Weighted Average Calculator
Calculate the weighted average of values with different weights.
Weight Mode
| Label | Value / Score | Weight (%) | |
|---|---|---|---|
What Is the Weighted Average Calculator?
The Weighted Average Calculator computes a weighted mean for any number of items, each assigned an importance weight. Two modes are supported: Percentage mode (weights must total 100%) and Raw mode (any positive weights). The calculator displays the per-item contribution breakdown, simple average for comparison, min/max values, and, when scores are in the 0–100 range, the corresponding letter grade.
Formula
WA = Σ(vᵢ × wᵢ) / Σ(wᵢ)WA = Σ(vᵢ × wᵢ%) [if Σwᵢ = 100%]cᵢ = (vᵢ × wᵢ) / Σ(wᵢ)How to Use
- ›Select a weight mode: Percentage (must total 100%) or Raw (any positive values).
- ›Edit the default rows or click "+ Add row" to add more items.
- ›Enter a label, score/value, and weight for each row.
- ›In Percentage mode, the weight total indicator turns green when weights sum to 100%.
- ›Click Calculate to see the weighted average, letter grade, and per-item breakdown.
Example Calculation
Example 1, Course grade calculation
Example 2, Portfolio weighted return (Raw mode)
Understanding Weighted Average
What Is a Weighted Average?
A weighted average is a mean that accounts for the relative importance of each data point. Unlike a simple arithmetic mean, which divides the sum of values by count, the weighted average multiplies each value by its weight before summing, then divides by the total weight. The formula is:
Letter Grade Scale Reference
| Score range | Letter grade | GPA points | Interpretation |
|---|---|---|---|
| 97–100 | A+ | 4.0 | Outstanding |
| 93–96 | A | 4.0 | Excellent |
| 90–92 | A− | 3.7 | Near excellent |
| 87–89 | B+ | 3.3 | Above average |
| 83–86 | B | 3.0 | Good |
| 80–82 | B− | 2.7 | Slightly above average |
| 77–79 | C+ | 2.3 | Average+ |
| 73–76 | C | 2.0 | Satisfactory |
| 70–72 | C− | 1.7 | Below satisfactory |
| 67–69 | D+ | 1.3 | Poor |
| 63–66 | D | 1.0 | Barely passing |
| 0–62 | F | 0.0 | Failing |
Common Applications
- ›Academic grading, Course grades weight exams, quizzes, homework, and participation differently.
- ›GPA calculation, Credits are weights; grade points are values.
- ›Investment portfolios, Portfolio return = weighted average of individual asset returns.
- ›Market indices, The S&P 500 is a float-adjusted market-cap weighted average.
- ›WACC, Corporate cost of capital weights debt and equity by their proportions.
- ›Survey analysis, Likert scale responses weighted by respondent demographics.
- ›Moving averages, Exponential moving averages weight recent data more heavily.
Weighted vs. Simple Average: When It Matters
| Scenario | Simple avg gives | Weighted avg gives | Correct choice |
|---|---|---|---|
| 3 exams (different credit value) | Each exam equal influence | Higher-credit exams dominate | Weighted |
| 3 student grades in equal class | Correct class average | Same result (equal weights) | Either |
| Portfolio: 80% bonds, 20% stocks | Ignores allocation | Reflects true exposure | Weighted |
| Average price of 2 items bought in bulk | Wrong if quantities differ | Quantity-weighted mean | Weighted |
Frequently Asked Questions
What is the difference between a simple average and a weighted average?
A simple average treats all values equally: average = Σvᵢ / n. A weighted average assigns different importance to each value. If your final exam is worth 40% and homework 20%, you cannot just average the raw scores, the final must count twice as much as homework. The weighted average correctly reflects this.
Do my weights have to add up to 100%?
Only in Percentage mode. In Raw mode, the calculator divides by the total weight automatically, so any positive numbers work. For example, weights of 3, 2, 5 and 10, 6.67, 16.67 will give the same result, what matters is the ratio. Use Percentage mode when your course syllabus specifies exact percentages.
How is GPA calculated?
GPA is a weighted average of grade points, weighted by credit hours. Each course earns a letter grade converted to quality points (A = 4.0, B = 3.0, etc.), then multiplied by credit hours. Divide the total quality points by total credit hours: GPA = Σ(grade_points × credits) / Σ(credits).
- ›A in a 4-credit course contributes 4.0 × 4 = 16 quality points.
- ›B+ in a 3-credit course contributes 3.3 × 3 = 9.9 quality points.
What is a weighted average used for in finance?
- ›Portfolio returns, each asset weighted by its dollar value or allocation percentage.
- ›WACC (Weighted Average Cost of Capital), debt and equity weighted by capital structure.
- ›Index funds, the S&P 500 is a market-cap-weighted average of 500 stock prices.
- ›Inventory costing, AVCO (average cost) method weights purchase quantities.
Can weighted average values exceed the range of individual values?
No. A weighted average always falls within the range [min value, max value]. If all weights are positive, the weighted average is a convex combination of the values, it cannot be lower than the minimum or higher than the maximum input value. If a result appears outside this range, check for negative weights or data entry errors.