Aviation & Aeronautics
Basic

Center of Gravity

The center of gravity is the total moment divided by total weight — the core of every weight-and-balance calculation.

Formula

CG=∑M∑WCG = \dfrac{\sum M}{\sum W}

Variables

CGCenter of gravity (arm)
\sum MSum of moments (weight × arm)
\sum WTotal weight

Example

Moments 250,000 in-lb, weight 2,500 lb: CG = 100 in

How it works

The center of gravity (CG) tells you where the aircraft’s total weight can be considered to act as if it were concentrated at a single point. It is found by dividing the total moment by the total weight because moment is the turning effect produced by each weight about a reference datum, so the weighted average of all the arms gives the balance point. If the CG moves too far forward or aft, the aircraft’s handling and stability can change significantly.

When to use it

Use this formula in weight-and-balance calculations for airplanes, helicopters, and loaded cargo when you need to find the overall balance point. It is especially important before takeoff, after loading passengers or baggage, or when checking whether an aircraft stays within its approved CG limits.

Worked example, step by step

Step 1: Find the total moment. Moments = 180,000 in-lb Step 2: Find the total weight. Weight = 1,800 lb Step 3: Divide total moment by total weight. CG = ΣM / ΣW = 180,000 / 1,800 Step 4: Calculate. CG = 100 in Final answer: The center of gravity is 100 inches from the datum.

Common mistakes to avoid

  • Using the wrong reference datum or arm units
  • Dividing by the number of items instead of the total weight
  • Mixing units, such as moments in lb-ft and weight in pounds without converting consistently

Did You Know?

A CG outside limits can make an aircraft uncontrollable — weight and balance is checked before every flight.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026