Weighted grade averages: marks, weights and target grades

A school average is not always the sum of your marks divided by the number of assessments. A test with a weight of 2 counts twice as much as homework with a weight of 1. Marks of 12 and 18 can therefore give an average of 14 rather than 15.

To check a result or plan a target, collect the relevant marks, their weights and the rules for the reporting period. The same calculation can then tell you what you need on your next assessment.

Calculate a weighted average

The formula is:

average = sum of (mark × weight) ÷ sum of weights

Consider two assessments, both marked out of 20:

Assessment	Mark	Weight	Weighted points
Test	12	2	24
Homework	18	1	18
Total		3	42

The average is 42 ÷ 3 = 14/20. Divide by the total weight, 3, rather than the number of assessments, 2. Use the weighted grade calculator to enter marks and compare different weights.

Weights are relative: replacing 2 and 1 with 4 and 2 leaves the result unchanged because both weights have doubled.

Put marks on the right scale

Before combining marks out of 10, 20 or 30, check the school’s method. With proportional rescaling, 7/10 becomes 14/20. A test scored at 14/20 with weight 2 and homework scored at 7/10 with weight 1 therefore average 14/20.

Adding earned points and available points is a different method. For 8/10 and 12/20, averaging the two rescaled marks gives (16 + 12) ÷ 2 = 14/20. Pooling the points gives 20 ÷ 30 × 20 ≈ 13.33/20. In the second method, the assessment out of 20 carries twice as much weight.

Neither method reproduces the school’s result unless it matches its marking policy. The guide to test scores and grade scales explains proportional conversions and their limits.

Keep assessment weights and subject weights separate

A report average may require two stages:

1. Calculate each subject average using its assessment weights.
2. Combine subject averages using the report’s subject weights.

Suppose mathematics averages 14/20 with subject weight 3, and history averages 16/20 with weight 2. Their combined average is (14 × 3 + 16 × 2) ÷ 5 = 14.8/20.

Putting every test into one list could give too much influence to the subject with more assessments. The calculator uses the weights you enter; it cannot infer the school’s reporting structure.

Find the mark you need next

Return to 42 weighted points across a total weight of 3. To finish at 15/20 after one more test with weight 1, you need 15 × 4 = 60 weighted points altogether. The next test must contribute 60 − 42 = 18: you need 18/20.

If the next test has weight 2, the required mark becomes (15 × 5 − 42) ÷ 2 = 16.5/20.

In general:

required mark = (target average × final total weight − points already earned) ÷ next assessment weight

On a 0–20 scale, a requirement above 20 means the target cannot be reached with that assessment alone. A result of zero or less means even a zero would meet the target. Both conclusions assume the existing marks remain in place and no other assessment is added.

Check absences, reporting periods and rounding

An unknown mark, an exemption and an awarded zero are different situations. Check whether each result belongs in the average, including assessments cancelled or replaced after a resit.

Use the correct reporting period: a second-term mark does not belong in a first-term average. Keep the most precise figures available and apply the school’s rounding rule at the appropriate stage. Rounding every mark first can change the final average.

Work out attendance separately

Attendance records participation, not attainment. Attending 27 of 30 sessions gives 27 ÷ 30 × 100 = 90%.

Suppose a course has 40 sessions. You have attended 18 of the first 20, and the attendance requirement is 80%. You need 32 attendances overall, so another 32 − 18 = 14 among the 20 remaining sessions. Under this counting rule, at most six further absences are possible.

If you have attended only 14 of 20 sessions, reaching 80% by attending every subsequent session requires solving (14 + n) ÷ (20 + n) ≥ 0.80. You need ten consecutive attendances. With only eight sessions left, the target cannot be reached in that course.

Use the attendance calculator to explore these scenarios. The course policy determines how authorised absences, exemptions and sessions of different lengths are counted.

Build a useful estimate

Keep each mark’s maximum, weight, subject and reporting period. Establish the current position, then try realistic scenarios for the assessments still to come. This separates recorded results from achievable targets and policy questions. For university courses weighted by credits, continue with GPA and cumulative GPA.

Common questions

Is a zero weight the same as a zero mark? No. An excluded assessment adds neither points nor weight. A zero mark with a positive weight still counts in the calculation.

Does averaging two term results give the annual average? Only if those are exactly the periods used and both have equal weight. Other periods or weights may apply.

Will a mark below my average always lower it? Yes, if it is added with positive weight without replacing another mark. Its effect depends on its share of the new total weight.

Why does my result differ from the school’s software? Check exclusions, subject weights, scale conversions and rounding. Correct arithmetic with different inputs cannot reproduce the same report.