Weighted score out of total

They mix homework, labs, midterms, and finals—each on its own max and each with a different weight—and students still need one number on the published scale: a grade out of twenty, a mark out of ten, or a combined score on one hundred. This calculator turns that weighted set of category scores into a single mark out of a total you choose. Enter every category with the points earned, points possible, and weight, then set out_of (for example 20 for a classic note sur 20). The engine normalizes each row to a ratio, takes the weight-average of those ratios, multiplies by your total, and returns mark, mark_display, and a per-category breakdown.

What a weighted score out of a total means

The math is the same everywhere: each category contributes score divided by max_score, that ratio is multiplied by the category weight, those products are summed, the sum is divided by the total weight, and the result is multiplied by out_of. Example: homework eighty-five of one hundred at weight thirty, midterm sixteen of twenty at weight thirty, final forty-two of fifty at weight forty, out_of twenty. People who search for weighted score out of total, grade out of 20, or category mark on a fixed scale want this conversion as the headline result, with a clear mark_display string they can paste into a report or parent message. Because every category is normalized by its own max_score, you can mix a quiz scored out of ten with a project scored out of one hundred without forcing everything onto one raw point pool first.

Input contract, rounding, and error behaviour

Optional label names the category for the breakdown. Weights need not sum to one hundred—the engine renormalizes automatically—so you can enter thirty, thirty, forty or zero point three, zero point three, zero point four with the same ratios and the same mark. POST a JSON body with two required fields. categories is a non-empty array of up to fifty objects; each object must include score (non-negative finite points earned), max_score (strictly positive points possible), and weight (strictly positive relative weight). Aliases items, rows, and components map to categories. out_of is the strictly positive target total for the combined mark; aliases total, scale, and max_mark are accepted. Optional decimals is an integer from zero to six inclusive and defaults to two; alias precision is accepted. On success the response includes mark (rounded half-up to decimals), out_of, mark_display such as 16.62 / 20, weighted_percent, weighted_ratio, total_weight, category_count, decimals, a categories array with ratio, weight_share, and contribution_to_mark per row, plus formula and method weighted_category_scale for stable clients. Missing categories or out_of, empty arrays, non-objects in the list, negative scores, non-positive max_score or weight, non-positive out_of, and decimals outside zero through six fail with invalid_input and messages that name the field; validation failures are not billed.

Where a mark-out-of-N weighted API earns its keep

Teachers who grade in mixed instruments but report on a fixed institutional scale need one oracle that students, parents, and spreadsheets can all trust. Tutors can walk a learner through each category contribution without inventing custom arithmetic each session. Failed validation does not consume balance. Advising offices near midterms answer how much is this out of twenty after weights dozens of times; a shared deterministic endpoint removes Discord-bot drift and hand calculator mistakes. Keep requests small, pin mark and mark_display in tests, and you get reproducible scaled marks for classroom demos, edge workers, and syllabus calculators without standing up custom grading infrastructure of your own.