Find an average where some numbers count for more than others. Enter your numbers, and a matching weight for each one.
Each value is multiplied by its own weight.
Those products are added together.
The total is divided by the sum of the weights, not by the number of items.
When every weight is equal, the result is the same as a plain average.
Weighted average: Σ(value × weight) ÷ Σ(weight)
Σ: The sum across all items
A student scores 80 in a 4-credit subject and 60 in a 2-credit subject.
Values: 80, 60
Weights (credits): 4, 2
Multiply each: (80 × 4) + (60 × 2) = 320 + 120 = 440
Add the weights: 4 + 2 = 6
Divide: 440 ÷ 6 = 73.33
Answer: 73.33 (the plain average would have been 70)
A weighted average calculator finds an average in which each value counts in proportion to a weight you assign. A plain average treats every number as equally important. A weighted average lets a four-credit course count twice as much as a two-credit course, or a ₹50,000 investment count ten times as much as a ₹5,000 one.
In India the most familiar weighted average is the SGPA or CGPA that universities compute from grade points and course credits. Teachers use it to combine unit tests, practicals and final exams with fixed weightages. Investors use it to find the average buying price of a share bought in several lots, and shopkeepers use it to find the average cost of stock purchased at different rates. The calculator answers: what single value represents this mix fairly?
1. List each value x and its weight w in matching order.
2. Multiply each value by its weight to get x × w.
3. Add all the products: Σ(x × w).
4. Add all the weights: Σw.
5. Divide: weighted average = Σ(x × w) ÷ Σw.
6. Check that the answer lies between the smallest and largest value, and sits closer to the values with bigger weights.
Think of each weight as the number of times a value appears. A value of 78 with weight 4 behaves like four copies of 78. Summing value × weight gives the total of all these copies, and dividing by the total weight gives the ordinary mean of the expanded list. That is why weights do not need to add up to 1 or 100. Credits of 4, 3, 2 and 1 work exactly the same as 40%, 30%, 20% and 10%, because only their relative sizes matter.
If every weight is the same number w, the formula becomes w × Σx ÷ (n × w), which simplifies to Σx ÷ n, the ordinary average. So the simple mean is a special case of the weighted mean. A weight of zero removes that value entirely, which is sometimes useful, for example when a dropped course carries no credit. Negative weights have no sensible meaning in averaging and can push the result outside the range of the data, so avoid them.
Suppose one section of 20 students averages 70 marks and another of 40 students averages 85. The combined average is not (70 + 85) ÷ 2 = 77.5. Each section average must be weighted by its size: (70 × 20 + 85 × 40) ÷ 60 = 80. The same trap appears when averaging returns across months with different amounts invested, or speeds over legs of different lengths. Whenever groups differ in size, their averages must be weighted.
Sneha scored grade points of 9, 7, 8 and 6 in four semester courses carrying 4, 3, 3 and 2 credits respectively, and wants her SGPA.
Multiply each value by its weight: 9 × 4 = 36 7 × 3 = 21 8 × 3 = 24 6 × 2 = 12
Add the products: 36 + 21 + 24 + 12
Add the weights: 4 + 3 + 3 + 2
Divide: 93 ÷ 12
Answer: Weighted average 7.75; Sum of (value × weight) 93; Total weight 12
Dividing by the number of items instead of the sum of the weights.
Listing weights in a different order from the values, so each weight attaches to the wrong number.
Averaging subject percentages directly when the university formula uses credit-weighted grade points.
Averaging the purchase prices of share lots without weighting by the number of shares in each lot.
Taking a simple average of section or class averages that have different numbers of students.
Computing SGPA and CGPA from grade points and course credits.
Combining internal assessment, practical and theory marks with fixed weightages.
Finding the average buying price of shares or mutual fund units bought in several instalments.
Finding the average cost per kilogram of grain or stock bought at different rates.
Building index numbers, such as a household's own inflation rate weighted by spending share.
How do I calculate a weighted average of marks with different credits?
Multiply each subject's marks or grade points by its credits, add the products, and divide by the total credits. For 8 points in a 4-credit subject and 6 points in a 2-credit subject: (8 × 4 + 6 × 2) ÷ (4 + 2) = 44 ÷ 6 = 7.33.
How do I find the average price I paid over several purchases?
Use the price as the value and the quantity as the weight. Buying 10 shares at ₹200 and 30 at ₹240 gives an average cost of (10 × 200 + 30 × 240) ÷ 40 = ₹230, not the simple average of ₹220.
How is a weighted average different from a simple average?
A simple average treats every value as equally important. A weighted average lets some values count more. When all weights are equal, the two give the same answer.
When should I use a weighted average instead of a normal one?
Whenever the items are not equally important. Course marks weighted by credit hours, investment returns weighted by amount invested, and survey results weighted by group size all need a weighted average.
Do the weights have to add up to 100?
No. The formula divides by the total weight, so any consistent scale works — credits, rupees, percentages, or plain counts.
What if a weight is zero?
That value is left out of the average, which is the mathematically correct result.