# Percentile Calculator

Free percentile calculator. Find what percentile a score is in, or find the score at a given percentile using a normal distribution.

## What this calculates

Calculate the percentile rank of a score or find the score at a specific percentile using a normal distribution. Useful for standardized tests, grading curves, and data analysis.

## Inputs

- **Calculation Mode** — options: Score → Percentile, Percentile → Score — Choose whether to find the percentile from a score, or find the score at a percentile.
- **Score / Value** — The score or value to find the percentile for.
- **Mean (μ)** — The mean (average) of the distribution.
- **Standard Deviation (σ)** — min 0.0001 — The standard deviation of the distribution.
- **Target Percentile (%)** — min 0.01, max 99.99 — The percentile to find the score for (Percentile → Score mode).

## Outputs

- **Percentile Rank** — The percentile rank of the given score.
- **Z-Score** — The standardized z-score.
- **Score at Percentile** — The score corresponding to the given percentile.
- **Interpretation** — formatted as text — What the percentile means.

## Details

A percentile indicates the percentage of scores that fall below a given value.

Score → Percentile

- Calculate z = (score - mean) / standard deviation

- Look up z in the standard normal distribution

- The CDF value × 100 = percentile rank

Percentile → Score

- Convert percentile to a decimal (e.g., 90% → 0.90)

- Find the z-score using the inverse normal CDF

- Score = mean + z × standard deviation

## Frequently Asked Questions

**Q: What does the 90th percentile mean?**

A: Being at the 90th percentile means your score is higher than 90% of all scores in the distribution. Only 10% of scores are higher than yours.

**Q: Is a higher percentile always better?**

A: It depends on what is being measured. For test scores and income, higher percentiles are typically better. For metrics like response time or error rates, lower percentiles (meaning faster/fewer) are better.

**Q: Does this assume a normal distribution?**

A: Yes, this calculator assumes data follows a normal (bell curve) distribution. For non-normal data, percentiles should be calculated directly from the sorted data rather than using z-scores.

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Source: https://vastcalc.com/calculators/statistics/percentile
Category: Statistics
Last updated: 2026-04-21