How to Calculate a Weighted Average

Why a plain average is not always enough

A simple average treats every value as equally important. But a final exam usually counts far more than a short quiz, and a large stock position moves your portfolio more than a tiny one. A weighted average captures that difference by attaching a weight to each value.

When all weights are equal, the weighted average reduces exactly to the simple average — so the simple average is just a special case where nothing is emphasized over anything else.

Worked example: a course grade

Suppose homework is 20% of the grade at 95, the midterm is 30% at 80, and the final is 50% at 88. The weighted average is (0.20×95 + 0.30×80 + 0.50×88) / (0.20 + 0.30 + 0.50) = (19 + 24 + 44) / 1 = 87. Because the weights already sum to 1, the denominator is simply 1.

The simple average of 95, 80, and 88 would be about 87.7. The weighted result is slightly lower because the heavily weighted final of 88 dominates the mix.

Worked example: a portfolio return

If 60% of a portfolio returned 8% and 40% returned 3%, the weighted return is 0.60×8 + 0.40×3 = 4.8 + 1.2 = 6%. Here the weights are the portfolio shares, and they already add to 100%, so no extra division is needed.

The key habit is to make sure your weights and values line up correctly. Mixing up which weight belongs to which value is the most common mistake, so double-check the pairing before summing.

Frequently asked questions

Do the weights have to add up to 1 or 100%?

No. The formula divides by the sum of the weights, so any positive weights work. Weights that already add to 1 just make the division trivial, but weights like 3, 1, and 2 are equally valid.

Can a weight be zero?

Yes. A weight of zero simply removes that value from the average entirely, contributing nothing to either the numerator or the denominator.

What happens with negative weights?

Negative weights are mathematically allowed but rarely meaningful, and they can push the result outside the range of your values. In everyday use, keep weights positive.

Is GPA a weighted average?

Yes. A grade point average weights each course grade by its credit hours, so a five-credit course influences the average more than a one-credit course.