Weighted Average Calculator

The weighted average formula is WA = Σ(xᵢ × wᵢ) / Σwᵢ, where xᵢ is each value and wᵢ is the corresponding weight. It generalises the arithmetic mean by allowing each value to contribute differently based on its importance. When all weights are equal, the weighted average equals the arithmetic mean.

A simple arithmetic mean gives equal importance to every value: (x₁ + x₂ + … + xₙ) / n. A weighted average allows some values to count more than others. For example, an exam worth 60% of the grade counts three times more than a homework assignment worth 20%. The weighted average captures this importance correctly.

If all weights are zero, the denominator of the formula equals zero, which would cause a division-by-zero error. The calculator handles this edge case gracefully and returns 0 instead of an error. Always ensure at least one entry has a weight greater than zero to get a meaningful result.

Yes. The calculator accepts decimal weights such as 1.5 or 2.5. The weighted average formula works identically for integers and decimals. In practice, integer weights (1, 2, 3) are most common in schools, but decimal weights appear in university credit-hour systems and statistical analyses.

Assign numeric values to letter grades (e.g. A=4.0, B=3.0, C=2.0) and use the number of credit hours as the weight. For example: History (A=4.0, 3 credits) and Maths (B=3.0, 4 credits): WA = (4.0×3 + 3.0×4)/(3+4) = 24/7 ≈ 3.43. This is the standard credit-hour GPA calculation.

No. The weighted average is always within the range of the input values — it can never be higher than the highest value or lower than the lowest value in your dataset. It is simply a position between those extremes, weighted towards the values with higher weights.

The weighted sum Σ(x×w) and the sum of weights Σw are intermediate results that help you verify the calculation manually. Dividing the weighted sum by the sum of weights gives the final weighted average. Displaying them separately makes the calculation transparent and easier to audit.

Yes. Many European universities, especially those following the Bologna Process, calculate the Weighted Grade Point Average (wGPA) using ECTS credits as weights. Each module's grade is multiplied by its ECTS credits, and the total is divided by the sum of ECTS credits taken.

The online calculator supports up to 5 value–weight pairs. If you have more entries, you can aggregate them in multiple steps: calculate the weighted average of the first 5 entries, then treat that intermediate result as one value with the sum of its weights as the combined weight for the next step.

The calculator rounds the final result to 2 decimal places (e.g. 4.33 or 4.25). All intermediate computations are performed using full floating-point precision (IEEE 754 double). Rounding is applied only to the displayed output. Minor differences of ±0.01 can occur due to standard floating-point rounding.