GPA Calculator

Definition

Grade Point Average (GPA) on this page is a credit-weighted mean of grade points assigned to letter grades. Formally:

GPA = Σ_i (p_i · c_i) / Σ_i c_i,

where p_i is the letter’s points (or a number entered directly) and c_i is the credit hours of course i, strictly positive. The quotient is a weighted mean in the statistical sense: credits are the weights. When all credits are equal, the formula reduces to the arithmetic mean of the points. The calculator rounds the display to two decimal places (ordinary computer rounding).

Base 4.0 letter table: A = 4.00; A− = 3.70; B+ = 3.30; B = 3.00; B− = 2.70; C+ = 2.30; C = 2.00; C− = 1.70; D+ = 1.30; D = 1.00; D− = 0.70; F = 0. A+ is either 4.00 (4.0 scale) or 4.30 (4.3 scale), per the control above the rows. This is a US grading convention, not a Polish ministry rule and not any single university’s catalog.

Historical and conceptual context

Letter grades A–F became a compact quality code in US higher education. Converting letters to numbers (grade points) made it possible to aggregate many courses into one GPA figure used for scholarships, honors, transfer, and graduate admissions. Semester credit hours reflect course load: a three-credit course weighs three times a one-credit course with the same letter.

In Poland, transcripts more often use numeric marks weighted by ECTS. That is a different model: A–F letters are not the USOS default, and ECTS is not identical to a US credit hour. This calculator therefore does not claim to compute a “Polish index GPA”; it only evaluates Σ(points × credits)/Σ(credits) on the letter scale above. The ECTS average lives on a sibling page.

Conceptually, GPA is not a single-test percent, not a median of letters, and not a class percentile. It is a weighted mean of points. Schools may use custom plus/minus tables, P/F rules, withdrawals, or repeat policies — this calculator does not implement those.

Formal properties

Domain: p_i ∈ [0, 4.3], c_i > 0. GPA ∈ [0, max p]. Weight homogeneity: scaling all credits by λ > 0 leaves GPA unchanged. Monotonicity: raising p_j with fixed credits does not lower GPA. With a prior block G₀ over C₀ credits, the combined GPA is (Σ p c + G₀ C₀) / (Σ c + C₀) — appending one already-aggregated mean.

Target T with remaining credits M: the required average on the rest is (T·(Σc+M) − Σpc) / M. If that exceeds A+ on the chosen scale, the target is unreachable with those M — the calculator reports the number and the caveat.

Two-decimal rounding is presentation; internally the calculator uses floating-point arithmetic. Excel may differ by about 0.01 after rounding on awkward credit fractions.

Full derivation

Step 1. Map each letter to points using the table and the chosen A+ scale.

Step 2. For each filled row, quality points q_i = p_i · c_i.

Step 3. Sum Q = Σ q_i and C = Σ c_i. If a prior GPA is present, add G₀·C₀ to Q and C₀ to C.

Step 4. GPA = Q / C. Round to two decimals: round(100·GPA)/100.

Step 5 (optional). With target T and credits M: need = (T·(C+M) − Q) / M.

Worked path (4.0 scale): A at 3 credits and B at 3 → Q = 12 + 9 = 21, C = 6, GPA = 3.50. Second path: A at 4 and C at 2 → Q = 16 + 4 = 20, C = 6, GPA = 3.333… → 3.33.

Special cases

Equal credits: GPA equals the arithmetic mean of the points. One course: GPA equals that letter’s points. Prior GPA only (no rows): the result is the entered GPA with credits C₀. A+ on the 4.0 scale does not exceed A. An F with positive credits lowers the mean because quality points stay zero while the denominator grows. A raw number (for example 3.7) skips the letter-to-points conversion.

Empty rows are skipped. A row with only a grade or only credits fails validation. Credits ≤ 0 are rejected. Target and remaining credits must both be empty or both filled — the same pairing rule applies to prior GPA and prior credits.

Numerical notes

The calculator adds the values in floating-point arithmetic and rounds the result to two decimal places. Commas and dots in inputs are equivalent. Six rows are a form limit, not a mathematical limit of the weighted mean.

The calculator does not model pass/fail without points, incompletes, grade replacement on repeats, non-US scales, or any school’s official scholarship cutoffs. The result is educational — compare it with your registrar transcript.

Related concepts and sources

Related: general weighted mean Σ(w·x)/Σw, ECTS weighted average (numeric mark × ECTS), grade calculator (test percent → letter/school mark). Cumulative vs term GPA is the same formula over different course sets; the prior fields merge a term into a cumulative figure.

Sources: Wikipedia — Academic grading in the United States; Wikipedia — Grading in education; College Board / campus registrar glossaries on grade points and credit hours (general descriptions). The tool does not replace a university catalog or an official transcript.