How a weighted GPA is actually worked out

A GPA looks like a mysterious number until you see it built. It is not mysterious. It is a weighted average, and you can work it out on paper in about a minute. Do this once, and afterwards you can check any figure an app or a portal shows you, instead of taking it on trust.

The three ingredients

Every GPA needs the same three things:

• A grade point for each course. Your school's grading scale decides this. On a 4.0 scale with plus and minus, an A is 4.0, an A minus is 3.7, a B plus is 3.3, and so on.
• A credit weight for each course. Usually the credit hours, so a 4-credit course counts twice as much as a 2-credit one. Some schools do not weight at all and simply average the courses.
• One division at the end. Not an average of averages. One sum divided by one other sum.

Quality points are the whole trick

Multiply each course's grade point by its credits, and you get its quality points. That is the number that makes the weighting work.

Then divide once:

43.00 quality points / 12 credits = 3.5833...

Rounded to two places, that is a 3.58. Notice what would have happened if you had averaged the four grade points on their own: 4.00, 3.30, 3.70 and 3.00 average to 3.50. The 4-credit A pulls the real figure higher, and any method that ignores credits gets it wrong.

Where the weighted figure comes in

A weighted GPA adds a bump for harder courses. Most US high schools use a 5.0 scale for this: an A in an AP or IB course is worth 5.0 rather than 4.0. An A in an Honours course lands somewhere between.

The arithmetic does not change. Only the grade point does:

• Take the ordinary grade point for the course.
• Add the bump the school gives that level of rigour. A common pair is 0.5 for Honours and 1.0 for AP, IB or dual enrolment, but schools genuinely differ, so use your own school's numbers.
• Cap it at the top of the weighted scale, and never bump a zero. An F stays an F, however hard the course was.

Two things follow. First, a weighted GPA above 4.0 is normal and does not mean anything went wrong. Second, the unweighted figure has not disappeared. Plenty of applications ask for it, so it is worth keeping both figures in front of you rather than choosing one.

Your cumulative GPA, and the mistake to avoid

A cumulative GPA covers every term. It is worked out the same way as a single term: add up the quality points from all of them, add up the credits from all of them, and divide once.

The mistake is averaging the term GPAs. A 3.2 across 16 credits and a 3.8 across 4 credits do not make a 3.5. They make:

(3.2 x 16) + (3.8 x 4) = 51.2 + 15.2 = 66.4
66.4 / 20 = 3.32

A light term simply counts for less, which is exactly what a credit-weighted average is for.

The markers that are not zeros

Withdrawn, incomplete and audit are not grades. Treating them as zeros will wreck a GPA that is perfectly healthy. The usual convention is:

• Pass earns its credits and stays out of the GPA entirely.
• Withdrawn, incomplete and audit count neither towards credits attempted nor credits earned.
• A failed course does count as credits attempted, with zero quality points, and earns nothing. That is why an F hurts twice.

This is also why credits attempted and credits earned are tracked as separate numbers rather than one.

Rounding decides the last digit, and only the last

Rounding is the step people argue about, because different institutions do it differently. Half up is the most common: 3.455 becomes 3.46. Some schools truncate instead, so 3.459 stays 3.45 and nothing is ever rounded up in your favour.

Rounding should be the very last thing that happens. If the intermediate sums are rounded, small errors accumulate and the final figure drifts. Work exactly, divide once, then round for display.

Checking a figure you have been given

If a number does not look right, work through it in this order:

1. Check the grade points against your school's own scale, especially the plus and minus rows. An A minus is 3.7 at some institutions and 3.67 at others.
2. Check the credits on each course, including any half credits.
3. Add the quality points and the credits yourself, then do the single division.
4. Only then compare the rounding.

Nine times out of ten the difference is in step one or step two, not in the arithmetic.

Simply GPA does all of this on your device. It shows you the same working, line by line: every quality point, both totals, the division and the rounding rule that produced the last digit. If you want the tables the app ships with, they are set out in the grading scales guide.