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Weighted Average Calculator

Calculate the weighted average (weighted mean) of values with assigned weights. Each value contributes to the average proportionally to its weight.

Reviewed by Chase FloiedUpdated

This free online weighted average calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.

Enter the values to average

Enter corresponding weights (must match number of values)

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the Weighted Average Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

2

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

3

Read the results

The Weighted Average Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.

4

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

Formula Reference

Weighted Average Calculator Formula

See calculator inputs for the governing equation

Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.

When to Use This Calculator

  • •Use the Weighted Average Calculator when you need a quick mathematical result without writing out all the steps manually, saving time on repetitive calculations.
  • •Use it to verify hand calculations on tests or assignments and catch arithmetic mistakes.
  • •Use it when teaching or explaining mathematical concepts to others, demonstrating how changing inputs affects the result.
  • •Use it to explore the behavior of mathematical functions across a range of inputs.

About This Calculator

The Weighted Average Calculator is a free mathematical calculation tool for students, educators, and professionals who need quick, reliable results. Calculate the weighted average (weighted mean) of values with assigned weights. Each value contributes to the average proportionally to its weight. The underlying algorithms implement well-established mathematical formulas and numerical methods. Results are computed instantly in the browser. This tool is useful for learning, verification of hand calculations, and rapid exploration of mathematical relationships. All computation happens locally — no data is sent to a server.

About Weighted Average Calculator

A weighted average assigns different levels of importance (weights) to each value before averaging. While a simple arithmetic mean treats all values equally, a weighted average reflects the reality that some data points matter more than others. GPA calculations use weighted averages where course credits serve as weights — an A in a 4-credit course contributes more than an A in a 1-credit course. Financial portfolio returns are weighted by the proportion invested in each asset. In physics, the center of mass is a weighted average of positions, with masses as weights. Survey results are often weighted to account for demographic representation. The weighted average always lies between the minimum and maximum of the input values, and it equals the simple average when all weights are equal. Understanding weighted averages is crucial for making informed decisions with data of varying reliability, importance, or frequency.

The Math Behind It

The weighted average generalizes the arithmetic mean. When all weights are equal, it reduces to the simple average. Key properties: (1) The weighted average lies between min(xᵢ) and max(xᵢ). (2) If weights are probabilities summing to 1, the weighted average equals the expected value E[X]. (3) The weighted average minimizes the weighted sum of squared deviations: argmin_c Σwᵢ(xᵢ − c)². In statistics, the weighted least squares method uses weighted averages to account for heteroscedasticity (unequal variances). The weighted variance is Σwᵢ(xᵢ − x̄w)² / Σwᵢ, analogous to the ordinary variance. In signal processing, weighted moving averages smooth data while allowing recent observations to have more influence. Convex combinations — weighted averages where weights are non-negative and sum to 1 — are fundamental in convex geometry, optimization, and barycentric coordinates. The inverse-variance weighted average minimizes the variance of the combined estimate.

Formula Reference

Weighted Average

x̄w = (w₁x₁ + w₂x₂ + ... + wₙxₙ) / (w₁ + w₂ + ... + wₙ)

Variables: xᵢ = values, wᵢ = weights

Worked Examples

Example 1: GPA Calculation

Calculate GPA with grades A(4.0) in 4 credits, B(3.0) in 3 credits, A-(3.7) in 3 credits

Step 1:Weighted sum: (4.0 × 4) + (3.0 × 3) + (3.7 × 3) = 16 + 9 + 11.1 = 36.1
Step 2:Total credits: 4 + 3 + 3 = 10
Step 3:GPA = 36.1 / 10 = 3.61

Weighted GPA = 3.61

Example 2: Portfolio Return

Portfolio: 50% stocks (+12%), 30% bonds (+4%), 20% cash (+1%)

Step 1:Weighted sum: (0.50 × 12) + (0.30 × 4) + (0.20 × 1) = 6 + 1.2 + 0.2 = 7.4
Step 2:Weights sum to 1.00 (percentages)
Step 3:Weighted average return = 7.4%

Portfolio return = 7.4%

Common Mistakes & Tips

  • !Not matching the number of values with the number of weights.
  • !Forgetting to divide by the sum of weights instead of the count of values.
  • !Using negative weights unintentionally — weights should typically be non-negative.
  • !Confusing weights (importance) with values (data points).

Related Concepts

Average (Arithmetic Mean)

The special case of weighted average with all equal weights.

Geometric Mean

A multiplicative average for rates and ratios.

Used in These Calculators

Calculators that build on or apply the concepts from this page:

Average Calculator (Mean)

Frequently Asked Questions

How is a weighted average different from a regular average?

A regular average treats all values equally. A weighted average multiplies each value by its weight before summing and dividing by total weight. Values with larger weights have more influence on the result.

Do weights need to sum to 1?

No, the formula divides by the sum of weights, so they can be any positive values. If they already sum to 1 (like probabilities), the denominator is simply 1.