CalcMate

Test Score Calculator

Enter how many questions you answered correctly and how many there were, and get the score as a percentage, the letter grade and the error rate — plus a z-score and percentile when you know how the class did.

Score84%42 of 50 on the plus/minus scale
Letter gradeB
Questions missed8
Error rate16%
Z-score standard deviations from the class average1.4
Estimated percentile91.92%

The percentile assumes class scores follow a normal curve — it estimates the share of classmates you outscored, not your exact class rank.

Formula and calculation

percentage=correcttotal×100error rate=wrongtotal×100z=percentage−class averageclass standard deviationpercentile=Φ(z)×100\begin{gathered}\text{percentage} = \dfrac{\text{correct}}{\text{total}} \times 100\\[6pt]\text{error rate} = \dfrac{\text{wrong}}{\text{total}} \times 100\\[6pt]z = \dfrac{\text{percentage} - \text{class average}}{\text{class standard deviation}}\\[6pt]\text{percentile} = \Phi(z) \times 100\end{gathered}
Letter grades follow the common US plus/minus scale: A− 90, B+ 87, B 83, B− 80, C+ 77, C 73, C− 70, D+ 67, D 63, D− 60, F below 60 — the ranges in the College Board's letter-grade chart. The simple scale drops the plus and minus steps and uses 90/80/70/60. The percentile uses the normal distribution (Φ is the standard normal CDF), so it assumes the class spread is roughly bell-shaped — a straight 100-point test with a few zeros is not.

Worked example

For 42 correct out of 50 on the plus/minus scale: the score is 84%, a B, with 8 questions missed — an error rate of 16%. If the class averaged 70% with a standard deviation of 10, the z-score is 1.4 and the estimated percentile is 91.92%.

What the results mean

Score
Your score as a percentage: correct answers divided by the total, times 100. This is the number a gradebook records, and the one the letter grade is based on.
Letter grade
The letter your percentage falls in on the selected scale. Cutoffs differ between schools, so treat a score sitting right on a boundary as uncertain.
Questions missed
How many questions you missed — the total minus the correct answers. This is the list to work through when you review the test.
Error rate
The share of the test you got wrong, as a percentage. An error rate of 20% means one question in five was missed.
Z-score
How many standard deviations your score sits from the class average. Zero is exactly average; above 2 is roughly the top of a normal curve. Shown when you enter both the class average and its standard deviation.
Estimated percentile
The estimated share of the class you outscored, assuming class scores follow a normal curve — a z-score of 0 is the 50th percentile. Treat it as an estimate of standing, not your exact rank.

Frequently asked questions

How do I calculate my test score percentage?

Divide the number of correct answers by the total number of questions and multiply by 100: 42 out of 50 is 42 ÷ 50 × 100 = 84%. The letter grade, error rate and z-score all follow from that percentage.

What is a z-score on a test?

It measures how far your score is from the class average, in units of the class standard deviation: z = (your score − class average) ÷ standard deviation. A z of 0 is exactly average, and a z of 1.5 means you scored one and a half spreads above the class.

Is the percentile the same as my class rank?

No. The percentile assumes scores follow a normal curve and estimates the share of classmates you outscored. A rank is a count of actual people, and real class distributions are lumpier than the curve — often with a clump of high scores that lowers your percentile.

What letter grade is 80%?

On the simple 90/80/70/60 scale, 80% is a B. On the plus/minus scale it is a B−, because a plain B starts at 83. Use whichever scale your syllabus prints — the page shows the full table for both.

Can I use this for a test with partial credit?

Yes, as long as both numbers are in the same units. Enter the points you earned and the points the test was worth — 34.5 out of 40 produces the same percentage as counting questions, 86.25%.