What is a weighted average and when should I use it?

A weighted average assigns different importance (weights) to different values before averaging. Formula: Weighted Average = Σ (value × weight) / Σ weight. Use it when data points contribute unequally: course grades with different credit hours (midterm worth 30%, final worth 40%), portfolio returns with different position sizes, customer satisfaction scores with different response counts, or price indices with different basket quantities. Simple average treats all values equally — correct only when all items have the same importance or frequency.

How do I calculate a weighted average for grades?

Multiply each grade by its weight (credit hours, percentage contribution), sum those products, then divide by total weight. Example: Homework 85% (weight 20%), Midterm 72% (weight 30%), Final 91% (weight 50%). Weighted average = (85×20 + 72×30 + 91×50) / (20+30+50) = (1700+2160+4550)/100 = 8410/100 = 84.1%. Simple average would be (85+72+91)/3 = 82.7% — different because the final (highest score) carries more weight. Weights do not need to sum to 100; a GPA calculation using credit hours (3, 4, 3) works the same way.

What is the weighted average cost of capital (WACC)?

WACC is the weighted average of a company's debt and equity costs, weighted by their proportions in the capital structure. Formula: WACC = (E/V × Re) + (D/V × Rd × (1 − T)), where E = equity value, D = debt value, V = E + D, Re = cost of equity, Rd = pre-tax cost of debt, T = tax rate. Example: 60% equity at 12% cost + 40% debt at 5% cost (with 25% tax) → WACC = (0.6 × 12%) + (0.4 × 5% × 0.75) = 7.2% + 1.5% = 8.7%. WACC is used as the discount rate in NPV calculations — a project must return at least WACC to create value.

How do I calculate a weighted average for a portfolio?

Portfolio weighted return = Σ (position weight × return). Weights = position value / total portfolio value. Example: Stock A: $40,000 (40%), return 15%. Stock B: $35,000 (35%), return 8%. Stock C: $25,000 (25%), return −5%. Portfolio return = 0.40×15% + 0.35×8% + 0.25×(−5%) = 6.0% + 2.8% − 1.25% = 7.55%. A simple average (15+8−5)/3 = 6% ignores that Stock A is the largest position. Use the portfolio weighting to understand your actual blended return and how allocation changes affect total performance.

What is weighted standard deviation and when is it useful?

Weighted standard deviation measures the spread of values around the weighted mean, accounting for different item weights. Formula: σ_w = √[Σ w_i × (x_i − x̄_w)² / Σ w_i]. It is more informative than simple standard deviation when data points have different sample sizes or importances. Example: survey results where 1,000 respondents gave 5 stars and 50 gave 1 star — the variance should reflect that the 1-star ratings are outliers in a large dataset. Weighted variance is used in portfolio risk analysis, statistics education, and quality control where subgroups have different sizes.

Do weights need to add up to 100% or any specific value?

No — weights can be any positive numbers; the calculator normalizes them automatically. A weight of 30 in a set of [30, 20, 40, 10] behaves identically to 30% in a set of percentages. You can use: credit hours (3, 4, 3, 2), response counts (120, 85, 42, 18), arbitrary importance scores (high=3, medium=2, low=1), or market cap in dollars. The only requirement is all weights must be positive and at least two values must be provided. Zero-weight items are excluded from the average (set weight to 0 to temporarily disable a row without deleting it).

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Weighted Average Calculator

Weighted average = Σ (value × weight) / Σ weight. Example: grades 85/72/91 with weights 30/20/40 → (85×30 + 72×20 + 91×40)/(30+20+40) = (2550+1440+3640)/90 = 7630/90 = 84.8. Simple average = (85+72+91)/3 = 82.7 — different because the final (highest score) carries more weight. Weights do not need to sum to 100; they are normalized automatically. Use for GPA calculation, portfolio returns, survey ratings, or any dataset where items contribute unequally.

Calculate weighted average (weighted mean) for any dataset. Enter values and weights — add as many rows as needed. Shows weighted average, simple average, weighted variance, weighted standard deviation, and a per-item contribution breakdown. Weights can be percentages, counts, or any positive numbers.

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Values & Weights

Value

Weight

Weights can be percentages (that add to 100), raw counts, or any positive numbers — they are normalized automatically.

Results

Weighted Average

83.1

Simple Average

Total Weight

100

Weighted Variance

73.49

Weighted Std Dev

8.5726

Breakdown — Contribution per Item

#	Value	Weight	Weight %	Contribution
1	85	30	30.0%	25.5
2	72	20	20.0%	14.4
3	91	40	40.0%	36.4
4	68	10	10.0%	6.8
Total		100	100.0%	83.1

Formula: Weighted Average = Σ (value × weight) / Σ weight. Weights do not need to add to 100 — they are normalized. Weighted Variance = Σ w_i × (x_i − x̄)² / Σ w_i. Use for grade calculations (course weights), portfolio returns (position sizes), survey responses (response counts), or any dataset where items contribute unequally.

How to Use

1
Enter value and weight pairs
Type each item's value in the left column and its weight in the right column. Weights can be percentages, credit hours, position sizes, or any positive numbers — they are normalized automatically.
2
Add or remove rows
Click "+ Add row" to add more items. Click × to remove a row. You need at least 2 rows for a meaningful result.
3
Use a preset
Click "Grade weights" for a GPA example, "Portfolio" for investment returns by allocation, or "Survey (1-5)" for rating distributions.
4
Read the weighted average
The main result is the weighted mean. Compare it to the simple average below — if they differ, your weights are having a material effect on the result.
5
Review the breakdown table
The per-item breakdown shows each value's weight percentage and contribution to the total. Items with the highest weight % drive the weighted average most — use this to understand which inputs have the most impact.

Frequently Asked Questions

What is a weighted average and when should I use it?: A weighted average assigns different importance (weights) to different values before averaging. Formula: Weighted Average = Σ (value × weight) / Σ weight. Use it when data points contribute unequally: course grades with different credit hours (midterm worth 30%, final worth 40%), portfolio returns with different position sizes, customer satisfaction scores with different response counts, or price indices with different basket quantities. Simple average treats all values equally — correct only when all items have the same importance or frequency.
How do I calculate a weighted average for grades?: Multiply each grade by its weight (credit hours, percentage contribution), sum those products, then divide by total weight. Example: Homework 85% (weight 20%), Midterm 72% (weight 30%), Final 91% (weight 50%). Weighted average = (85×20 + 72×30 + 91×50) / (20+30+50) = (1700+2160+4550)/100 = 8410/100 = 84.1%. Simple average would be (85+72+91)/3 = 82.7% — different because the final (highest score) carries more weight. Weights do not need to sum to 100; a GPA calculation using credit hours (3, 4, 3) works the same way.
What is the weighted average cost of capital (WACC)?: WACC is the weighted average of a company's debt and equity costs, weighted by their proportions in the capital structure. Formula: WACC = (E/V × Re) + (D/V × Rd × (1 − T)), where E = equity value, D = debt value, V = E + D, Re = cost of equity, Rd = pre-tax cost of debt, T = tax rate. Example: 60% equity at 12% cost + 40% debt at 5% cost (with 25% tax) → WACC = (0.6 × 12%) + (0.4 × 5% × 0.75) = 7.2% + 1.5% = 8.7%. WACC is used as the discount rate in NPV calculations — a project must return at least WACC to create value.
How do I calculate a weighted average for a portfolio?: Portfolio weighted return = Σ (position weight × return). Weights = position value / total portfolio value. Example: Stock A: $40,000 (40%), return 15%. Stock B: $35,000 (35%), return 8%. Stock C: $25,000 (25%), return −5%. Portfolio return = 0.40×15% + 0.35×8% + 0.25×(−5%) = 6.0% + 2.8% − 1.25% = 7.55%. A simple average (15+8−5)/3 = 6% ignores that Stock A is the largest position. Use the portfolio weighting to understand your actual blended return and how allocation changes affect total performance.
What is weighted standard deviation and when is it useful?: Weighted standard deviation measures the spread of values around the weighted mean, accounting for different item weights. Formula: σ_w = √[Σ w_i × (x_i − x̄_w)² / Σ w_i]. It is more informative than simple standard deviation when data points have different sample sizes or importances. Example: survey results where 1,000 respondents gave 5 stars and 50 gave 1 star — the variance should reflect that the 1-star ratings are outliers in a large dataset. Weighted variance is used in portfolio risk analysis, statistics education, and quality control where subgroups have different sizes.
Do weights need to add up to 100% or any specific value?: No — weights can be any positive numbers; the calculator normalizes them automatically. A weight of 30 in a set of [30, 20, 40, 10] behaves identically to 30% in a set of percentages. You can use: credit hours (3, 4, 3, 2), response counts (120, 85, 42, 18), arbitrary importance scores (high=3, medium=2, low=1), or market cap in dollars. The only requirement is all weights must be positive and at least two values must be provided. Zero-weight items are excluded from the average (set weight to 0 to temporarily disable a row without deleting it).