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Average Calculator
Choose a simple mean, a weighted average, or the score you need on the remaining items to hit a target average. Enter your numbers and see the working.
The simple average
The arithmetic mean is the sum of the values divided by their count. It treats every value as equally important. For 85, 90 and 78 the sum is 253 and the mean is 253 ÷ 3 = 84.33. Use this form when each item counts the same, such as five quizzes with equal marks.
The weighted average
When items matter by different amounts, multiply each value by its weight, add the products, and divide by the total weight:
Weighted average = Σ(value × weight) ÷ Σ(weights)
Weights can be percentages, credit hours, quantities or any positive scale, because dividing by the total weight cancels the scale. Giving 90, 80 and 70 the weights 50, 30 and 20 produces (4,500 + 2,400 + 1,400) ÷ 100 = 83, while the plain mean would be 80. Weighted averages appear in course grades, portfolio returns, and the average price paid across purchases of different sizes.
The score needed to reach a target
Suppose you want an overall average of T across n items you have already completed plus k more. The total points required is T × (n + k). Subtract the points you already hold and divide by k:
Needed per remaining item = (T × (n + k) − current sum) ÷ k
This assumes every item counts equally. If the remaining item is worth more than the earlier ones, switch to weighted mode and solve for the missing score using its weight. Enter the highest possible score to be warned when the target cannot be reached.
A worked grading example
A student has quiz scores of 70 and 80 and wants a final average of 85 across four equally weighted items. The total needed is 85 × 4 = 340 points. The student already holds 150, so 190 points remain, which is 95 on each of the last two items. If only one item remains, the same arithmetic gives 85 × 3 − 150 = 105, which is impossible when the maximum is 100. That is the situation the out-of-reach warning is designed to catch early, while there is still time to change the plan or the target.
Where averages mislead
- An average hides the spread. Two sets with the same mean can look very different; see the standard deviation calculator.
- Averaging percentages from groups of different sizes gives the wrong answer unless you weight by group size.
- Rates such as speed over equal distances need a harmonic mean, not the arithmetic mean used here.
- A single outlier can drag the mean; check the median as well.
Worked example
A course counts coursework at 20%, a midterm at 30% and the final exam at 50%. The marks are 72, 88 and 95.
Inputs
| What do you want to find? | Weighted average |
|---|---|
| Values | 72, 88, 95 |
| Weights (one per value) | 20, 30, 50 |
Result
Weighted average of 3 values.
| Sum of value × weight | 8,830 |
|---|---|
| Sum of weights | 100 |
| Unweighted mean, for comparison | 85 |
Working
| Value | Weight | Value × weight | Share of total weight |
|---|---|---|---|
| 72 | 20 | 1,440 | 20% |
| 88 | 30 | 2,640 | 30% |
| 95 | 50 | 4,750 | 50% |
Accuracy note: Results use standard double-precision arithmetic, so very large or very small values may be rounded. Check important results by another method.
Frequently asked questions
How do I calculate an average?
Add all the values and divide by how many values there are. The average of 4, 8 and 15 is 27 ÷ 3 = 9.
What is the difference between mean and weighted average?
The mean gives every value equal importance. A weighted average multiplies each value by a weight first, so more important values influence the result more.
Do my weights need to add up to 100?
No. The calculator divides by the sum of the weights, so any positive scale gives the same result. Weights of 1, 2, 1 behave exactly like 25, 50, 25.
How do I find the score I need on my next test?
Multiply the target average by the total number of tests including the next one, subtract the points you already have, and divide by the number of tests still to come.
Can I include negative numbers?
Yes for values, and the maths works the same. Weights cannot be negative.
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References and sources
- Standard definitions of the arithmetic mean and weighted mean, as in introductory statistics textbooks.
- NIST/SEMATECH e-Handbook of Statistical Methods: measures of location. Link