What Is a Weighted Average?
A weighted average is an “average with priorities.” In a normal (simple) average, every number counts the same. In a weighted average, some values matter more than others because they carry larger weights. That’s exactly how many real systems work: an exam may be worth more than a quiz, a course with more credits affects GPA more, and a portfolio position with more shares affects your average cost more.
This calculator lets you enter any set of values and weights, then computes the weighted average using the standard formula. It also shows a breakdown table so you can see how each row contributes to the final result.
The Weighted Average Formula
The core rule is straightforward:
Weighted Average = (Σ(value × weight)) ÷ (Σ(weight))
If your weights are percentages that add up to 100, the denominator is effectively 100. If your weights are credits, points, shares, or any other units, you simply divide by the total weight. The important part is that the weight is consistent across rows.
Why Normalizing Weights Helps
Normalizing weights means converting them into proportions that sum to 1 (or 100%). It does not change the final weighted average; it just makes the weights easier to interpret. For example, if your weights are 2, 3, and 5, the normalized weights are 0.2, 0.3, and 0.5. The calculator can show both the raw weight and the normalized share so you can understand influence at a glance.
When to Use Percent Weights vs “Any Weights”
Percent weights are common for grading rubrics: 20% assignments, 30% midterm, 50% final. In that case, your weights are intended to total 100. In many other cases, weights are “counts” (credits, shares, units). Those do not need to total 100. This tool supports both styles and will warn you if percent weights are out of range.
Grades: Weighted Average for Course Components
A classic use is computing a final grade. Each component has a score and a weight. If you scored 85 on assignments worth 20%, 78 on a midterm worth 30%, and 92 on a final worth 50%, your weighted average reflects those priorities. This is more realistic than a simple average of 85, 78, and 92 because the final exam carries more impact.
If your class uses points instead of percentages, you can still compute the weighted average by using point totals as weights. The logic is identical: higher point categories matter more.
GPA-Style Averages Using Credits
Another practical use is GPA-style averaging. Each course has a grade point value (your “value”) and a credit hour count (your “weight”). A 4-credit class should influence your overall average more than a 1-credit lab. By entering grade points and credits, you get a weighted average that mirrors how GPA is computed in many systems.
Finance: Average Cost and Portfolio Metrics
Weighted averages are everywhere in finance. One common example is average cost per share. If you buy 10 shares at $100 and later buy 5 shares at $130, your average price is not (100 + 130) / 2. It is weighted by shares: the 10-share purchase counts twice as much as the 5-share purchase.
The same idea works for blended prices, average interest rates across loans, or any “combined” metric where different quantities contribute unequally.
Business KPIs and Scorecards
Many teams use scorecards: quality, speed, customer satisfaction, compliance, and cost. Each metric may have a different importance. A weighted average turns those individual scores into a single composite score that reflects what matters most. This is useful for performance dashboards, vendor scoring, and operational reporting.
How to Interpret the Breakdown Table
The breakdown table shows each row’s value, weight, normalized weight, and the product (value × weight). The product is the “contribution numerator” for that row. When you add all row products together and divide by total weight, you get the weighted average.
If something looks off, scan the table for an outlier weight. A single unusually large weight can dominate the result, which might be correct—or it might be a typo.
Common Mistakes and Quick Fixes
- Weights are missing: rows without both value and weight are ignored.
- Percent weights don’t add to 100: normalization can still compute the correct ratio, but your rubric may be inconsistent.
- Negative or zero weights: most systems assume weights are positive. Use positive weights to reflect importance or quantity.
- Mixing units: don’t combine credits with percentages in the same calculation. Choose one weighting system per run.
What If You Want to Compare Scenarios?
Weighted averages are great for “what if” planning. You can adjust weights to simulate changes (like a final exam becoming more important) or adjust values to test targets (like “what score do I need on the final to reach 90 overall?”). Run the calculator multiple times and use the History tab to keep track or export results to a spreadsheet.
Accuracy, Rounding, and Precision
The calculator computes using standard floating-point math and then formats to your chosen precision. If you want cleaner presentation for reports, choose 2 or 4 decimals. If you want maximum detail for analysis, choose 10 or 16 decimals. Remember: if your inputs are approximate, extra decimals don’t create extra real-world accuracy.
FAQ
Weighted Average Calculator – Frequently Asked Questions
Answers about formulas, normalization, grades, GPA-style credit weighting, and how to interpret your breakdown.
A weighted average is an average where each value contributes according to its weight. Instead of treating all values equally, you multiply each value by its weight, add them up, and divide by the total weight.
Weighted Average = (Σ(value × weight)) ÷ (Σ(weight)). If your weights are already percentages that sum to 100%, you can divide by 100% instead of Σ(weight).
No. Weights can be any positive numbers (credits, points, quantities). This calculator can normalize them so you still get the correct weighted average even when they don’t sum to 100.
A simple average treats every value equally. A weighted average gives some values more influence based on their weights, which is common for grade components, portfolio allocations, and KPIs.
Yes. Use the grade points as values and credit hours as weights. The result is the weighted average grade points across your courses.
Typically no. Most real-world weighting systems use non-negative weights. This calculator expects weights greater than 0 for included rows to avoid confusing results.
Rows with missing or invalid value/weight are ignored. Use the breakdown table to confirm which rows were included in the final average.
Normalized weights are your weights converted into proportions that sum to 1 (or 100%). It helps you see each item’s share of the total weight.
No. All calculations run in your browser. Your inputs and results are not sent to a server or stored.
Yes. You can export your inputs and results to CSV from the History tab for easy pasting into spreadsheets.