Aircraft Weight and Balance Calculator

How Aircraft Weight and Balance Is Calculated

Weight and balance ensures an aircraft’s center of gravity (CG) falls within the approved envelope. An out-of-limit CG makes an aircraft difficult or impossible to control.

Moment Formula:

Moment = Weight × Arm

CG = Total Moment / Total Weight

Where:

• Weight = mass of item in lbs or kg
• Arm = distance from reference datum in inches or meters
• Moment = weight × arm (in-lbs or kg-m)
• CG = center of gravity location (same unit as arm)

Worked Example (Cessna 172 typical values):

• CG = 93,436 / 2,269 = 41.18 inches
• Check against the 172S envelope. The aft limit is 47.3 inches at every weight. The forward limit is 35.0 inches up to 1,950 lbs and slides to 41.0 inches at 2,550 lbs, so at 2,269 lbs it sits near 38.2. 41.18 is between the two → Within limits ✓

Max Gross Weight: Cessna 172S = 2,550 lbs. Never exceed this, even if CG is in range.

Check the landing CG as well as the takeoff one. Fuel burns off during the flight, and its arm is not the same as the CG’s. In this example the fuel sits at 48 inches, aft of the 41.18 CG, so burning it moves the CG forward. Burn 30 gallons (180 lbs) and the airplane lands at 2,089 lbs with 84,796 in-lbs of moment, a CG of 40.59. The forward limit at that weight is about 36.4, so it is still fine. In a heavily loaded airplane with the seats full up front, that same forward drift is how a takeoff that was legal turns into a landing that is not.

Many Pilot’s Operating Handbooks print moment divided by 1,000 to keep the loading graphs readable. If your POH says 68.6 where this page says 68,596, that is the same number.

Aft CG danger: Elevator authority insufficient; aircraft can enter unrecoverable pitch-up. Forward CG: excessive nose-down tendency, higher stall speed, more drag.