Free tool Weighted average calculator and formula
A weighted average lets some values count more than others: an exam worth 40% of the grade, a channel with ten times the visits. Type or paste each value with its weight, one pair per line, and the calculator shows the result, how far it is from the plain average, and which item moved it.
- Percent or raw weights
- Paste two columns
- Runs locally
Values and weights
Results update as you type. A label in front of the numbers is kept (“Final exam 81 40%”); a header row is skipped.
Label (optional), value, weight. Separate with spaces, tabs or commas; a block copied from Excel or Google Sheets works as is. Values and weights may carry %, $ or other currency signs. Use thousands separators only in tab-separated data.
Separate with spaces, commas or line breaks.
Same count and order as the values.
Results
Weighted average
82.6
Σ(x·w) ÷ Σw
Simple average
84
Every item counted once.
Weighted − simple
−1.4
Negative: heavy items are below the plain average.
Items
4
Sum of weights (Σw)
100
Sum of products Σ(x·w)
8,260
Weighted standard deviation
8.015
√(Σw(x − x̄w)² ÷ Σw), population form.
Effective number of items
3.5088
Kish: (Σw)² ÷ Σw². Equal weights give n.
Weighted average, step by step
The formula with your numbers.
| Step | Calculation |
|---|---|
| Multiply each value by its weight and add | Σ(x·w) = 95×20 + 88×15 + 72×25 + 81×40 = 8260 |
| Add the weights | Σw = 20 + 15 + 25 + 40 = 100 |
| Weighted average | x̄w = Σ(x·w) ÷ Σw = 8260 ÷ 100 = 82.6 |
| Simple average, for comparison | x̄ = Σx ÷ n = 336 ÷ 4 = 84 |
Item by item
Share of weight is w ÷ Σw. The contributions add up to the weighted average, so the largest one tells you what drives the result.
| # | Item | Value x | Weight w | Share of weight | x × w | Contribution |
|---|---|---|---|---|---|---|
| 1 | Homework | 95 | 20% | 20% | 1900 | 19 |
| 2 | Quizzes | 88 | 15% | 15% | 1320 | 13.2 |
| 3 | Midterm | 72 | 25% | 25% | 1800 | 18 |
| 4 | Final exam | 81 | 40% | 40% | 3240 | 32.4 |
| Total | 100% | 100% | 8260 | 82.6 |
Share these inputs: the values go after the # in the link, so they never reach a server.
https://tapcub.com/tools/weighted-average-calculator
Version v1.0Updated Update history
Why the weighted average moved
The default example is a course grade: homework 20%, quizzes 15%, midterm 25%, final exam 40%.
Weighted vs simple average
The four scores average 84, but the grade is 82.6. The two components that carry the most weight, the final (81) and the midterm (72), are below 84, so they pull the result down. When the weighted average sits above the simple one, the heavy items are the strong ones.
Contributions
Each row’s contribution is its share of weight times its value, and the contributions add up to the result: 19 + 13.2 + 18 + 32.4 = 82.6. The final exam alone supplies 32.4 points, which is why one more point on it is worth 0.4 points of grade.
Weights that are not percentages
Credits, order counts or visits work directly; the formula divides by their total. Percent weights that add to 100 are just a special case. If they add to something else, the calculator says so, because it is usually a typo.
Spread and effective number of items
The weighted standard deviation (8.0 points) shows how far the components sit from 82.6. The effective number of items (3.5 of 4) shrinks when a few weights dominate; survey analysts use it to judge how much information a weighted sample really holds.
A weighted average is only as good as its weights. Check that each weight measures what you mean by “importance”: credits for a GPA, orders for an average order value, visits for a conversion rate.
Paste, check, read
No button to press; results refresh as you type.
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1
Enter the pairs
One item per line: an optional label, the value, then the weight. Or copy a label, value and weight block straight from a spreadsheet. If your columns are weight first, switch the column order.
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2
Or use two lists
Switch the input to two lists when values and weights live in separate columns. They must have the same count.
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3
Read the contributions
Compare the weighted and simple averages, then look at the item table to see which line drives the result. The scenario buttons load a GPA, an average order value and a conversion-rate example.
Multiply, add, divide by the total weight
The weighted average multiplies each value by its weight, adds the products and divides by the sum of the weights. If every weight is the same, it reduces to the ordinary mean. If the weights are percentages that add to 100%, dividing by Σw is the same as dividing by 100.
- x̄w = (x₁w₁ + x₂w₂ + … + xₙwₙ) ÷ (w₁ + w₂ + … + wₙ)
- Weights only need to be zero or positive; they do not have to add up to 1 or 100
- Excel / Google Sheets: =SUMPRODUCT(values, weights) / SUM(weights)
- An average of rates weighted by their denominators equals the overall rate: conversion rates weighted by visits give total conversions ÷ total visits
- Weighted standard deviation here is the population form √(Σw(x − x̄w)² ÷ Σw); frequency weights for a sample would divide by Σw − 1 instead
Weighted average
x̄w = Σ(x·w) ÷ Σw
Course grade: (95×20 + 88×15 + 72×25 + 81×40) ÷ 100 = 82.6
Grade point average
GPA = Σ(grade points × credits) ÷ Σcredits
(3.7×4 + 4.0×3 + 3.3×3 + 3.0×1 + 3.7×2) ÷ 13 = 47.1 ÷ 13 = 3.62
Effective number of items (Kish)
n_eff = (Σw)² ÷ Σw²
Weights 20, 15, 25, 40: 100² ÷ 2850 = 3.51
Average order value across three channels
Three channels with different average order values (AOV) and order counts. Averaging the three AOVs gives $78.83, but that treats the 400 email orders as if they mattered as much as the 1,200 search orders. Weighting by orders gives the store’s true AOV.
| Channel | AOV x | Orders w | x × w (revenue) |
|---|---|---|---|
| Search | $82.50 | 1,200 | $99,000 |
| Social | $56.00 | 800 | $44,800 |
| $98.00 | 400 | $39,200 | |
| Total | 2,400 | $183,000 |
Weighted AOV = $183,000 ÷ 2,400 = $76.25, which is exactly total revenue ÷ total orders. The simple average, $78.83, overstates it because the high-AOV email channel has few orders. Example data.
Where weighted averages go wrong
The arithmetic is easy; picking the weights is where errors creep in.
Averaging rates directly
Organic 3.2%, paid 1.8%, email 6.5%: the plain average is 3.83%, but with 12,000, 8,000 and 1,500 visits the site converts at 2.91%. Weight a conversion rate by its visits, an AOV by its orders.
Dividing by the count instead of the total weight
Σ(x·w) ÷ n is not a weighted average unless the weights add up to n. Divide by Σw.
Percent weights that do not add to 100
20% + 15% + 25% + 30% = 90%. Dividing by 100 would silently lose a tenth of the grade; dividing by Σw rescales. Either way, a missing component is usually the real problem.
Weights that measure the wrong thing
Weighting a channel’s AOV by its visits instead of its orders, or a GPA by hours spent instead of credits, gives a precise answer to the wrong question.
Weighted numbers you do not have to rebuild
Several TapCub reports are weighted averages already, built from the raw events instead of from averages of averages.
Product health score
Activation, retention, engagement depth and referral combined into one weighted index from 0 to 100, with adjustable weights.
Learn moreRevenue by channel
Revenue split by channel, product and cohort, with orders, average order value and LTV beside it.
Learn moreFormulas and custom metrics
Pro mode combines metrics with formulas, and SQL is there for anything the models do not cover.
Learn moreWeighted average questions
Still have a question?
Chat with the team behind TapCub — we usually reply within a few hours on business days.
What is the weighted average formula, and how do you calculate it?
Weighted average = Σ(x × w) ÷ Σw: multiply each value by its weight, add up the products, and divide by the sum of the weights. For scores 95, 88, 72, 81 weighted 20%, 15%, 25%, 40%: (95×20 + 88×15 + 72×25 + 81×40) ÷ 100 = 8,260 ÷ 100 = 82.6.
Do the weights have to add up to 100%?
No. The formula divides by the total weight, so credits, order counts or any positive numbers work. Percentages that add up to 100 are a convenient special case. If percentage weights add up to something else, the calculator still works but flags it, since a missing component is the usual cause.
What is the difference between a weighted and a simple average?
A simple (arithmetic) average counts every value once. A weighted average lets items count in proportion to their weight. The two are equal when all weights are equal; otherwise the weighted average moves toward the heavily weighted values.
How do I calculate a weighted average in Excel or Google Sheets?
Put values in one column and weights in the next, then use =SUMPRODUCT(B2:B5, C2:C5) / SUM(C2:C5). SUMPRODUCT multiplies the two columns row by row and adds the results. You can also paste those two columns into this calculator to check the result and see the steps.
How do I calculate a GPA with credit hours?
Multiply each course’s grade points by its credits, add them up, and divide by the total credits. Grades of 3.7, 4.0, 3.3, 3.0 and 3.7 with 4, 3, 3, 1 and 2 credits give 47.1 ÷ 13 = 3.62. Grade-point scales differ between schools, so convert letter grades with your school’s table first.
Why can’t I just average conversion rates by channel?
Because each rate rests on a different number of visits. Weight each rate by its visits and the result equals total conversions ÷ total visits. In the example, the plain average of 3.2%, 1.8% and 6.5% is 3.83%, while the site actually converts at 2.91%.
What is the effective number of items?
Kish’s effective sample size, (Σw)² ÷ Σw². With equal weights it equals the number of items; the more unequal the weights, the smaller it gets. Survey analysts use it to judge how much a weighted sample is really worth; for a course grade it just shows how concentrated the weights are.
Update history
New features, fixes and data refreshes for this tool, newest first.
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· v1.0
LaunchedFirst release.
Missing something or found an error? Tell us — requests that come up often go into the next update. All tool updates
From an average to its spread
Once you have the average, the next questions are how much the values vary and how unusual a single value is.