Turn practice results into comparable scores for admissions. See percentiles, stanines, and T-scores in seconds. Export tables to share with tutors and classmates easily.
| Raw (x) | Mean (μ) | SD (σ) | z | Approx. Percentile | Stanine |
|---|---|---|---|---|---|
| 85 | 70 | 10 | 1.5000 | 93.32% | 8 |
| 72 | 70 | 10 | 0.2000 | 57.93% | 5 |
| 66 | 70 | 10 | -0.4000 | 34.46% | 4 |
These percentiles assume scores follow a bell-shaped distribution.
z = (x − μ) / σPercentile = CDF(z) × 100 (normal curve)T = 50 + 10zIQ = 100 + 15zIf your exam uses a different scale, keep z and change the mean/SD formulas accordingly.
Standard scores make different exams easier to compare by expressing performance relative to a reference group. When you supply a mean and standard deviation, the calculator converts each raw value into z, percentile, and familiar reporting scales used in many admissions and placement contexts.
A z-score tells you how many standard deviations your result sits above or below the average. For example, z = 1.00 means one deviation above the mean, which corresponds to about the 84th percentile under the normal curve. This helps you target realistic improvement goals.
Percentile is computed from the cumulative distribution function, CDF(z) × 100. If z is negative, the percentile drops below 50 because more of the curve lies to the right. The chart visualizes this idea by placing a vertical marker at your z value.
Many programs report T-scores (mean 50, SD 10) or IQ-style scores (mean 100, SD 15). Stanines compress results into nine bands for quick ranking, with 5 near average and 9 at the top end. Converting from z keeps these scales consistent.
Batch mode lets you paste multiple practice scores and convert them in one run, making weekly tracking easier. Exporting CSV supports spreadsheets for trend analysis, while PDF is useful for sharing a clean snapshot with a tutor or study group.
Use the most relevant reference group you can find: your class, a published norm table, or a recent mock-test cohort. If the distribution is heavily skewed, percentiles from a normal model can be misleading, so treat results as an estimate and validate with official score reports.
Then the percentile is only an approximation. Keep z for relative comparison, but rely on official percentiles or rank-based methods when distributions are skewed or bounded.
Use the norms that match your target exam and population. Class averages work for local comparisons, while published norms are better for broader benchmarking.
Because σ controls spread. A larger σ makes the same raw difference smaller in standard deviation units, lowering z and moving the percentile closer to 50.
It indicates above-average performance. Stanine 5 is near typical, 6 is moderately above, 7–8 is strong, and 9 is exceptional relative to the reference group.
You can compare standardized values when each subject uses appropriate norms. Comparisons are most meaningful when both tests measure similar skills and have stable reference statistics.
It is a clean, single-page summary intended for sharing. For large batches, CSV is better because it preserves every row without page constraints.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.