Weighted average and weighted grade calculator

The weighted average formula

In a weighted average, each score counts more or less depending on its weight. Multiply each score by its weight, add the products, then divide by the sum of the weights.

\[ \text{weighted average} = \dfrac{s_{1} \times w_{1} + s_{2} \times w_{2} + \ldots}{w_{1} + w_{2} + \ldots} \]

Average = 8,395 ÷ 100 = 83.95%. A simple average of the three scores would be 85, because it ignores that the final exam is worth the most.

Finding the score you need on the remaining work

If a final exam or project worth weight w is still to come and you want an overall grade G, solve the same formula for the missing score x.

\[ x = \dfrac{G \times (\text{current total weight} + w) - \text{current points}}{w} \]

With 8,395 points over a weight of 100 and a final worth 100 more, a target of 90 requires \( x = \dfrac{90 \times 200 - 8{,}395}{100} = 96.05 \). If x is above the maximum, the target is out of reach; if x is zero or negative, you have already secured it.

Percent weights and point weights are the same thing

Whether a syllabus lists weights as percents (30%, 25%, 45%) or as points (300, 250, 450), the result is identical because only the proportions matter. The weights do not have to add up to 100, so you can enter the categories you have graded so far and see your current standing.

For a college GPA based on credit hours, use the GPA calculator, which converts letter grades to points.

Weighted average: a detailed example

Take three categories with different weights. Then calculate the average step by step.

The products add up to 83.95. Since the weights total 100%, the weighted average is 83.95%. A simple average, in contrast, would be 85, because the lower final score would count the same as homework.

Weighted average: what score do you need next

To reach a target, isolate the missing score. For example, you have 90 on homework (20%) and 80 on the midterm (30%). You want an 85 overall, with a final worth 50%.

First, compute the points earned: 0.2 x 90 + 0.3 x 80 = 18 + 24 = 42. Next, you still need 85 - 42 = 43 points. Finally, divide by the final's weight: 43 / 0.5 = 86.

So you need an 86 on the final. If the result exceeds the maximum possible, the goal is out of reach.

Weighted average: mistakes to avoid

The biggest mistake is averaging the averages. It gives a wrong answer when the groups carry different weights.

• Always use the official weights from the syllabus.
• Divide by the total weight, not by the number of scores.
• Check that every score uses the same scale.
• Round only at the end.

Also, when one score is out of 50, convert it to a percentage before you combine it with others.

Weighted average: where to go next

To plan the end of a class, use the final grade calculator. To turn grades into GPA points, try the GPA calculator or the percent to GPA converter. Next, measure your progress with the percent change calculator. Finally, simplify a ratio with the fraction calculator.

Weighted average: special cases

Some cases need a little care. First, if a weight is 0, that score does not count. Next, if all weights are equal, the weighted average equals the simple average. Finally, if one weight dominates, the average moves close to that score.

For example, with 98 (weight 10) and 70 (weight 1), the average is 1,050 / 11, about 95.5. It sits near 98. Also, one extra score moves the average less when the total weight is large. So a quiz worth 5% matters little next to a final worth 40%.