Quick answer
A weighted average is Σ(value × weight) ÷ Σ weight. Values 90, 80 and 70 with weights 30, 30 and 40 average to (2,700 + 2,400 + 2,800) ÷ 100 = 79.
Enter the values and their weights in the same order. The calculator returns the weighted average.
Related tools: Average Calculator: Arithmetic mean, sum, count, minimum and maximum of a list of numbers. Fraction Calculator: Add, subtract, multiply and divide fractions with simplified and mixed-number results. Ratio Calculator: Simplify a ratio of two whole numbers.
How to use the Weighted Average Calculator
- Type values, for example 90, 80, 70.
- Type weights (same order), for example 30, 30, 40.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Values | Text, such as 90, 80, 70 | — |
| Weights (same order) | Text, such as 30, 30, 40 | — |
Formula and method
Formula
Σ(value × weight) ÷ Σ weight
IEEE-754 double precision; shown to at most 6 decimal places.
Weights are normalised.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Values = 90, 80, 70; Weights (same order) = 30, 30, 40.
| Result | Value |
|---|---|
| Weighted average | 79 |
Example 2
Inputs: Values = 1 2 3; Weights (same order) = 1 1 1.
| Result | Value |
|---|---|
| Weighted average | 2 |
The first line is the headline result (weighted average). IEEE-754 double precision; shown to at most 6 decimal places.
Not the simple mean
The plain average of 90, 80 and 70 is 80, but the 70 carries the heaviest weight (40), pulling the result down to 79.
Typical uses
Course grades, portfolio returns, average cost and survey results with unequal group sizes. Weights need not total 100, and must be positive. Lists must be the same length.
Weights versus a plain average
With scores 90, 80, 70 and weights 30, 30, 40 the weighted average is (2,700 + 2,400 + 2,800) ÷ 100 = 79. The plain average is 80, so the heavier weight on the lowest score pulls the result down.
The weights are divided by their own total, so they do not have to add to 100: weights 3, 3, 4 give the same 79.
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Weights (same order): entering "1" shows "Enter one weight per value." beside that field and no result.
Choosing between the Weighted Average Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Average Calculator](/math/average-calculator/) | numbers | Average (mean) |
| [Fraction Calculator](/math/fraction-calculator/) | numerator 1, denominator 1 and operation | Result |
| [Ratio Calculator](/math/ratio-calculator/) | first number and second number | Simplified ratio |
| [Long Division Calculator](/math/long-division-calculator/) | dividend and divisor | Quotient |
| [Percent Off Calculator](/math/percent-off-calculator/) | original price and discount | Sale price |
Background: rounding and basic arithmetic
Rounding to a place looks at the digit just to its right: 0 to 4 rounds down and 5 to 9 rounds up (the half-up convention, so 2.5 becomes 3). Rounding 838.274 gives 800 to the nearest hundred, 840 to the nearest ten and 838 to the nearest one.
Some systems use banker's rounding (half to even), which sends 2.5 to 2 and 3.5 to 4; check which convention your task requires, and round only at the end of a multi-step calculation.
Assumptions and limitations
- Equal list lengths
- Positive weights
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for weights (same order) to confirm this.
Frequently asked questions
What if weights are equal?
The result is the simple mean.
Do weights have to be percentages?
No, any positive numbers.
How is it different from a mean?
Each value counts differently.
Do the weights have to add up to 100?
No. The calculator divides by the sum of the weights, so 3, 3 and 4 give the same answer as 30, 30 and 40.
Why is the weighted average different from the simple average?
A simple average treats every value equally, while a weighted average lets some values count more.
What does the Weighted Average Calculator calculate?
Weighted mean of values and weights. It returns Weighted average.
What formula does the Weighted Average Calculator use?
Σ(value × weight) ÷ Σ weight. Weights are normalised.
What do I need to enter in the weighted Average Calculator?
You enter Values and Weights (same order).
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Equal list lengths.
What are the limits of this calculator?
Equal list lengths. Positive weights.
What is an example of a weighted Average result?
With values 90, 80, 70 and weights (same order) 30, 30, 40, the weighted average is 79.
Where does the method come from?
The method follows: OpenStax, Introductory Statistics 2e (Rice University): measures of center and spread, correlation and regression.
Related calculators
- Average Calculator — Arithmetic mean, sum, count, minimum and maximum of a list of numbers.
- Fraction Calculator — Add, subtract, multiply and divide fractions with simplified and mixed-number results.
- Ratio Calculator — Simplify a ratio of two whole numbers.
- Long Division Calculator — Divide whole numbers to a chosen number of decimal places.
- Percent Off Calculator — Find the sale price and savings after a percentage discount.
- Rounding Calculator — Round a number to decimal places, with up, down or nearest modes.
Sources
- OpenStax, Introductory Statistics 2e (Rice University): measures of center and spread, correlation and regression
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.