Weighted Average Calculator

What this calculator answers

The average of values that don’t count equally: a course grade from categories worth different percentages, a GPA from courses with different credit hours, the average price of purchases of different sizes, or the blended rate on loans with different balances. It shows what each item adds to the result, how far the plain average is from it, and which item pulls the average down most. Switched to Value needed, it works backward: the score one item still to come, such as a final exam, needs for the average you want.

How to use it

• Find: Weighted average, or Value needed for a target average.
• Weights are: Percentages when the weights are parts of 100, such as a syllabus that makes the final exam 35% of the grade. Other numbers for credits, pounds, shares, balances or counts. The math is the same; percentages also get a check that they add up to 100.
• Values and weights: one row per item. Value is the score, price or rate (negative values are fine: press ± on a phone). Weight is how much it counts, 0 or more. Name is optional and labels the row in the results. Add item adds a row; Paste rows reads two or three columns copied from a spreadsheet, in the order value, weight, name. The running Total weight under the rows shows what the weights add up to as you type.
• Target average, Weight still to come and the optional Lowest possible value and Highest possible value appear for Value needed. The range (such as 0 to 100 for a percentage score) lets the calculator say when a target is out of reach or already secured.

Results update as you type. The Try buttons load the cases worked through below: the score needed on a final, a GPA, an average price per pound and a blended loan rate. To compare two plans, such as two target grades, press Save for comparison, change the inputs and save again. When the weights are whole-number counts entered as Other numbers, Continue in the Mean, Median and Mode Calculator carries the list over as a frequency table for the median and quartiles.

How to calculate a weighted average

Multiply each value by its weight, add the products, and divide by the sum of the weights.

$$\bar{x}_w = \frac{\sum w_i x_i}{\sum w_i} = \frac{w_1 x_1 + w_2 x_2 + \dots + w_n x_n}{w_1 + w_2 + \dots + w_n}$$

• $x_i$ is the value of item $i$: a score, a price, a rate.
• $w_i$ is its weight: a percentage, credits, a quantity, a balance. Weights are 0 or more, and at least one is above 0.
• $\sum w_i x_i$ is the sum of the products, and $\sum w_i$ the total weight.

Only the proportions of the weights matter. Dividing by the total turns each weight into its share, so weights of 15, 20, 30 and 35, of 0.15, 0.2, 0.3 and 0.35, or of 3, 4, 6 and 7 all give the same average. Each item’s share times its value is its contribution, and the contributions add up to the average.

In a spreadsheet with the values in B2:B5 and the weights in C2:C5, the same calculation is =SUMPRODUCT(B2:B5,C2:C5)/SUM(C2:C5). The results show this line with your own ranges.

Weighted grade example: exams, quizzes and homework

A course counts homework 15%, quizzes 20%, the midterm exam 30% and the final exam 35%. The category averages are 97, 84, 71 and 83.

1. Multiply each score by its weight: 97 × 15 = 1,455; 84 × 20 = 1,680; 71 × 30 = 2,130; 83 × 35 = 2,905.
2. Add the products: 1,455 + 1,680 + 2,130 + 2,905 = 8,170.
3. Add the weights: 15 + 20 + 30 + 35 = 100.
4. Divide: 8,170 ÷ 100 = 81.7.

The simple average of the four scores is (97 + 84 + 71 + 83) ÷ 4 = 83.75, which is 2.05 higher, because the two exams carry 65% of the weight and are the lowest scores. The contributions are 14.55 from homework, 16.8 from quizzes, 21.3 from the midterm and 29.05 from the final, which add up to 81.7.

The midterm pulls the grade down most: without it, the average of the other three would be (8,170 − 2,130) ÷ 70 = 86.29, which is 4.59 higher. The Average without it column shows this for every row.

What score do I need on the final?

Take the weighted total your target average needs, subtract what the graded work already supplies, and divide by the final’s weight. Before the final exam, the same course has three scores covering 65% of the grade: 97 × 15 + 84 × 20 + 71 × 30 = 5,265, so the current average is 5,265 ÷ 65 = 81. To finish with 80:

1. Total weight with the final: 65 + 35 = 100.
2. An average of 80 needs a weighted total of 80 × 100 = 8,000.
3. The final must supply 8,000 − 5,265 = 2,735.
4. Divide by its weight: 2,735 ÷ 35 = 78.14. With whole-point scores, that means at least 79.

The general formula, for a target average $T$ and an item still to come with weight $r$, is

$$x_{\text{needed}} = \frac{T \times \left(\sum w_i + r\right) - \sum w_i x_i}{r}$$

A target of 90 would need (9,000 − 5,265) ÷ 35 = 106.71, more than the 100 maximum, so it is out of reach: a perfect 100 gives (5,265 + 35 × 100) ÷ 100 = 87.65. At the other end, a 0 on the final would leave 52.65. Each point on the final adds 0.35 to the course average, so each point of target needs 100 ÷ 35 ≈ 2.86 points on the exam. The Value needed for other target averages table lists the neighbors: 49.57 for 70, 63.86 for 75 and 92.43 for 85.

When weights are percentages that don’t add up to 100

The average still works: it divides by whatever the weights add up to, so each item counts as its share of that total. What the result means is the question.

• Less than 100 because some work is still to come. With only the homework, quizzes and midterm entered (15 + 20 + 30 = 65%), the result is 81, your current average on the work graded so far, not your final grade. Dividing by 100 instead, 5,265 ÷ 100 = 52.65, treats the missing 35% as a score of 0. The calculator says what the weights add up to and offers a button to find the value needed on the rest.
• Decimals instead of percentages. Weights of 0.15, 0.2, 0.3 and 0.35 add up to 1 and give the same 81.7. The calculator points out that they look like decimals. Decimals that add up to less than 1, such as 0.15 + 0.2 + 0.3 = 0.65, are read as 65% of the total, with 35% still to come.
• More than 100. The average divides by the larger total, which shrinks every item’s share. Check for a typo or a category entered twice before trusting it.

Weighted average price or cost per unit

Weight each price by the quantity bought at it. For example, coffee beans bought three times: 40 lb at $11.50, 25 lb at $12.20 and 60 lb at $10.80.

• Total cost: 40 × 11.50 + 25 × 12.20 + 60 × 10.80 = 460 + 305 + 648 = $1,413.
• Total quantity: 40 + 25 + 60 = 125 lb.
• Average price: $1,413 ÷ 125 = $11.304 a pound, about $11.30.

The simple average of the three prices, $11.50, is too high because the largest order was the cheapest. The same method gives the average cost per share of a stock bought in several lots; to add fees and a current value to that, use a dollar-cost averaging calculator.

GPA and blended rates

A GPA is a weighted average of grade points, weighted by credit hours. With an A (4.0) in a 3-credit biology course, a B+ (3.3) in a 4-credit calculus course, an A− (3.7) in a 3-credit English course and a C (2.0) in a 2-credit art course, the grade points are 12 + 13.2 + 11.1 + 4 = 40.3 over 12 credits, a GPA of 40.3 ÷ 12 = 3.358. The simple average of the four grades is 3.25; the GPA is higher because the C carries only 2 credits. Schools differ in their scales and in how they show the result. The University of Florida, for example, counts an A− as 3.67 and a B+ as 3.33, which makes the same grades 40.33 grade points, and it shows a GPA to the hundredths place without rounding up: 40.33 ÷ 12 = 3.3608 is shown as 3.36. Enter the grade points from your own school’s scale.

A blended interest rate weights each rate by its balance. For example, $12,000 at 6.8%, $8,500 at 4.5% and $3,200 at 7.9% blend to 145,130 ÷ 23,700 = 6.124% on the $23,700 total, compared with a simple average of 6.4%. A year’s interest on those balances at those rates is $1,451.30, the same as 6.124% of $23,700. The blend changes as the balances do.

Weighted vs. simple average: why the results differ

A simple average counts every value once. A weighted average counts each value in proportion to its weight, so the two are always equal when every weight is the same (or every value is) and usually differ otherwise. The weighted average is lower when the heavy items have the low values (the course above: 81.7 vs. 83.75) and higher when the heavy items have the high values (the GPA: 3.358 vs. 3.25).

Counts are weights too. If three students scored 90 and one scored 70, the average of all four is (3 × 90 + 1 × 70) ÷ 4 = 85, while the simple average of the two scores, 80, treats one 70 as if it were as common as three 90s. This is also why averaging group averages or percentages from groups of different sizes goes wrong unless each is weighted by its group’s size.

Reading the result

• The headline is the weighted average, or for Value needed the score the item still to come needs. Its label says when that score is out of reach (above the highest possible value) or already secured (below the lowest).
• Simple average is the plain average of the values, with how far weighting moves the result.
• Total weight is what the weights add up to, with the sum of value × weight under it.
• Lowers the average most names the item whose removal would raise the average the most, and the average without it. For Value needed, the tiles show the current average, the share still to come and the range of final averages the remaining item allows.
• How this was calculated lists the products, the sums and the division with your numbers, then the spreadsheet formula.
• The table gives each item’s share of the total weight, its contribution and the average without it, with a totals row. Download CSV saves it.
• The bar splits the average into each item’s contribution, for 2 to 12 items when every value is 0 or more.
• Value needed for other target averages (Value needed only) repeats the calculation for targets above and below yours.

Assumptions and limitations

• Values are used as entered. The calculator doesn’t drop a lowest score, apply a curve or cap a category; if your course does, enter the values after those rules.
• Value needed treats what is left as one item. With several items still to come, enter their combined weight: the answer is what they must average together, each counted by its own weight.
• Whether a final average just below a cutoff, such as 79.95 for an 80, rounds up is set by your school or agreement, not by the math.
• Averages are rounded for display only, to two more decimal places than the most precise value entered (from 2 to 6).
• A course grade, GPA or loan rate from this page is an educational estimate. The official figure is whatever your school or lender calculates under its own rules.

Common mistakes

• Dividing by the number of items instead of the total weight. That gives the simple average, 83.75 in the course example instead of 81.7.
• Dividing by 100 when the weights entered so far add up to less. Missing work then counts as 0: 52.65 instead of the current 81.
• Mixing decimals and percentages. Typing the midterm’s weight as 0.3 while the others are 15, 20 and 35 makes it count almost nothing, and the grade comes out 86.22 instead of 81.7. When percentages don’t add up to 100 and the list mixes the two, the calculator says so.
• Reading a current average as the final grade. 81 on 65% of the course still leaves 35% to be decided: the final grade can end anywhere from 52.65 to 87.65.
• Averaging prices, rates or percentages from groups of different sizes without weights. Weight each by its quantity, balance or group size.