Convert Percentile to Score
Easily convert a given percentile rank into an actual z-score and then calculate the corresponding raw score using the mean and standard deviation of your dataset. This tool is helpful in statistics, education testing, and research where you want to translate percentile positions into meaningful scores.
✅ Calculator Prompt
Enter your values below to calculate the score from a given percentile:
Calculated Results:
Step-by-step Explanation:
🔢 Formula Used
Find the Z-Score from Percentile
$$ Z = \text{Inverse Normal}(P) $$ Where P is the percentile (in decimal form, e.g., 95% = 0.95).
Convert Z-Score to Raw Score
$$ X = \mu + Z \times \sigma $$
📊 Example Calculation
Percentile: 90%
Mean (μ): 100
Standard Deviation (σ): 15
Step 1: Find Z from percentile → $Z \approx 1.28$
Step 2: Raw Score → $100 + (1.28 \times 15) = 119.2$
✅ So, at the 90th percentile, the score is 119.2.
📘 User Guide
- Step 1: Enter the percentile rank (1–99).
- Step 2: Enter your dataset’s mean.
- Step 3: Enter the standard deviation.
- Step 4: Click “Calculate” to get both the Z-score and the raw score.
👉 This is widely used in education (SAT, GRE, GMAT scores), psychology tests, and any field that uses normal distribution analysis.
🔗 Related Calculators
❓ FAQs
- Q1: What is the purpose of converting percentile to score?
- A: A percentile shows relative position, but converting it to a score makes it meaningful compared to the dataset.
- Q2: Can I use this for exam scores like SAT or GRE?
- A: Yes. Just enter the official mean and standard deviation for the test.
- Q3: What happens if my percentile is 50?
- A: At 50th percentile, Z = 0, so the score equals the mean.
- Q4: Why is the Z-score important?
- A: It standardizes percentiles, making comparison possible across different datasets.
- Q5: Is this calculator only valid for normally distributed data?
- A: Yes, because the conversion relies on the properties of the normal distribution curve.