The arithmetic in a homeschool transcript
A transcript is a formatted list of courses with a number at the bottom. The formatting is a chore; the number is where the errors are, and it is the number somebody else will check.
Start with the rule that is not ours to give
Before any arithmetic: what a transcript must contain, what counts as a course, how credits are defined and what is required to graduate are set by the place that receives the transcript and by the rules that apply where you live. Those differ from one country, region and institution to the next, and they change.
Nothing on this page — and nothing in the tool — tells you what those requirements are. Ask the receiving institution directly, in writing, and use their answer. It is the only one that counts. Everything below is about making the sums on the page correct, which is a separate problem and entirely yours to solve.
GPA is a weighted average
The rule is: total quality points divided by total credits, where a course's quality points are its grade points multiplied by its credits.
The common error is averaging the grade points instead. That treats a half-credit course as equal to a full-credit one, and it produces a different answer whenever the credit values are not all the same. Somebody will re-add it.
The worked example
One year, six courses, on a scale where A = 4.0, A- = 3.7, B+ = 3.3 and B = 3.0. Credits and grades as follows.
- Algebra — 1 credit, A.
4.0 × 1 = 4.0 - Biology with Lab — 1 credit, B+.
3.3 × 1 = 3.3 - English — 1 credit, A-.
3.7 × 1 = 3.7 - World History — 0.5 credit, A.
4.0 × 0.5 = 2.0 - Spanish — 1 credit, B.
3.0 × 1 = 3.0 - PE and Health — 0.5 credit, A.
4.0 × 0.5 = 2.0
Total credits: 1 + 1 + 1 + 0.5 + 1 + 0.5 = 5.0.
Total quality points: 4.0 + 3.3 + 3.7 + 2.0 + 3.0 + 2.0 = 18.0.
GPA: 18.0 ÷ 5.0 = 3.60.
Now the wrong way, for contrast. Averaging the six grade points gives (4.0 + 3.3 + 3.7 + 4.0 + 3.0 + 4.0) ÷ 6 = 22.0 ÷ 6 = 3.67. Seven hundredths of a point apart, from the same six courses. The gap grows with every half-credit course you add.
Adding a second year
Six more courses come to 5.5 credits and 20.0 quality points, so that year is 20.0 ÷ 5.5 = 3.64.
The cumulative GPA is not the average of the two year GPAs. Add the raw components: credits 5.0 + 5.5 = 10.5, quality points 18.0 + 20.0 = 38.0, so cumulative GPA is 38.0 ÷ 10.5 = 3.62. Averaging 3.60 and 3.64 happens to land close here, and will not next time.
Weighted courses
If you mark some courses as more demanding and add a bonus to their grade points, do it as a second column, not a replacement. Suppose one 1-credit course in year two carries a bonus of 1.0: its grade points go from 3.3 to 4.3, so year two's quality points become 20.0 + 1.0 = 21.0 and its weighted GPA is 21.0 ÷ 5.5 = 3.82. Cumulatively, 18.0 + 21.0 = 39.0 over 10.5 credits gives 39.0 ÷ 10.5 = 3.71.
Show both columns. There is no standard bonus, the size of it is yours, and a reader who can see the unweighted figure beside it has no reason to distrust either.
Two habits worth keeping
- Never round mid-calculation. Round once, at the point of printing. A GPA rounded to two decimals and then fed into the next sum will stop reconciling with its own components.
- Keep the running list somewhere you own — a document or spreadsheet — and rebuild the transcript from it. The list is the record; the transcript is a rendering of it.
The tool
The Homeschool Transcript Builder takes one course per line — title, year, credits, grade, and an optional mark for a weighted course — and prints courses grouped by year, per-year credits and GPA, cumulative credits, and cumulative unweighted and weighted GPA side by side, with a signature and date line at the end.
The grading scale is a field you fill in, not a built-in table, and a grade you did not define is flagged rather than scored. It always uses the credit-weighted formula. It stores nothing between visits, contains no rules about requirements of any kind, and cannot tell you whether a transcript will be accepted — only the receiving institution can answer that.