Academics & Courses
Weighted Grade Calculator
Calculate your overall course grade from assignments, quizzes, and midterm weights, plus find the exact score needed on your final exam.
Syllabus WeightingLetter Grades (A–F)Final Target Solver
Weighted Average Calculator
Preset
Every weighted average calculation runs inside the browser. No dataset is uploaded, stored on a server, or shared.
About the Weighted Average Calculator
A weighted average calculator multiplies every individual value by its weight, adds the products into a weighted sum, then divides that weighted sum by the total of weights. The output is the weighted average, named the weighted mean or the weighted arithmetic mean in statistics.
This weighted average calculator delivers 4 benefits: a weighted average calculation that updates on every keystroke, a step-by-step breakdown of each value-weight pair, a direct comparison against the standard arithmetic mean, and control over decimal places and the rounded result.
Students, teachers, and analysts use the weighted average calculator for 5 tasks: course grades, grade point average (GPA), portfolio returns, average selling price, and discrete probability distributions.
The calculator holds 5 parts: value fields, weight fields, a preset selector for grade and GPA and portfolio work, a decimal places control, and a result panel that reports the weighted average, the sum of weighted values, the sum of weights, and the count of selected rows.
How to Use the Weighted Average Calculator
To use the weighted average calculator, enter each value with the weight that value carries, then read the weighted average from the result panel. The calculation runs on every keystroke, so no Calculate button is needed.
Enter Values and Weights
Enter each individual value in the Value field and the matching weight in the Weight field. One row holds one value-weight pair, and the calculator accepts an unlimited number of rows.
- Add entry creates a new row. The Enter key on the last row does the same thing.
- Label names the row, such as Homework, Midterm, or Equities. The label stays optional.
- Preset switches the wording of both columns across 4 modes: General, Course Grades, GPA, and Portfolio.
- Decimal places sets the rounded result between 0 and 6 digits.
- Reset clears the dataset and returns 3 empty rows.
Weights accept decimals, whole numbers, percentages, and credits. The calculator will ignore blanks, include zeros in the count of selected rows, and flag invalid tokens such as letters or stray symbols under the entry area.
View Your Weighted Average
View your weighted average at the top of the result panel, printed in the decimal places you selected. Four supporting figures sit below the result:
- Sum of weighted values — every value multiplied by its weight, added together.
- Sum of weights — the total of weights across the dataset.
- Selected rows — the count of value-weight pairs used in the calculation.
- Simple average — the standard arithmetic mean of the same values, for comparison.
A mini visualization under those figures splits one bar by weight, so the share held by each individual value stays visible. Copy result copies the number alone. Copy step-by-step breakdown copies every multiplication, the weighted sum, the total of weights, and both averages as plain text.
What Is a Weighted Average?
A weighted average is an average in which each value carries a weight that sets how much that value affects the result. The weighted average equals the weighted sum divided by the total of weights.
The weighted average definition covers 3 names for one statistical measure: weighted average, weighted mean, and weighted arithmetic mean. A normal mean treats every value as equal, so every weight equals 1. A weighted average replaces those equal weights with numbers that describe importance, frequency, quantity, or size.
A dataset of 3 exam scores shows the difference. Scores of 90, 75, and 60 produce an arithmetic mean of 75. Attach weights of 3, 2, and 5 to those same numerical grades, and the weighted average drops to 72, because the score of 60 holds half of the total of weights.
(90 × 3) + (75 × 2) + (60 × 5) = 720 → 720 ÷ 10 = 72
How to Calculate a Weighted Average
To calculate a weighted average, multiply each value by its weight, add the products, add the weights, then divide the weighted sum by the sum of weights. The weighted average method needs 4 steps and works on any dataset of value-weight pairs.
Step-by-Step Weighted Average Calculation
Calculate the weighted average of 3 modules scored 88, 74, and 91, carrying 4 credits, 2 credits, and 6 credits:
- Multiply each value by its weight. 88 × 4 = 352, 74 × 2 = 148, and 91 × 6 = 546.
- Add the products into the weighted sum. 352 + 148 + 546 = 1,046.
- Add the weights into the total of weights. 4 + 2 + 6 = 12 credits.
- Divide the weighted sum by the sum of weights. 1,046 ÷ 12 = 87.17.
The weighted average of those 3 modules is 87.17. The simple average of the same 3 values reaches 84.33, so the 6-credit module lifts the semester average by 2.83 points.
| Module | Value | Weight (credits) | Weighted value |
|---|---|---|---|
| Module A | 88 | 4 | 352 |
| Module B | 74 | 2 | 148 |
| Module C | 91 | 6 | 546 |
| Total | — | 12 | 1,046 |
| Weighted average | — | — | 87.17 |
Weighted Average Formula
The weighted average formula is x̄w = ∑(wi × xi) ÷ ∑wi, the sum of weighted values divided by the sum of weights.
x̄w = ∑ wi · xi ∑ wi
The weighted average formula holds 3 terms. Each individual value takes the symbol xi, each weight takes the symbol wi, and the weighted arithmetic mean takes the symbol x̄w. Multiplying every value-weight pair produces the weighted sum in the numerator, and adding every weight produces the total of weights in the denominator.
Weights carry any consistent unit: percentages, credits, dollars, shares, counts, or probabilities. The division by the total of weights cancels the scale, so weights of 2, 3, and 5 return the same weighted average as weights of 20%, 30%, and 50%.
Weighted Average Example
A course grade built from 3 assessments shows the weighted average formula in use. Homework scores 92 at a 20% grade weight, the midterm scores 78 at 30%, and the final exam score reaches 85 at 50%.
| Assignment | Grade value | Percentage weight | Weighted grade value |
|---|---|---|---|
| Homework | 92 | 20% | 1,840 |
| Midterm exam | 78 | 30% | 2,340 |
| Final exam | 85 | 50% | 4,250 |
| Total | — | 100% | 8,430 |
| Final grade | — | — | 84.30 |
(92 × 20) + (78 × 30) + (85 × 50) = 8,430 → 8,430 ÷ 100 = 84.30
The final grade lands at 84.30, while the simple average of 92, 78, and 85 reaches 85.00. The 30% midterm weight pulls the course grade down by 0.70 points.
Weighted Average vs. Simple Average
The weighted average assigns a different weight to each value, and the simple average assigns the same weight to every value. The difference between mean and weighted average appears whenever the weights stop matching each other.
| Attribute | Weighted average | Simple average |
|---|---|---|
| Weighting | Each value carries its own weight | Every value carries a weight of 1 |
| Formula | Sum of weighted values ÷ sum of weights | Sum of values ÷ number of values |
| Inputs | Value-weight pairs | Values only |
| Use | Course grades, GPA, portfolio returns, probability | Datasets of equal importance |
| Result on 92, 78, 85 | 84.30 at weights of 20%, 30%, 50% | 85.00 |
When Does Weighted Average Equal the Arithmetic Mean?
The weighted average equals the arithmetic mean when every weight in the dataset holds the same number. Equal weights cancel in the division, which reduces the weighted average formula to the sum of values divided by the count of values.
Three values weighted 5, 5, and 5 return the same result as the same 3 values weighted 1, 1, and 1. The weighted average calculator prints a note whenever the weighted average and the standard arithmetic mean match, so equal weighting stays obvious.
When to Use a Weighted Average
Use a weighted average when values in the dataset carry different importance, frequency, quantity, or size. Six situations call for the weighted average method.
- Course grades built from assignments and exams that hold different grade weights.
- Grade point average (GPA) across modules that hold different credits.
- Portfolio returns across holdings that hold different allocations.
- Average selling price across orders that hold different weight quantities.
- Survey results across segments that hold different sample sizes.
- Probability distributions where each outcome holds its own probability.
How to Choose Weights
Choose weights by measuring the quantity that makes one value count more than another value. Three weighting schemes cover most datasets:
- Percentage weighting — a grading scheme states 20% homework, 30% midterm, 50% final exam.
- Credit weighting — a transcript states 4 credits, 3 credits, and 5 credits per course.
- Quantity weighting — an invoice states 120 units, 45 units, and 300 units per order.
Keep one unit across the full dataset. Mixing credits with percentages inside a single weighted average calculation distorts the total of weights and the result.
What If Weights Don't Add Up to 100%?
Weights do not need to add up to 100%. The weighted average formula divides by the sum of weights, which auto-normalizes any scale, so weights of 4, 3, and 5 credits return a valid weighted average without conversion.
Two cases still need attention. A strict sum-to-1 scheme, used in probability distributions, requires weights that total exactly 1.0 for the result to read as an expected value. A total of weights equal to 0 makes the division impossible, so the calculator returns no result and prints a warning instead.
Weighted Average for Grades and GPA
Academic grading runs on 2 weighted averages: the course grade, weighted by assignment weight, and the grade point average (GPA), weighted by credits.
Weighted Average for Grades
Calculate a weighted grade by multiplying each grade value by its percentage weight, then dividing the total by 100. A grading scheme of 40% coursework and 60% final exam turns a coursework mark of 72 and a final exam grade of 65 into a final grade of 67.80.
(72 × 40) + (65 × 60) = 6,780 → 6,780 ÷ 100 = 67.80
Final grade planning reverses the same weighted average calculation. Enter the marks already earned, add a row for the final exam score, then adjust that row until the weighted average reaches the target mark percentage. A student holding 72 in coursework worth 40% needs 85.33 on a final exam worth 60% to finish the course at 80.
Weighted Average for GPA
Calculate GPA by multiplying each course grade point by the credits attached to that course, then dividing by the total credits. The 4.0 GPA scale, also written as the 4-point grading scale, converts every letter grade into a grade point.
| Letter grade | Grade point | Letter grade | Grade point |
|---|---|---|---|
| A | 4.0 | C+ | 2.3 |
| A− | 3.7 | C | 2.0 |
| B+ | 3.3 | C− | 1.7 |
| B | 3.0 | D | 1.0 |
| B− | 2.7 | F | 0.0 |
A semester of 4 courses — 4.0 across 4 credits, 3.0 across 3 credits, 3.7 across 5 credits, and 2.7 across 2 credits — produces 48.9 weighted grade points across 14 credits, so the semester GPA reaches 3.49.
Unweighted GPA
Unweighted GPA caps every course at 4.0 and ignores course difficulty. A high school GPA of 4.0 unweighted means straight A grades across College Prep classes and Advanced Placement (AP) courses alike.
Weighted GPA
Weighted GPA adds points for course difficulty, which lifts the scale above 4.0. Most high school grading schemes add 1.0 for AP courses and International Baccalaureate (IB) courses and 0.5 for Honors courses.
Weighted Average Applications
The weighted average appears across statistics, finance, academic grading, and mathematics, wherever proportions and ratios differ between the values of a data set.
Weighted Average in Statistics
Statistics uses the weighted average to compute the expected value of a discrete probability distribution. Each outcome takes its probability as the weight, and the weights sum to 1.0, so the weighted sum alone returns the expected value.
A fair 6-sided die carries 6 outcomes at a probability of 0.1667 each, which produces an expected value of 3.5. Weighted averages also combine survey segments by sample size, so a group of 900 respondents counts 3 times a group of 300 respondents.
Weighted Average in Finance
Finance uses the weighted average in 4 calculations: portfolio returns, stock market indices, average selling price, and interest rates.
- Portfolio returns weight the return of each holding by its allocation. Returns of 11.4%, 3.2%, and 1.5% at allocations of 55%, 30%, and 15% produce 7.46%.
- Stock market indices such as the S&P 500 weight each company by market capitalization, so larger companies move the index more.
- Average selling price weights each price by the weight quantity sold, which corrects the distortion of averaging prices alone.
- Weighted average interest rate weights each rate by the outstanding balance of the matching loan.
Weighted Average vs Other Types of Averages
Mathematics defines 4 averages for a data set: the weighted average, the arithmetic average, the geometric average, and the harmonic average. Each average answers a different question about the same values.
| Average | Method | Result |
|---|---|---|
| Weighted average | Sum of weighted values ÷ sum of weights, at weights of 1, 2, 7 | 10.60 |
| Arithmetic average | Sum of values ÷ number of values | 8.33 |
| Geometric average | Cube root of the product of the 3 values | 7.56 |
| Harmonic average | Count ÷ sum of the reciprocals | 6.75 |
Arithmetic Average
The arithmetic average adds every value and divides by the number of values. The standard arithmetic mean fits datasets of equal importance, such as 30 daily temperature readings taken by one station.
Geometric Average
The geometric average multiplies n values and takes the nth root of that product. Compounding figures use the geometric average, such as an annual growth rate measured across 5 years.
Harmonic Average
The harmonic average divides the count of values by the sum of their reciprocals. Rates measured over a fixed distance or a fixed cost use the harmonic average, such as an average speed across 2 legs of one journey.
CALCULATOR SUITE
Specialized Weighted Calculators
Explore our dedicated calculation tools tailored for academic grading, GPA, statistical datasets, inventory costing, and finance.
High School & College
Weighted GPA Calculator
Compute semester and cumulative GPA with standard AP (+1.0), Honors (+0.5), and IB grade point weighting on 4.0 and 5.0 scales.
AP, IB & HonorsQuality PointsSemester & Cumulative
Percentages & Math
Weighted Percentage Calculator
Calculate weighted percentage totals from percentage or raw score components, and calculate exact percentage contribution per item.
Percentages & Raw ScoresWeight Shares100% Normalization
Statistics & Datasets
Weighted Mean Calculator
Compute the arithmetic weighted mean for any dataset or frequency distribution, and solve for any missing value or weight.
Missing Value SolverFrequency WeightsFull Step Breakdown
University Grading
Weighted Average Mark (WAM)
Work out your university WAM across course units with credit-point and year-level weighting schemes and Honours classifications.
Credit-Point WeightingYear Level MultipliersHonours Bands
Finance & Procurement
Weighted Average Cost Calculator
Determine the weighted unit cost across multiple inventory batches, wholesale lots, or tiered purchase price orders.
Batch Lot CostingUnit Cost BreakdownValuation Solver
Accounting & Stock
Weighted Average Inventory (COGS)
Calculate ending inventory valuation and Cost of Goods Sold (COGS) using periodic and perpetual moving average costing methods.
Periodic & Moving AvgCOGS & Ending StockTransaction Log
Loans & Consolidation
Weighted Average Interest Rate
Calculate the effective blended interest rate and annual/monthly finance charges across mortgages, student loans, or credit cards.
Blended Rate APRLoan ConsolidationMonthly Interest Cost
Trading & Markets
Volume Weighted Average Price (VWAP)
Calculate intraday VWAP, typical price bars (H+L+C)/3, running session volume, and anchored price benchmark deviations.
Intraday Price BarsAnchored VWAPSession Deviation %
Frequently Asked Questions
Is Weighted Mean the Same as Weighted Average?
Yes, the weighted mean is the same as the weighted average. Statistics prefers the term weighted arithmetic mean, academic grading prefers weighted average, and both terms name the sum of weighted values divided by the sum of weights.
Can Weights Be Decimals?
Yes, weights can be decimals. Probabilities of 0.25 and 0.75, credits of 1.5, and allocations of 33.33% all work inside the weighted average formula, because the total of weights normalizes any scale.
Do Weights Have to Add Up to 100%?
No, weights do not have to add up to 100%. Credits of 4, 3, and 5 total 12 and still produce a correct weighted average, since the division by the sum of weights rescales the weighted sum automatically.
Can Weighted Average Handle Negative Numbers?
Yes, a weighted average handles negative numbers. Negative values, such as a −4.2% return, calculate normally. Negative weights push the result outside the range of the values, so the calculator flags any negative weight in the entry area.
How Do You Calculate a Weighted Average in Excel?
Calculate a weighted average in Excel with =SUMPRODUCT(A2:A10,B2:B10)/SUM(B2:B10), where column A holds the values and column B holds the weights. SUMPRODUCT builds the weighted sum, and SUM builds the total of weights.
How Do You Calculate a Weighted Average in Google Sheets?
Calculate a weighted average in Google Sheets with =AVERAGE.WEIGHTED(A2:A10,B2:B10), where A2:A10 holds the values and B2:B10 holds the weights. The SUMPRODUCT formula from Excel works in Google Sheets too.
How Do You Calculate a Weighted Average for Grades?
Calculate a weighted average for grades by multiplying each grade value by its grade weight, adding those weighted grade values, then dividing by the total weights. Scores of 92, 78, and 85 at weights of 20%, 30%, and 50% produce a final grade of 84.30.
How Do You Calculate a Weighted Average When Coursework Is Worth 40%?
Multiply the coursework mark by 40, multiply the exam mark by 60, add both weighted grade values, then divide by 100. Coursework of 72 and an exam of 65 produce a course grade of 67.80.
What Is the Difference Between Weighted and Unweighted GPA?
Weighted GPA counts course difficulty and unweighted GPA ignores it. Unweighted GPA caps at 4.0 on the 4-point grading scale, while weighted GPA adds 1.0 for AP courses and IB courses and 0.5 for Honors courses, which lifts a high school GPA above 4.0.
How Do You Calculate a Weighted Average Interest Rate?
Calculate a weighted average interest rate by weighting each rate by its loan balance. Balances of $20,000 at 6% and $5,000 at 3% produce (120,000 + 15,000) ÷ 25,000, a weighted average interest rate of 5.4%.
Can You Average Averages?
Yes, you can average averages, on the condition that each average carries the count behind it as its weight. Averaging averages without weights treats a group of 900 students and a group of 30 students as equals.
Is the Average of Averages Accurate?
No, the average of averages is not accurate at unequal group sizes. Class averages of 90 across 10 students and 60 across 90 students return 75 unweighted, while the weighted average returns 63 — a 12-point error.
Calculate Weighted Average Online
Every value-weight pair, one weighted average.
The weighted average calculator multiplies each value by its weight, adds the weighted sum, divides by the total of weights, and prints the weighted average beside the standard arithmetic mean. Course grades, GPA, portfolio returns, and probability distributions all run through the same 4 steps.
Open the Weighted Average Calculator