Aircraft Performance
Use the weight and balance calculator below to verify that your aircraft remains within approved weight and center of gravity (CG) limits. Enter the empty weight, fuel weight, occupant weights, and baggage weight. The calculator computes total weight, total moment, and CG position for the zero-fuel, ramp, takeoff, and landing phases of flight. It then compares each condition with the aircraft's certified CG envelope to confirm that the aircraft remains within limits.
Usage Guide
The steps below explain how to use the calculator to compute total weight and CG position at each phase of flight and how to verify that the result falls within the aircraft's certified CG envelope.
Select a preset aircraft, such as the Cessna 172S or PA-28-181 Archer, to auto-fill CG limits, maximum weights, and VA. Alternatively, enter these values manually from the POH for any other aircraft. Select the weight unit, volume unit, fuel type, and moment index used by the aircraft's weight and balance documentation.
Enter the weight for each occupant and baggage station in the loading stations table. Select a standard passenger weight from the FAA or EASA tables, or enter actual passenger weights. Enter the fuel volume loaded into each tank. The calculator converts fuel volume to weight using the selected fuel type and computes the moment for each station automatically.
The calculator computes total weight, total moment, and CG position for the zero-fuel, ramp, takeoff, and landing phases of flight. The flight phase summary table shows whether each phase falls within the certified CG envelope. The CG envelope diagram plots each phase against the aircraft's weight and CG limits.
VA is the maneuvering speed at the current weight, calculated from the maximum maneuvering speed entered above. VA decreases as weight decreases, so VA at landing weight is lower than VA at takeoff weight. If a maximum zero fuel weight is entered, the calculator flags any zero-fuel weight that exceeds this limit. Confirm that every flight phase shows a status of within limits before using the loading configuration for flight.
Fundamentals
Weight and balance in aviation is the process of calculating and controlling an aircraft's load to ensure it remains within manufacturer-specified weight limits and center of gravity (CG) limits. The load includes passengers, cargo, and fuel. The process ensures safe aircraft performance and controllability.
Weight defines the total mass of the aircraft. Balance defines the position of the center of gravity (CG). Both parameters must remain within the certified limits defined in the POH or AFM.
Weight and balance affects aircraft performance and flight safety. Excess weight increases stall speed. Excess weight increases takeoff distance. Excess weight increases landing distance. Excess weight reduces climb performance.
Improper balance shifts the center of gravity outside safe limits. A forward CG increases stability but reduces elevator authority. An aft CG reduces stability and can reduce recovery capability from stall or spin conditions.
Fundamentals
The center of gravity (CG) in aviation is the point where an aircraft's total weight is considered to be concentrated and where the aircraft balances in pitch. The aircraft rotates around this point during flight.
CG position determines aircraft stability, control, and handling characteristics. The CG must remain within a manufacturer-defined range published in the POH or AFM to ensure safe operation.
Center of gravity affects aircraft stability and controllability. The CG is normally located slightly ahead of the center of lift. This position allows the aircraft to return to stable flight after disturbances. The aircraft rotates around the CG during pitch, roll, and yaw inputs. If CG moves outside safe limits, control response becomes unsafe.
CG is calculated by dividing total moment by total weight:
CG = Total Moment ÷ Total Weight
Key Terms
Datum, arm, and moment are the three reference values aircraft manufacturers use to calculate weight distribution before computing center of gravity. Datum is a fixed reference plane. Arm is a distance measurement. Moment is the rotational effect of a load.
The datum is an imaginary vertical plane defined by the aircraft manufacturer from which all horizontal distance measurements are taken. Datum location varies by aircraft type — common positions include the firewall, the wing leading edge, or a point forward of the nose. Distances aft of the datum are positive. Distances forward of the datum are negative when the datum sits behind the nose. The datum location is published in the aircraft's Type Certificate Data Sheet and POH.
The arm is the horizontal distance from the datum to the point where a specific load acts, measured in inches or metres. Each loading station has a fixed published arm value in the POH, including the pilot seat, passenger seats, baggage compartments, and fuel tanks. Arm is a geometric location and does not change with load weight.
The moment is the product of weight multiplied by arm, representing the rotational tendency of that load around the datum:
Moment = Weight × Arm
Moment is expressed in pound-inches or kilogram-metres. Many manufacturers publish moment as a moment index, dividing the raw value by 100 or 1000 to keep figures manageable on weight and balance worksheets.
Each loading station's weight, arm, and moment are entered into the calculation, then total moment and total weight together determine the CG position.
Key Terms
Mean aerodynamic chord (MAC) is the chord length of an imaginary, untapered wing that produces the same total lift and pitching moment as the aircraft's actual wing. MAC provides a standardized reference length for expressing CG position relative to the wing rather than to the fuselage datum.
Aircraft with tapered or swept wings generate lift unevenly along the span, so CG position relative to the wing's aerodynamic center matters more than CG position relative to a fixed fuselage point. Expressing CG as a percentage of MAC makes stability and control characteristics comparable across different loading conditions and aircraft configurations.
Percent MAC is calculated from the CG distance behind the leading edge of MAC (LEMAC) and the total length of MAC:
%MAC = (CG distance from LEMAC ÷ MAC length) × 100
Large and transport category aircraft typically publish CG limits as a %MAC range rather than as inches from datum. Most small general aviation aircraft express CG in inches or millimetres from datum and do not use %MAC. Converting between inches-from-datum and %MAC describes the same CG position — only the reference system changes.
CG Envelope
The CG envelope is a graph published in the aircraft's POH or AFM that defines the range of CG positions permitted at each aircraft weight. The horizontal axis shows CG position, in inches from datum or percent MAC. The vertical axis shows aircraft weight, from minimum weight to maximum gross weight.
The envelope is bounded by a forward CG limit line and an aft CG limit line, forming an enclosed area on the graph. The two limit lines are not always parallel — the forward limit commonly moves aft as weight decreases, narrowing the permissible CG range at lower weights. This narrowing exists because reduced weight lowers elevator effectiveness for stall recovery and landing flare.
Pilots plot the calculated weight and CG position for each phase of flight directly onto the envelope. A point that falls inside the envelope confirms the aircraft is within its certified weight and balance limits. A point that falls outside the envelope, in any direction, makes the flight illegal and unsafe regardless of how close the point is to the boundary.
Every phase of flight must be checked against the envelope separately, since weight and CG position both change as fuel burns and load shifts. A loading configuration that is within limits at takeoff can move outside the envelope by landing if fuel burn shifts CG in the wrong direction.
Calculation Method
Aircraft weight and balance is calculated by multiplying the weight of each load by its arm to produce a moment, then dividing total moment by total weight to find CG position. The calculation starts from the aircraft's basic empty weight and adds every item loaded for the flight.
Each load item is recorded with its own weight and arm: basic empty weight, pilot, front passenger, rear passengers, baggage, and fuel. Every item's weight is multiplied by its arm to produce that item's moment. All weights are summed to total weight. All moments are summed to total moment.
This calculation across every loaded item is expressed as:
Total Weight = W₁ + W₂ + W₃ ...
Total Moment = (W₁×A₁) + (W₂×A₂) + (W₃×A₃) ...
CG = Total Moment ÷ Total Weight
W = weight of each item, A = arm of each item
For example, an aircraft with an empty weight of 1,500 lb at a 39.0 in arm produces a moment of 58,500 lb-in. Adding a 170 lb pilot at a 37.0 in arm (6,290 lb-in) and 300 lb of fuel at a 48.0 in arm (14,400 lb-in) gives a total weight of 1,970 lb and a total moment of 79,190 lb-in. Dividing total moment by total weight gives a CG of 40.2 in from datum.
The calculation is repeated separately for ramp weight, takeoff weight, and landing weight, since fuel burn and load changes shift both total weight and CG between phases. Each resulting CG value is then plotted against the CG envelope to confirm the aircraft remains within certified limits.
CG Shift
Pilots calculate CG shift using two shortcut formulas that avoid recalculating total weight and total moment from scratch: one for moving existing weight within the aircraft, and one for adding or removing weight entirely.
When weight is moved from one station to another without changing total aircraft weight, the new CG is found using the weight shift formula:
ΔCG = (Weight Moved × Distance Moved) ÷ Total Weight
ΔCG = change in CG position · Distance Moved = arm distance between the old and new station
When weight is added to or removed from the aircraft, changing total weight, the new CG is found using the weight added/removed formula:
ΔCG = [Weight Added × (Arm − Old CG)] ÷ New Total Weight
Arm = station arm of the added or removed weight · Old CG = CG position before the change
These shortcut formulas are most useful for quickly checking the effect of a last-minute loading change, such as moving baggage between compartments or adding a passenger, without rebuilding the full weight and balance table. The result should still be plotted on the CG envelope to confirm the aircraft remains within limits.
POH Charts
Pilots use weight and balance charts from the POH by reading pre-calculated moment values directly off a loading graph, rather than multiplying weight by arm manually. Most piston aircraft POHs publish a loading graph and a weight and balance form specifically for this purpose.
The loading graph plots weight on the vertical axis against moment, often shown as moment divided by 1,000, on the horizontal axis. Each loading station — pilot and front passenger, rear passengers, baggage, and fuel — has its own diagonal line on the graph. A pilot locates the station's actual weight on the vertical axis, follows it across to that station's line, and reads the corresponding moment directly below on the horizontal axis.
The weight and balance form lists each loading station with its arm pre-printed. A pilot enters the weight for each station, finds the moment using the loading graph or by multiplying weight by arm, and records the result on the form. Total weight and total moment are summed at the bottom of the form, then divided to find CG.
The completed weight, moment, and CG values are then plotted on the CG envelope to confirm the loading falls within certified limits. Using the POH-published loading graph eliminates arithmetic errors and is the method most manufacturers recommend for routine preflight weight and balance checks.
Useful Load
Useful load is the difference between an aircraft's maximum gross weight and its basic empty weight, representing the total weight available for fuel, passengers, baggage, and cargo.
Useful Load = Max Gross Weight − Basic Empty Weight
Useful load is divided between fuel weight and payload. Payload is the weight of passengers, baggage, and cargo, excluding fuel. Adding more fuel reduces the payload available within the same useful load limit. Adding more payload reduces the fuel that can be carried.
A typical four-seat single-engine piston aircraft has a useful load between 900 lb and 1,200 lb. Filling the fuel tanks to maximum capacity while carrying four adult occupants often exceeds this limit, since fuel weight and occupant weight compete for the same useful load allowance.
Pilots must verify that the sum of fuel weight and payload weight does not exceed useful load before every flight. Exceeding useful load also exceeds maximum gross weight, since basic empty weight is fixed for a given aircraft.
Payload
Payload is the combined weight of every occupant, including the pilot, plus any baggage and cargo carried on a flight, excluding fuel weight, the aircraft's basic empty weight, and any fuel reserved as unusable. Payload is calculated by subtracting fuel weight from useful load.
Payload = Useful Load − Fuel Weight
Payload and fuel range are directly related, since both draw from the same useful load allowance. Carrying maximum payload reduces the fuel that can be loaded, which reduces range and endurance. Carrying maximum fuel for long-range flights reduces the payload available for passengers and cargo. This relationship is known as the payload-range trade-off.
Pilots calculate payload before every flight to confirm that passenger and baggage weight, combined with planned fuel load, does not exceed useful load. Commercial and charter operators use payload calculations to determine revenue-generating capacity for a given route and fuel requirement.
Weight Categories
Ramp weight, takeoff weight, zero fuel weight, and landing weight are four distinct weight categories used during preflight planning, each representing the aircraft at a different point before, during, or after fuel is loaded and burned.
Ramp weight, also called maximum taxi weight, is the total aircraft weight including all fuel before engine start, taxi, and run-up. Ramp weight is the heaviest weight condition of the flight, since it includes fuel that will be burned before takeoff.
Takeoff weight is ramp weight minus the fuel burned during taxi and run-up. For most piston GA aircraft, this difference is small, typically 1 to 3 gallons, or 6 to 18 lb. Takeoff weight must not exceed the aircraft's maximum gross weight published in the POH.
Zero fuel weight is the total aircraft weight with no usable fuel on board — basic empty weight plus payload, excluding fuel entirely. Many light GA aircraft do not publish a maximum zero fuel weight (MZFW), since wing-mounted fuel tanks relieve wing bending loads and a separate ZFW limit is unnecessary. Aircraft with fuel stored outside the wing, and most larger aircraft, publish an MZFW that must not be exceeded regardless of how much fuel is loaded.
Maximum landing weight (MLW) is the highest weight at which an aircraft is certified to land, based on the structural stress the landing gear and airframe can absorb at touchdown. Most light GA aircraft have the same maximum landing weight as maximum gross weight, since fuel burned in flight normally brings the aircraft below MTOW well before landing. Larger aircraft often publish an MLW lower than MTOW, since the difference accounts for fuel that must be burned before landing is permitted.
Ramp weight is always equal to or greater than takeoff weight. Takeoff weight is always equal to or greater than landing weight, since fuel continues to burn throughout the flight. Each of these weights must be checked separately against CG limits, since CG position shifts as fuel burns between phases.
Standard Weights
The FAA and EASA publish standard average passenger weights for use in weight and balance calculations when actual passenger weights are unavailable. These standard weights simplify load planning and mass and balance calculations.
The FAA uses seasonal standard weights. The FAA standard average adult passenger weight is 190 lb during the summer season, from May through October. The FAA standard average adult passenger weight is 195 lb during the winter season, from November through April. The higher winter value accounts for heavier clothing.
EASA uses a standard average adult passenger mass of 84 kg, which is approximately 185 lb. EASA does not apply seasonal adjustments.
The figures below summarize the standard average adult passenger weights used by each regulator.
Standard passenger weights provide convenient estimates for routine operations. Actual passenger weights provide more accurate weight and balance calculations. Pilots operating near maximum gross weight or center of gravity (CG) limits should use actual weights whenever possible.
Maneuvering Speed
Maneuvering speed (VA) is the maximum indicated airspeed at which full, abrupt control inputs can be made without exceeding the aircraft's structural load limits. Below VA, the wing reaches its critical angle of attack and stalls before structural loads become high enough to damage the airframe.
VA depends on aircraft weight because stall speed depends on weight. A lighter aircraft stalls at a lower indicated airspeed. As a result, the wing reaches its critical angle of attack at a lower speed. Therefore, maneuvering speed decreases as aircraft weight decreases.
Pilots calculate VA for the actual aircraft weight using the following relationship:
VA(actual) = VA(max) × √(Wactual ÷ Wmax)
Where:
A common misconception is that a lighter aircraft can safely fly faster in turbulence. The opposite is true. A lighter aircraft requires a lower maneuvering speed. Using the published VA for maximum gross weight when flying at a lower weight can expose the aircraft to excessive structural loads.
Aircraft weight decreases during flight as fuel is consumed. Therefore, maneuvering speed at landing weight is lower than maneuvering speed at takeoff weight. Pilots should determine VA for the actual aircraft weight whenever turbulence, abrupt control inputs, or aggressive maneuvering are expected.
Fuel Burn
Fuel burn affects center of gravity (CG) during flight because removing fuel changes both total weight and total moment, which changes the aircraft's CG position. The direction of the CG shift depends on the location of the fuel tanks relative to the current CG.
If the fuel tanks are aft of the CG, fuel burn moves the CG forward. If the fuel tanks are forward of the CG, fuel burn moves the CG aft. In many single-engine aircraft with wing-mounted fuel tanks, the fuel arm lies close to the empty-weight CG. As a result, the CG shift during flight is usually small and predictable.
Aircraft with multiple fuel tanks can experience larger CG changes. Uneven fuel consumption can create a significant CG shift. Fuel management procedures help maintain the aircraft within approved balance limits.
A CG position that is within limits at takeoff is not guaranteed to remain within limits at landing. Pilots therefore calculate weight and balance at both takeoff weight and landing weight. Fuel burn is the primary reason center of gravity changes during flight without any change in passengers, cargo, or baggage.
Pilots must ensure that the center of gravity remains within the certified CG envelope throughout the entire flight, not just at departure.
Lateral Balance
Lateral balance in aircraft weight and balance is the distribution of weight between the left and right sides of the aircraft. It affects roll stability and yaw tendencies during flight.
Most light aircraft do not publish formal lateral center of gravity (CG) limits. Manufacturers primarily define longitudinal CG limits because lateral balance is normally managed through operational procedures rather than envelope calculations.
Lateral imbalance typically occurs due to uneven fuel distribution between left and right wing tanks. A heavier wing produces a rolling moment toward that side. The pilot must apply opposite aileron or rudder input to maintain level flight.
Continuous control input to correct lateral imbalance increases aerodynamic drag. Increased drag reduces cruise efficiency. Uneven fuel burn is the most common operational cause of lateral imbalance in light aircraft.
Pilots manage lateral balance by alternating fuel tanks or using both tanks evenly during flight. Balanced fuel consumption reduces the need for continuous corrective control input.
Lateral balance does not normally require formal calculation in light aircraft. Longitudinal center of gravity (CG), by contrast, must always be calculated and verified against certified limits before flight.
Forward CG
A forward CG increases the aircraft's resistance to pitch changes and increases the elevator force required to raise the nose. The horizontal stabilizer must produce more downward force to balance the extra nose-heavy moment, which increases drag and reduces cruise efficiency.
During takeoff, a forward CG can prevent the aircraft from rotating to a climb attitude, particularly at low airspeed or with reduced engine power. In extreme cases, the elevator lacks enough authority to raise the nose at all.
During landing, a forward CG increases the elevator force needed to flare and reduces the aircraft's ability to round out before touchdown. A nose-heavy aircraft that cannot fully flare may land hard or strike the nosewheel first, risking structural damage.
A forward CG also increases stall speed slightly, since the wing must support both the aircraft weight and the additional download from the tail. This combination of higher stall speed and reduced elevator authority increases risk during low-speed phases of flight, such as takeoff and landing.
A forward CG most commonly results from heavy front-seat occupants combined with an empty baggage compartment, or from loading without rear-seat passengers. Pilots can correct a forward CG exceedance by adding weight aft, such as baggage, or by reducing weight forward.
Aft CG
A center of gravity (CG) that is too far aft reduces longitudinal stability and can make the aircraft difficult or impossible to recover from a stall or spin. An aft CG reduces the elevator force required to change pitch. The aircraft becomes more responsive, but it becomes less stable.
An aft CG reduces stick force per G. Small elevator inputs produce larger pitch changes. The pilot can inadvertently apply excessive G-load or enter an accelerated stall more easily.
An aft CG reduces the elevator's nose-down authority. This reduction limits the aircraft's ability to lower the nose during stall recovery. It also increases the risk that a spin will develop into a flat spin, a stable, near-level spin from which recovery is unlikely with normal control inputs. This is the most dangerous consequence of an aft CG exceedance.
An excessively aft CG also reduces the back-pressure needed to rotate on takeoff, which can cause the aircraft to lift off prematurely or rotate too quickly. In aircraft with limited tail clearance, an aggressive or uncommanded rotation caused by an aft CG can result in a tail strike.
An extreme aft CG can make the aircraft longitudinally unstable. The aircraft may develop uncommanded pitch oscillations that normal elevator inputs cannot stop. Loss of control can occur.
An aft CG also decreases stall speed slightly, since the wing carries less total load when the tail contributes less downward force. This small reduction in stall speed does not offset the greater risk created by reduced stability and reduced stall and spin recovery capability.
Common causes of an aft CG include heavy baggage loaded in an aft compartment, rear-seat passengers without sufficient weight in the front seats, and fuel stored in tanks located behind the center of gravity. Pilots can correct an aft CG condition by moving weight forward, reducing aft loading, or adding ballast forward. The aircraft must remain within the manufacturer-approved center of gravity envelope for safe and legal operation.
Common Mistakes
Common weight and balance mistakes include using outdated empty weight data, estimating rather than verifying actual weights, checking only takeoff conditions, exceeding individual compartment limits, and failing to recalculate after last-minute loading changes.
Pilots make errors when they use outdated empty weight and moment data. Aircraft modifications such as avionics upgrades, paint changes, or STCs alter empty weight and CG. Pilots must use the latest approved weighing report or updated POH data.
Pilots introduce error when they estimate passenger or baggage weight instead of verifying it. Estimation reduces accuracy of total weight and CG calculations. Pilots should use actual measured weights or approved standard passenger weights.
Pilots make errors when they calculate weight and balance only for takeoff conditions. Fuel burn changes weight and shifts CG during flight. Pilots must calculate both takeoff weight and landing weight.
Pilots exceed limits when they load baggage compartments without checking compartment-specific weight limits. Each compartment has a structural maximum weight independent of total aircraft weight and CG limits.
Pilots create unsafe conditions when they do not recalculate weight and balance after last-minute changes. Any change in passengers, baggage, or fuel requires a new calculation before departure.
Common Questions
Yes, weight and CG are independent limits, and an aircraft can exceed one without exceeding the other. An aircraft can be at or below maximum gross weight but still have its CG positioned outside the forward or aft limit for that weight, making the flight illegal even though weight alone is acceptable. Conversely, an aircraft can have a CG well within the envelope range but still exceed maximum gross weight if too much total weight is loaded. Both weight and CG must be checked and confirmed within limits independently before every flight.
Standard empty weight is the aircraft's weight as certified by the manufacturer, including the airframe, engine, unusable fuel, and full operating fluids such as oil, but excluding optional equipment. Basic empty weight is standard empty weight plus the weight of any optional equipment installed on that specific aircraft, such as additional avionics, interior modifications, or STCs. Basic empty weight is unique to each individual aircraft and changes whenever equipment is added or removed, while standard empty weight is the same for every aircraft of that model and configuration.
Yes, a new weight and balance calculation is required whenever the loading configuration changes, including changes in passengers, baggage, cargo, or fuel. Pilots cannot reuse a calculation from a previous flight unless the loading is verified to be identical. Even small changes, such as an added passenger or extra fuel, can shift CG enough to require a fresh calculation before departure.
Most light general aviation aircraft are not required to be reweighed on a fixed schedule, but manufacturers and regulators recommend reweighing after any modification that could change empty weight or CG, such as an avionics upgrade, paint job, repair, or major overhaul. Some operators choose to reweigh periodically, such as every few years, as a best practice even without a modification. Aircraft operated under commercial or charter rules often have stricter reweighing intervals required by their operating authority.
A weight and balance calculator determines total aircraft weight and CG position and verifies both fall within certified limits. A takeoff and landing performance calculator uses a known weight to determine the runway distance required for takeoff or landing under specific conditions, such as density altitude, wind, and runway surface. Weight and balance must be confirmed first, since takeoff and landing performance calculations depend on having an accurate, legal takeoff weight as a starting input.
Mass and balance and weight and balance refer to the same concept under different regulatory terminology. EASA and most international regulators use the term mass and balance, while the FAA uses weight and balance. Both describe the same process of calculating total aircraft mass or weight and confirming CG position falls within certified limits.
No, an aircraft that exceeds maximum gross weight is not legal or safe to fly, even if CG is within the certified envelope. Operating overweight increases stall speed, reduces climb performance, increases takeoff and landing distance, and can exceed structural load limits, regardless of CG position. Weight and CG are both independent requirements that must be satisfied together.
An aircraft's current weight and balance status is documented in its weight and balance report, equipment list, and the most recent weighing record, normally kept with the aircraft's permanent records or in the POH. These documents list basic empty weight, empty weight CG, and the installed equipment used to calculate that weight. Pilots should confirm these records are current and reflect any recent modifications before relying on them for preflight calculations.
Yes, many aircraft are certified for multiple categories, each with its own weight and CG limits. Normal category permits standard flight maneuvers with a wider CG range. Utility category, used for limited aerobatic maneuvers such as spins, requires a lighter weight and a narrower, more restrictive CG range. Pilots must confirm the aircraft is loaded within the limits of the specific category for the maneuvers being flown, since exceeding Normal category limits while performing Utility category maneuvers can cause structural damage.
Yes, an aircraft's empty-weight CG (EWCG) can legitimately fall outside the published CG envelope, since the envelope is designed around the aircraft in a ready-to-fly condition with a pilot, fuel, and oil on board. The empty-weight CG by itself serves only as a reference point for further calculations, not as a stand-alone indicator of airworthiness. Once standard items such as pilot weight and fuel are added, the resulting CG should move into the envelope for normal loading conditions.
Ballast is additional weight added to an aircraft solely to bring its CG within the approved envelope, rather than for any operational purpose. Ballast can be a fixed, permanently installed weight or a removable item carried only for specific flights. Pilots and mechanics can also use existing equipment as a form of ballast by relocating it, such as moving a battery further forward or aft, to shift CG without adding extra weight to the aircraft.