Weighted Average Calculator

Enter each value with its weight (points, quantity, hours and so on) to find the weighted average, and see how it differs from the simple average.

Values and weights (2 to 20 rows; the item name is optional; only rows with both a value and a weight are used)

Each value and each weight goes in its own box, so you never need a comma as a separator. A value can be negative (switch to a keyboard with a minus sign if needed). Weights must be 0 or more and do not have to add up to 100 or 1. Use a period as the decimal separator; commas are accepted only as thousands separators (1,234.5), and something like 1,5 is rejected rather than guessed.

Decimal places for the weighted average (rounded)

Weighted average —

Sum of the weights—

Sum of value × weight—

Simple average (no weights)—

Number of rows—

The value copied is the weighted average, without commas. Averages are shown with up to the number of decimal places you chose, and the sums with up to 6; trailing zeros are not shown (73 rather than 73.00).

How to calculate a weighted average

A weighted average multiplies each value by its weight, adds the products, and divides by the sum of the weights.

Weighted average = (sum of value × weight) ÷ (sum of weights)

A weight says how much a value counts toward the average. Typical weights are the points an exam is worth, the quantity of an item, or the hours worked. If every weight is the same, the result is the ordinary (simple) average.

The calculation uses exact fractions and rounds once at the end to the number of decimal places you chose. Negative values are rounded by their size and then given the minus sign back.

Examples

Grades weighted by points: Math 80 (weight 30) and Science 70 (weight 70) give 80 × 30 + 70 × 70 = 7,300. The weights add up to 100, so the weighted average is 73. The simple average is 75.
Average price: 3 items at $100 and 1 item at $150 give 100 × 3 + 150 × 1 = 450. With 4 items in total, the average price is $112.50.
A row with weight 0: it has no effect on the average.

Weighted average vs. simple average

A simple average gives every value the same weight. When the quantities or points differ, it can misrepresent the data. If you buy 3 items at $100 and 1 item at $150, the simple average of the two prices is $125, but the average you actually paid per item is $112.50.

For an average where every value counts equally, use the Mean & Median Calculator.

Notes

Enter a value and a weight together. A row with only one of them shows an error. A row with both boxes empty is ignored.
Values can have up to 9 digits before the decimal point; weights must be 0 or more with up to 9 digits. Both allow up to 6 decimal places.
If every weight is 0 (the weights add up to 0), the weighted average cannot be calculated.
Multiplying all the weights by the same number does not change the result. Weights of 30 and 70 give the same answer as 0.3 and 0.7.
This tool only calculates the average. It does not split a total amount in proportion to the weights.

Frequently asked questions

Do the weights have to add up to 100?

No. They can add up to 100, 1, 7 or anything else. The calculator divides by the sum of the weights, so the absolute size of the weights does not affect the result.

When do I use a weighted average?

When parts of the data count for different amounts: exams worth different points, items bought in different quantities, or periods of different lengths.

Can the values be negative?

Yes. Negative values are included in the calculation correctly.