Grade Average Calculator

A weighted average is what almost every course actually grades you on, and it is the one piece of arithmetic students most often do wrong — usually by averaging the averages, which quietly treats a five percent quiz as the equal of a thirty percent exam. This page does both sums and puts them side by side. The gap between them is the number worth looking at: it is exactly how much the weighting is helping or hurting you, and no single figure can show it. Leave the weights box empty and the two answers become the same thing, which is the honest way to say that an unweighted course has no weighting to argue about.

How it is calculated

weighted = Σ(wᵢ × gᵢ) ÷ Σwᵢ · plain = Σgᵢ ÷ n

The weighted mean is written here in the form NIST publishes it, where wi is the weight for the ith observation. Weights need no particular units and do not have to add up to a hundred: they are divided out again by the denominator, so 15 and 30 behave exactly like 1 and 2. The worked example loaded into the boxes is the one the University of Illinois Center for Innovation in Teaching and Learning publishes — attendance, group projects, clicker points, an extended response, a midterm and a final at 15, 15, 5, 15, 20 and 30 percent — and it comes out at 84.955, the figure printed in that handout.

Source: NIST DATAPLOT Reference Manual, 2-65, WEIGHTED MEAN — "the formula for the weighted mean xw is SUM[wi xi] / SUM[wi], where wi is the weight for the ith observation"

Questions people ask

Do my weights have to add up to 100?

No. The denominator is the sum of whatever you type, so 15, 15, 5, 15, 20, 30 and 3, 3, 1, 3, 4, 6 give the same answer. Adding up to a hundred is a convention of syllabuses, not a requirement of the arithmetic. It is still worth checking that they do, because a category you forgot to type in is invisible otherwise.

What happens if I type more grades than weights?

The shorter list wins and the page says so rather than padding the gap with an invented weight. Silently treating a missing weight as one, or as zero, would change your average without telling you which of the two it had chosen.

Why is the plain average different from the weighted one?

Because the plain average gives every entry the same say. In the loaded example the plain average is about 86.6 and the weighted one is 84.955: the lowest scores sit on the heaviest components, so weighting costs nearly two marks. When the weights are all equal the two figures agree exactly, which is a quick way to check you have typed the weights you meant.

Can I paste letter grades in here?

No — this page reads numbers. Letters have no fixed numeric value, and the value they take is a decision each institution publishes for itself. The GPA calculator handles letters, and it makes you pick whose published table it should use.

Is this a GPA?

Only if your weights are credit hours and your grades are grade points. A grade point average is a weighted mean with those two particular inputs, which is why the GPA page is a separate tool rather than a preset here: it needs a published letter-to-points table before it can start.

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