Weighted Average Calculator

Calculate weighted averages, grades with weights, and GPA with our free weighted average calculator

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What is a Weighted Average?

A weighted average is an average in which each quantity to be averaged is assigned a weight. These weights determine the relative importance of each quantity in the average. Unlike a simple average where all values have equal importance, a weighted average gives more importance to values with higher weights.

Weighted Average Formula

The weighted average is calculated by:

Weighted Average = (((Value × Weight)) ÷ Weight)

Applications

Weighted averages are used in many real-world scenarios, including calculating course grades (where assignments have different weights), determining GPA (where courses have different credit hours), analyzing financial portfolios (where assets have different weights), and calculating average prices (where quantities purchased vary).

Examples of Weighted Average Calculations

Here are several everyday situations that show how easy it is to use our weighted average calculator.

Example 1: UK Coffee Shop Average Price

You buy 2 kg of coffee beans from Waitrose at £15/kg and 3 kg from Tesco at £12/kg. What's the weighted average price?

You can use our calculator by entering:

What is the weighted average price per kg?

The calculator returns: £13.20/kg

Multiply each value by its weight: (2 kg * £15/kg) = £30, (3 kg * £12/kg) = £36
Sum the products: £30 + £36 = £66
Sum the weights: 2 kg + 3 kg = 5 kg
Divide the sum of products by the sum of weights: £66 / 5 kg = £13.20/kg

The formula used is:

(((2 × 15) + (3 × 12)) ÷ (2 + 3)) = ((30 + 36) ÷ 5) = (66 ÷ 5) = 13.2

Example 2: GCSE Course Grade Calculation

A student in Birmingham has GCSE scores: Coursework (80%, 20% weight), Mock Exam (75%, 30% weight), Final Exam (90%, 50% weight).

You can use our calculator by entering:

What is the student's overall GCSE grade?

The calculator returns: 84.5%

Multiply each score by its weight: (80 * 20) = 1600, (75 * 30) = 2250, (90 * 50) = 4500
Sum the products: 1600 + 2250 + 4500 = 8350
Sum the weights: 20 + 30 + 50 = 100
Divide the sum of products by the sum of weights: 8350 / 100 = 83.5%

The formula used is:

(((80 × 20) + (75 × 30) + (90 × 50)) ÷ (20 + 30 + 50)) = ((1600 + 2250 + 4500) ÷ 100) = (8350 ÷ 100) = 83.5

Example 3: UK University GPA Calculation

A student at a UK university took 3 courses: Mathematics (3 credits, A), English Literature (4 credits, B+), History (3 credits, C).

You can use our calculator by entering:

What is the student's GPA?

The calculator returns: 3.13

Convert grades to grade points: A=4.0, B+=3.3, C=2.0
Multiply grade points by credits: (4.0 * 3) = 12, (3.3 * 4) = 13.2, (2.0 * 3) = 6
Sum the grade points * credits: 12 + 13.2 + 6 = 31.2
Sum the credits: 3 + 4 + 3 = 10
Divide the sum of (grade points * credits) by the sum of credits: 31.2 / 10 = 3.12

The formula used is:

(((4.0 × 3) + (3.3 × 4) + (2.0 × 3)) ÷ (3 + 4 + 3)) = ((12 + 13.2 + 6) ÷ 10) = (31.2 ÷ 10) = 3.12

Example 4: UK Investment Portfolio Return

A UK investor has £5000 in Stock A (10% return), £3000 in Stock B (5% return), and £2000 in Stock C (15% return).

You can use our calculator by entering:

What is the weighted average return of the portfolio?

The calculator returns: 9.5%

Calculate return for each stock: (£5000 * 0.10) = £500, (£3000 * 0.05) = £150, (£2000 * 0.15) = £300
Sum the returns: £500 + £150 + £300 = £950
Sum the investments: £5000 + £3000 + £2000 = £10000
Divide total return by total investment: £950 / £10000 = 0.095 or 9.5%

The formula used is:

(((5000 × 0.10) + (3000 × 0.05) + (2000 × 0.15)) ÷ (5000 + 3000 + 2000)) = ((500 + 150 + 300) ÷ 10000) = (950 ÷ 10000) = 0.095

Example 5: Employee Performance Score

An employee's performance is rated on Quality (80, weight 40%), Speed (90, weight 30%), and Teamwork (70, weight 30%).

You can use our calculator by entering:

What is the employee's overall performance score?

The calculator returns: 80

Multiply each rating by its weight: (80 * 40) = 3200, (90 * 30) = 2700, (70 * 30) = 2100
Sum the products: 3200 + 2700 + 2100 = 8000
Sum the weights: 40 + 30 + 30 = 100
Divide the sum of products by the sum of weights: 8000 / 100 = 80

The formula used is:

(((80 × 40) + (90 × 30) + (70 × 30)) ÷ (40 + 30 + 30)) = ((3200 + 2700 + 2100) ÷ 100) = (8000 ÷ 100) = 80

Example 6: Chemical Mixture Concentration

You mix 5 liters of 20% acid solution with 10 liters of 30% acid solution.

You can use our calculator by entering:

What is the weighted average concentration of the final mixture?

The calculator returns: 26.67%

Calculate acid amount from each solution: (5 L * 20%) = 1 L, (10 L * 30%) = 3 L
Sum the acid amounts: 1 L + 3 L = 4 L
Sum the total volume: 5 L + 10 L = 15 L
Divide total acid by total volume: 4 L / 15 L ≈ 0.2667 or 26.67%

The formula used is:

(((5 × 20) + (10 × 30)) ÷ (5 + 10)) = ((100 + 300) ÷ 15) = (400 ÷ 15) ≈ 26.67

Example 7: Student's Final Exam Score Needed

A student has an 80% average (70% weight) and needs a 90% overall. The final exam is 30% weight.

You can use our calculator by entering:

What score does the student need on the final exam?

The calculator returns: 113.33% (This indicates it's impossible to reach 90% overall with current scores)

Target Grade: 90%
Current Average: 80%
Current Weight: 70%
Final Exam Weight: 30%
Total Weight: 70% + 30% = 100%
Required Final Exam Score = ((90 * 100) - (80 * 70)) / 30
Required Final Exam Score = (9000 - 5600) / 30
Required Final Exam Score = 3400 / 30 = 113.33%

The formula used is:

Required Final Exam Score = (((Target Grade × Total Weight) - (Current Average × Current Weight)) ÷ (Final Exam Weight))

Example 8: UK Investment Portfolio Rebalancing

You have £10,000 in UK stocks (expected return 8%) and £5,000 in UK bonds (expected return 4%).

You can use our calculator by entering:

What is the weighted average expected return of your portfolio?

The calculator returns: 6.67%

Calculate expected return for stocks: (£10,000 * 0.08) = £800
Calculate expected return for bonds: (£5,000 * 0.04) = £200
Sum the expected returns: £800 + £200 = £1000
Sum the total investment: £10,000 + £5,000 = £15,000
Divide total expected return by total investment: £1000 / £15,000 ≈ 0.0667 or 6.67%

The formula used is:

(((10000 × 0.08) + (5000 × 0.04)) ÷ (10000 + 5000)) = ((800 + 200) ÷ 15000) = (1000 ÷ 15000) ≈ 0.0667

Example 9: Survey Satisfaction Score

A survey has 10 responses with a score of 5, 20 responses with a score of 4, and 5 responses with a score of 3.

You can use our calculator by entering:

What is the weighted average satisfaction score?

The calculator returns: 4.29

Multiply each score by its frequency: (10 * 5) = 50, (20 * 4) = 80, (5 * 3) = 15
Sum the products: 50 + 80 + 15 = 145
Sum the frequencies: 10 + 20 + 5 = 35
Divide the sum of products by the sum of frequencies: 145 / 35 ≈ 4.14

The formula used is:

(((10 × 5) + (20 × 4) + (5 × 3)) ÷ (10 + 20 + 5)) = ((50 + 80 + 15) ÷ 35) = (145 ÷ 35) ≈ 4.14

Example 10: Manufacturing Defect Rate

Batch A (1000 units) has a 2% defect rate. Batch B (500 units) has a 3% defect rate.

You can use our calculator by entering:

What is the overall weighted average defect rate?

The calculator returns: 2.33%

Calculate defects for each batch: (1000 * 0.02) = 20, (500 * 0.03) = 15
Sum the defects: 20 + 15 = 35
Sum the total units: 1000 + 500 = 1500
Divide total defects by total units: 35 / 1500 ≈ 0.0233 or 2.33%

The formula used is:

(((1000 × 0.02) + (500 × 0.03)) ÷ (1000 + 500)) = ((20 + 15) ÷ 1500) = (35 ÷ 1500) ≈ 0.0233

Summary

These examples show how our weighted average calculator can handle:

  • •Calculating average prices with different quantities
  • •Determining final grades in a course
  • •Calculating Grade Point Average (GPA)
  • •Analyzing financial portfolios with varying asset weights

You can adapt any real-life situation involving weighted averages to one of these patterns and let the calculator do the work for you.

How to Use the Weighted Average Calculator

  1. Select the type of weighted average calculation you need.
  2. Enter the values and their corresponding weights.
  3. View the calculated weighted average and step-by-step breakdown.

Frequently asked questions

What is a weighted average?

A weighted average is an average in which each quantity to be averaged is assigned a weight. These weights determine the relative importance of each quantity in the average.

How is a weighted average calculated?

The weighted average is calculated by multiplying each value by its weight, summing these products, and then dividing by the sum of all weights.

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About this tool

Published by Online Tools Center

Last updated:

Check the units, assumptions and rounding before using a result. Health and financial estimates are educational and do not replace individual professional advice.

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