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.

Weighted Average Calculator

Q: 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.

Q: 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.

Q: 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.

Q: 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.

Q: 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.

Calculate weighted average for any values and weights — also doubles as a CGPA calculator.

Values (comma or line separated)

Weights (same order as values)

⚖️ 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

Weighted Average = Σ(w_i × x_i) ÷ Σw_i

x_i = each individual value

w_i = the weight assigned to each value

Σ(w_i × x_i) = sum of all (value × weight) products

Σw_i = sum of all weights (the normalisation factor)

Example: Values = [80, 90, 70], Weights = [3, 2, 1] → (3×80 + 2×90 + 1×70) / (3+2+1) = 490/6 ≈ 81.67

CGPA = Σ(Grade Points_i × Credits_i) ÷ ΣCredits_i

Grade Points = numeric value for letter grade (O=10, A+=9, A=8, B+=7, B=6, C=5, P=4, F=0)

Credits = credit hours for each subject

This is the same formula as weighted average, with grade points as values and credits as weights.

📖 How to Use This Calculator

Steps to Calculate Weighted Average

Select a mode: Custom for any values and weights, or CGPA/GPA for the Indian grading system with letter grades and credit hours.

Enter your data. In Custom mode, type values and weights as comma-separated lists (e.g., "80, 90, 70" and "3, 2, 1"). The number of values and weights must match. In CGPA mode, fill each subject row with a grade and credit hours, and add more rows as needed.

Click Calculate to see the weighted average, the simple average for comparison, total weight, and a full per-item breakdown showing each value's contribution.

💡 Example Calculations

Example 1 — Exam Scores with Different Weightings

Midterm (30%), Assignment (20%), Final Exam (50%)

Scores: Midterm = 72, Assignment = 88, Final = 79. Weights: 30, 20, 50

Weighted sum = (30 × 72) + (20 × 88) + (50 × 79) = 2,160 + 1,760 + 3,950 = 7,870

Total weight = 30 + 20 + 50 = 100. Weighted Average = 7,870 ÷ 100 = 78.7

Weighted average score = 78.7 · Simple average = (72+88+79)/3 = 79.67

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Example 2 — Investment Portfolio Return

Three funds with different returns and investment amounts

Fund A: 12% return, ₹2,00,000 invested. Fund B: 8% return, ₹5,00,000. Fund C: 15% return, ₹3,00,000

Weighted sum = (2,00,000 × 12) + (5,00,000 × 8) + (3,00,000 × 15) = 24,00,000 + 40,00,000 + 45,00,000 = 1,09,00,000

Total invested = 10,00,000. Weighted Average Return = 1,09,00,000 ÷ 10,00,000 = 10.9%

Portfolio weighted average return = 10.9% · Simple average = (12+8+15)/3 = 11.67%

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Example 3 — CGPA Calculation

Semester with 5 subjects using Indian 10-point grading

Maths: A+ (9 pts, 4 credits) | Physics: A (8 pts, 3 credits) | Chemistry: B+ (7 pts, 3 credits) | English: O (10 pts, 2 credits) | Lab: A (8 pts, 2 credits)

Numerator = (9×4) + (8×3) + (7×3) + (10×2) + (8×2) = 36 + 24 + 21 + 20 + 16 = 117

Total credits = 4+3+3+2+2 = 14. CGPA = 117 ÷ 14 = 8.36

Semester CGPA = 8.36 / 10

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Example 4 — Weighted Average vs Simple Average

Why weights matter: same scores, very different averages

Scores: 50, 90, 90, 90. Simple average = (50+90+90+90) / 4 = 320/4 = 80

Now weight that 50-score 5 times more (weight=5) and the three 90s equally (weight=1 each): WA = (5×50 + 1×90 + 1×90 + 1×90) / (5+1+1+1) = (250+90+90+90)/8 = 520/8 = 65

Simple average = 80 · Weighted average = 65 — a 15-point difference driven purely by the weights

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❓ Frequently Asked Questions

What is the formula for weighted average?+

Weighted Average = Σ(weight_i × value_i) / Σ(weight_i). Multiply each value by its weight, sum all the products, then divide by the total of all weights. Example: values [80, 90, 70] with weights [3, 2, 1]: WA = (3×80 + 2×90 + 1×70) / 6 = 490/6 ≈ 81.67.

How is weighted average different from simple average?+

Simple average treats every value equally (weight = 1 for all). Weighted average gives more influence to values with higher weights. For values [80, 60] with equal weights, simple average = 70. With weights [3, 1], weighted average = (3×80 + 1×60) / 4 = 300/4 = 75 — higher because 80 has more weight.

How do I calculate CGPA in Indian universities?+

CGPA = Σ(grade_point_i × credit_hours_i) / Σ(credit_hours_i). For each subject, multiply the grade point (O=10, A+=9, A=8, B+=7, B=6, C=5, P=4, F=0) by the subject's credit hours. Sum all these products and divide by total credit hours. Use the CGPA mode in this calculator to do this automatically for up to 20 subjects.

What is the weighted average formula in Excel?+

Use =SUMPRODUCT(values_range, weights_range) / SUM(weights_range). Example: values in A2:A6, weights in B2:B6 → =SUMPRODUCT(A2:A6,B2:B6)/SUM(B2:B6). SUMPRODUCT multiplies each pair of values and sums the results in one step, making it the most efficient approach.

Do weights need to sum to 100 or 1?+

No. Weights can be any positive numbers. The formula divides by the sum of weights, automatically normalising them. Weights [1, 2, 3] give the same result as [10, 20, 30] or [16.7%, 33.3%, 50%]. However, if your weights are already percentages that sum to 100, the denominator in the formula becomes 100 and can be omitted.

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. The weighted average is slightly higher because 90 (the highest score) has a weight of 2, pulling the result upward.

How is weighted average used in finance?+

In finance: portfolio return (weighted by investment amount), bond yield to maturity (weighted by coupon timing), weighted average cost of capital or WACC (weighted by proportion of debt and equity), and price-earnings ratios in stock indices (weighted by market capitalisation). The S&P 500 is a market-cap-weighted index — Apple's weight is proportional to Apple's total market value relative to all 500 companies.

Can weighted average be outside the range of input values?+

No. The weighted average is always between the minimum and maximum input values (inclusive). It is a convex combination: each value is multiplied by a non-negative weight that sums to 1 (after normalisation), so the result cannot exceed the maximum or fall below the minimum of the input set.

What is the weighted average of exam scores with different component weights?+

Example: Midterm (30%) = 75, Assignment (20%) = 88, Final (50%) = 82. Weighted average = (30×75 + 20×88 + 50×82) / 100 = (2,250 + 1,760 + 4,100) / 100 = 8,110 / 100 = 81.1. The final exam has the biggest influence because it carries the most weight (50%).

How does weighted average affect GPA calculations?+

Universities use weighted GPA so that high-credit core subjects count more. A student getting A (8 points) in a 4-credit maths course and C (5 points) in a 1-credit elective has CGPA = (4×8 + 1×5) / 5 = 37/5 = 7.4. A simple average of the two grades would be (8+5)/2 = 6.5 — significantly lower, and unfairly so, because it ignores that maths carries 4× the workload.

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📌 Quick Tips

💡The weighted average equals the simple average only when all weights are equal. Unequal weights shift the average towards the values with higher weights.

💡Weights do not need to sum to 100 or any specific number. The formula automatically normalises them by dividing by the total weight.

💡For CGPA: multiply each subject's grade point by its credit hours, sum the products, then divide by total credit hours. The CGPA mode does this automatically.

💡A weighted average can be less than the simple average if low values have high weights, or more than the simple average if high values have high weights.

💡In finance, portfolio returns are weighted averages where weights are the proportion of capital in each investment.