Weighted Average Calculator

A weighted average is a mean calculated by giving different values different levels of importance (weights). Unlike a simple average where all values contribute equally, a weighted average reflects the fact that some data points matter more than others.

Core formula: Weighted Average = Σ(Value × Weight) ÷ Σ(Weights)

Or expanded: WA = (V₁×W₁ + V₂×W₂ + V₃×W₃ + … + Vₙ×Wₙ) ÷ (W₁ + W₂ + W₃ + … + Wₙ)

If weights already sum to 1 (or 100%): WA = Σ(Value × Weight Fraction)

What each variable means:

• Value (Vᵢ): the individual data points (grades, prices, measurements, etc.).
• Weight (Wᵢ): the relative importance or contribution of each value. Any non-negative numbers will do. They do not need to sum to 1 or to 100 first, because dividing by Σ(Weights) normalizes them for you. A negative weight is not meaningful here and the calculator rejects it: it would let the answer land outside the range of your own values, which no average can do.
• Σ(Weights): the sum of all weights used as the denominator to normalize the result.

Common real-world applications:

Worked example 1: final course grade A student has these scores and weights:

• Homework: 82/100 → 20% weight
• Midterm: 74/100 → 30% weight
• Final Exam: 91/100 → 50% weight

Weighted Average = (82 × 0.20) + (74 × 0.30) + (91 × 0.50) = 16.4 + 22.2 + 45.5 = 84.1 (Final grade: 84.1%)

Simple average (incorrect): (82 + 74 + 91) ÷ 3 = 82.3, which understates how much the final exam counts.

Worked example 2: portfolio return

• Stock A: 12% return, $15,000 invested
• Stock B: −3% return, $5,000 invested
• Stock C: 8% return, $30,000 invested

WA return = (0.12×15,000 + (−0.03)×5,000 + 0.08×30,000) ÷ 50,000 = (1,800 − 150 + 2,400) ÷ 50,000 = 4,050 ÷ 50,000 = 8.1% portfolio return

Simple average: (12 − 3 + 8) ÷ 3 = 5.67%, badly misleading because it ignores how much money sat in each position.

The gap between 8.1% and 5.67% is the whole reason this calculator exists. The plain average treats a $5,000 loser as counting exactly as much as a $30,000 winner, and in this portfolio that understates the real return by nearly a third.

A check worth doing every time

A weighted average always lands between the smallest and largest of your values. If it comes out above the highest or below the lowest, the weights are wrong, and the usual cause is a negative one that crept in. There is no set of valid weights that puts the answer outside that range.