Weighted Average Calculator
Calculate weighted average for any values and weights - also doubles as a CGPA calculator.
⚖️ What is Weighted Average?
A weighted average (also called weighted mean) is an average that accounts for the relative importance or frequency of each value in the dataset. Unlike a simple arithmetic mean that treats every data point equally, a weighted average multiplies each value by a weight before summing, and then divides by the total weight. This produces a more representative central value when different items contribute unequally to the whole.
Weighted averages appear in almost every quantitative field. In education, CGPA and GPA calculations weight each course by its credit hours - a 4-credit maths course affects your GPA more than a 1-credit elective. In finance, portfolio returns are weighted by the value of each holding, mutual fund performance is weighted by assets under management, and bond yield calculations weight each coupon by its present value. In science and engineering, weighted averages are used for calibration, sensor fusion, and image processing. Even weather reports use weighted averages - a 5-day forecast weighs nearer days more heavily than distant ones.
The critical insight is that weights represent relative importance, not absolute quantities. A weight of 4 does not mean the value appears 4 times - it means it should count 4 times as much as a value with weight 1. Weights do not need to sum to any specific number (not 1, not 100) because the formula automatically normalises by dividing by the total weight. Weights of [1, 2, 3] are equivalent to [10, 20, 30] or [16.7%, 33.3%, 50%] for this purpose.
This calculator supports two modes: a flexible custom mode for any values and weights (entered as comma-separated lists), and a CGPA mode tailored for Indian university grading systems with letter grades (O, A+, A, B+, B, C, P, F) and credit hours. The breakdown table shows each item's individual contribution to the final average, making it easy to see which subjects or items are most influential.
📐 Formula
📖 How to Use This Calculator
Steps to Calculate Weighted Average
💡 Example Calculations
Example 1 — Exam Scores with Different Weightings
Midterm (30%), Assignment (20%), Final Exam (50%)
Example 2 — Investment Portfolio Return
Three funds with different returns and investment amounts
Example 3 — CGPA Calculation
Semester with 5 subjects using Indian 10-point grading
Example 4 — Weighted Average vs Simple Average
Why weights matter: same scores, very different averages
❓ Frequently Asked Questions
🔗 Related Calculators
What is the formula for weighted average?
Weighted Average = Σ(weight_i × value_i) / Σ(weight_i). Multiply each value by its corresponding weight, sum all the products, then divide by the total weight. Example: values [80, 90, 70] with weights [3, 2, 1]: WA = (3×80 + 2×90 + 1×70) / (3+2+1) = (240+180+70)/6 = 490/6 ≈ 81.67.
How is weighted average different from simple average?
Simple average treats every value equally. Weighted average gives more influence to values with higher weights. If you scored 80 on a test worth 3 credits and 60 on a test worth 1 credit, your simple average is 70 but your weighted average is (3×80 + 1×60) / 4 = 300/4 = 75.
How do I calculate CGPA in Indian universities?
CGPA = Σ(grade_point_i × credit_hours_i) / Σ(credit_hours_i). Multiply each subject's grade point by its credit hours, sum all products, and divide by total credit hours. A subject worth 4 credits with grade A (8 points) contributes 32 to the numerator. Use the CGPA mode in this calculator for automatic computation.
What is the weighted average formula in Excel?
Use =SUMPRODUCT(values_range, weights_range) / SUM(weights_range). Example: values in A1:A5, weights in B1:B5 → =SUMPRODUCT(A1:A5,B1:B5)/SUM(B1:B5). This is the most efficient Excel formula for weighted average.
Do weights need to sum to 100?
No. Weights can be any positive numbers. The formula divides by the sum of weights, which automatically normalises them. Weights of [1, 2, 3] give the same weighted average as [10, 20, 30] or [16.7%, 33.3%, 50%] - all three represent the same relative importance.
What is the weighted average of 80, 90, and 70 with weights 3, 2, 1?
Weighted Average = (3×80 + 2×90 + 1×70) / (3+2+1) = (240 + 180 + 70) / 6 = 490 / 6 ≈ 81.67. The simple average is (80+90+70)/3 = 80. The weighted average is higher because the high-scoring 90 receives a weight of 2, pulling the average upward.
How is weighted average used in finance?
In finance, weighted average appears in portfolio returns (weighted by investment amount), bond yields (weighted by face value), P/E ratios (market-cap-weighted), and cost of capital calculations (WACC). The weighted average cost of capital weights debt and equity costs by their proportions in the capital structure.
What is the weighted average of exam scores with different marks?
If a subject has a midterm worth 30 marks and a final worth 70 marks, the weighted average score is (30 × midterm_score + 70 × final_score) / (30 + 70). A student scoring 75 in midterm and 85 in final: WA = (30×75 + 70×85) / 100 = (2250 + 5950) / 100 = 82.
Can weighted average be outside the range of the input values?
No. The weighted average is always between the minimum and maximum input values (inclusive). It is a form of convex combination of the input values, so it cannot be smaller than the minimum or larger than the maximum value in your dataset.
How does weighted average affect GPA calculations?
Most universities use weighted GPA (CGPA) where credit-intensive subjects count more. A student getting an A in a 4-credit maths course and a B in a 1-credit PE class has a weighted average heavily influenced by maths. Using simple average (equally weighting all subjects) would understate the importance of high-credit core subjects.