What a weighted average is, and how it differs from a simple one
A simple (arithmetic) average is the one everyone knows from school: add up all the grades and divide by how many there are. The problem is that in this calculation a course worth one credit point "counts" exactly as much as a course worth five, even though they do not represent the same amount of study.
A weighted average fixes this by giving each grade a relative weight based on the size of the course, meaning its credit points. A course with more credits has more influence on the final average, and a course with fewer credits has less. This is the method most academic institutions in Israel use to compute the average of a degree, a semester or a year, so it is worth understanding properly before moving on to more complex calculations.
The logic is simple: a course's credits are meant to reflect how much time and effort went into it. A five-credit course usually takes far more hours of study, practice and exam preparation than a one-credit course, so it makes sense for the grade in the large course to weigh more in the result. With a plain average, a student who scored high in a single one-credit course could pull the average up exactly as much as a student who excelled in a major, demanding course, which is a misleading picture of real achievement.
The basic formula
The formula has only two steps:
Step 1: multiply each grade by the credit points of its course (grade × credits). This gives each course its own "weighted score".
Step 2: add up all the weighted scores and divide by the total credit points (not by the number of courses!).
In mathematical form:
weighted average = (grade₁ × credits₁ + grade₂ × credits₂ + … + gradeₙ × creditsₙ) / (credits₁ + credits₂ + … + creditsₙ)
The numerator is the sum of the grades each multiplied by its weight, and the denominator is the total of the weights, which here means all the credit points taken. That is the essential difference from a simple average, where the denominator is just the count of grades.
The formula works the same way however many courses there are, two or twenty. As long as you multiply each grade by its credits before adding, and divide by the total credits at the end (not midway), the result is right. Keep the exact numbers throughout and round only the final result, to avoid small drifts caused by rounding too early.
A worked example, step by step
Suppose a student finished a semester with four courses of different sizes and grades:
| Course | Grade | Credits | Grade × credits |
|---|---|---|---|
| Course A | 85 | 4 | 340 |
| Course B | 90 | 2 | 180 |
| Course C | 70 | 3 | 210 |
| Course D | 95 | 5 | 475 |
| Total | 14 | 1205 |
Now divide the total weighted score (1205) by the total credit points (14): 1205 ÷ 14 = 86.07.
The weighted average for this semester is 86.07. Compare it with a simple average, which ignores the credits: (85 + 90 + 70 + 95) / 4 = 85. The difference of about 1.07 points comes from the highest grade (95) also being the heaviest course (5 credits), which pulls the weighted average up more than it would pull a simple one.
Common mistakes
The most frequent mistake is dividing by the number of courses instead of the total credits. In the example above, dividing by 4 (the number of courses) instead of 14 (the total credits) would give an inflated, wrong average.
Another is leaving a course out midway, for example dropping it from the sum of weighted scores but keeping its credits in the denominator (or the other way around), which distorts the final result.
A third is mixing up grade and credits in the table, multiplying credits by credits or grade by grade instead of grade by credits. Always build a tidy table like the one above to reduce typing and arithmetic errors.
A fourth, less talked about but common, is rounding too early, for example rounding each course's weighted score separately (85 × 4 = 340, round, then add) instead of keeping the exact numbers and rounding only the final result. With many courses, repeated rounding can accumulate a drift of a few hundredths of a point, which looks negligible but can decide whether you clear a particular threshold.
Why use a calculator instead of doing it by hand
The manual calculation works well for four courses, but across dozens of courses and several years the chance of a typo, a forgotten course or a mixed-up column rises sharply. A single small slip can change the final average by tenths of a point, which can be exactly the difference that decides eligibility for a scholarship, an honors degree or admission to further study.
A calculator does the same arithmetic (grade times credits, sum, divide by total credits) without the risk of manual errors, and lets you change grades, add courses and see the effect on the overall average at once, without rebuilding the table each time. You can calculate your weighted average automatically here and get the exact result in seconds.