum('emptyArm'); var frontWt = getNum('frontSeatWeight'); var frontArm = getNum('frontSeatArm'); var rearWt = getNum('rearSeatWeight'); var rearArm = getNum('rearSeatArm'); var fuelGals = getNum('fuelGallons'); var fuelWt = fuelGals * 6; var fuelArm = getNum('fuelArm'); var bagWt = getNum('baggageWeight'); var bagArm = getNum('baggageArm'); // 2. Calculations var items = [ { name: "Basic Empty Weight", wt: emptyWt, arm: emptyArm }, { name: "Pilot & Front Pass", wt: frontWt, arm: frontArm }, { name: "Rear Passengers", wt: rearWt, arm: rearArm }, { name: "Fuel ("+fuelGals+" gal)", wt: fuelWt, arm: fuelArm }, { name: "Baggage Area 1", wt: bagWt, arm: bagArm } ]; var totalWeight = 0; var totalMoment = 0; var tableHTML = ""; for(var i=0; i < items.length; i++) { var mom = items[i].wt * items[i].arm; totalWeight += items[i].wt; totalMoment += mom; tableHTML += ""; tableHTML += "" + items[i].name + ""; tableHTML += "" + items[i].wt.toFixed(1) + ""; tableHTML += "" + items[i].arm.toFixed(1) + ""; tableHTML += "" + mom.toFixed(1) + ""; tableHTML += ""; } var cg = 0; if(totalWeight > 0) { cg = totalMoment / totalWeight; } // 3. Update DOM document.getElementById('manifestTableBody').innerHTML = tableHTML; document.getElementById('tblTotalWeight').innerText = totalWeight.toFixed(1); document.getElementById('tblTotalMoment').innerText = totalMoment.toFixed(1); document.getElementById('cgResult').innerText = cg.toFixed(2) + " in"; document.getElementById('totalWeightResult').innerText = totalWeight.toFixed(1) + " lbs"; document.getElementById('totalMomentResult').innerText = totalMoment.toFixed(0); document.getElementById('cgRangeResult').innerText = cg.toFixed(2); // Safety Logic var statusEl = document.getElementById('safetyStatus'); var weightMsgEl = document.getElementById('grossMargin'); var isSafe = true; // Check Weight var weightDiff = maxGross – totalWeight; if (weightDiff >= 0) { weightMsgEl.innerText = weightDiff.toFixed(1) + " lbs under max"; weightMsgEl.style.color = "var(–success)"; } else { weightMsgEl.innerText = Math.abs(weightDiff).toFixed(1) + " lbs OVER max"; weightMsgEl.style.color = "var(–danger)"; isSafe = false; } // Check CG if (cg aftLimit) { isSafe = false; } if (isSafe) { statusEl.className = "status-badge status-safe"; statusEl.innerText = "Within Limits"; } else { statusEl.className = "status-badge status-unsafe"; if (weightDiff maxGross); } function drawChart(currentCG, currentWeight, fwd, aft, maxWt, isOverWeight) { // Canvas dimensions var w = canvas.width = canvas.parentElement.offsetWidth; var h = canvas.height = canvas.parentElement.offsetHeight; ctx.clearRect(0, 0, w, h); // Chart Padding var pad = 50; var chartW = w – (pad * 2); var chartH = h – (pad * 2); // Scales // X Axis: CG. Range from (fwd – 5) to (aft + 5) var minX = fwd – 5; var maxX = aft + 5; var rangeX = maxX – minX; // Y Axis: Weight. Range from 0 to (maxWt + 500) var minY = 1000; // start y at 1000 for better visuals var maxY = maxWt + 200; var rangeY = maxY – minY; function getX(val) { return pad + ((val – minX) / rangeX) * chartW; } function getY(val) { return h – pad – ((val – minY) / rangeY) * chartH; } // Draw Axes ctx.beginPath(); ctx.strokeStyle = "#ccc"; ctx.lineWidth = 1; // Y Axis Line ctx.moveTo(pad, pad); ctx.lineTo(pad, h – pad); // X Axis Line ctx.lineTo(w – pad, h – pad); ctx.stroke(); // Draw Envelope Box (Simplified Rectangular Envelope for this generic calc) // A real envelope often has a slope at lower weights, but rectangle is standard for basic calculator ctx.fillStyle = "rgba(40, 167, 69, 0.1)"; ctx.strokeStyle = "#28a745"; ctx.lineWidth = 2; ctx.beginPath(); ctx.moveTo(getX(fwd), getY(minY)); ctx.lineTo(getX(fwd), getY(maxWt)); ctx.lineTo(getX(aft), getY(maxWt)); ctx.lineTo(getX(aft), getY(minY)); ctx.closePath(); ctx.fill(); ctx.stroke(); // Draw Limits Labels ctx.fillStyle = "#666"; ctx.font = "12px Arial"; ctx.textAlign = "center"; // X Axis Labels ctx.fillText(minX.toFixed(1), getX(minX), h – pad + 20); ctx.fillText(fwd.toFixed(1), getX(fwd), h – pad + 20); ctx.fillText(aft.toFixed(1), getX(aft), h – pad + 20); ctx.fillText(maxX.toFixed(1), getX(maxX), h – pad + 20); ctx.fillText("CG (inches)", w/2, h – 10); // Y Axis Labels ctx.textAlign = "right"; ctx.fillText(minY, pad – 10, getY(minY)); ctx.fillText(maxWt, pad – 10, getY(maxWt)); ctx.fillText(maxY, pad – 10, getY(maxY)); ctx.save(); ctx.translate(15, h/2); ctx.rotate(-Math.PI/2); ctx.textAlign = "center"; ctx.fillText("Weight (lbs)", 0, 0); ctx.restore(); // Draw Current Point var px = getX(currentCG); var py = getY(currentWeight); // Ensure point stays within canvas bounds roughly for visibility if (px w-pad) px = w-pad; if (py h-pad) py = h-pad; ctx.beginPath(); ctx.arc(px, py, 6, 0, 2 * Math.PI); ctx.fillStyle = (isOverWeight || currentCG aft) ? "#dc3545" : "#004a99"; ctx.fill(); ctx.strokeStyle = "white"; ctx.lineWidth = 2; ctx.stroke(); // Draw label near point ctx.fillStyle = "#333"; ctx.textAlign = "left"; ctx.font = "bold 12px Arial"; ctx.fillText("You", px + 10, py); } function resetCalculator() { document.getElementById('maxGrossWeight').value = 2300; document.getElementById('cgLimitFwd').value = 35.0; document.getElementById('cgLimitAft').value = 47.3; document.getElementById('emptyWeight').value = 1454; document.getElementById('emptyArm').value = 39.13; document.getElementById('frontSeatWeight').value = 340; document.getElementById('frontSeatArm').value = 37.0; document.getElementById('rearSeatWeight').value = 0; document.getElementById('rearSeatArm').value = 73.0; document.getElementById('fuelGallons').value = 40; document.getElementById('fuelArm').value = 48.0; document.getElementById('baggageWeight').value = 25; document.getElementById('baggageArm').value = 95.0; updateFuelWeight(); calculateWB(); } function copyResults() { var txt = "Aircraft Weight & Balance Calculation\n"; txt += "——————————–\n"; txt += "Total Weight: " + document.getElementById('totalWeightResult').innerText + "\n"; txt += "Total Moment: " + document.getElementById('totalMomentResult').innerText + "\n"; txt += "CG: " + document.getElementById('cgResult').innerText + "\n"; txt += "Status: " + document.getElementById('safetyStatus').innerText + "\n"; navigator.clipboard.writeText(txt).then(function() { alert('Results copied to clipboard!'); }, function(err) { console.error('Could not copy text: ', err); }); } // Initialize on load window.onload = function() { updateFuelWeight(); calculateWB(); // Resize listener for chart window.addEventListener('resize', function() { calculateWB(); }); };

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