How to use (3 steps)
- Pick a mode: from mean & SD, from a score list / frequency table, or reverse from a target percentile/deviation score.
- Enter your score or paste the data. Choose the SD type (population/sample) and tie handling if you use empirical data.
- Results update automatically: deviation score, percentile, top %, and estimated rank when a cohort size is provided. Copy the results or URL to share.
Numbers are processed in your browser only. Decimals and negative values are accepted.
Quick presets
Inputs
Results auto-update as you type. Percentile is based on a normal approximation in mode A/C and empirical counts in mode B.
Deviation score & percentile
Percentiles in A/C assume a normal distribution. Standardization alone does not require normality.
How it’s calculated
- z = (x − μ) / σ; T = 50 + 10z. T-score uses mean 50 and SD 10; values outside 0–100 are allowed. It is not Student’s t statistic.
- Percentiles in A/C assume a normal distribution. Standardization alone does not require normality. Φ(z) × 100; Φ(−z) × 100.
- The lower share counts scores below yours plus the selected share of ties. The upper share is its complement; only the at-or-below method excludes all ties from the upper share.
- Percentile and top percentage must be greater than 0 and less than 100. x = μ + σz; z = Φ⁻¹(p), −Φ⁻¹(p).
- Approximate rank (normal model): min(N, max(1, floor(Φ(−z) × N) + 1)).
Normal Distribution Calculator · Mean & Standard Deviation Calculator
FAQ
Should I use population or sample standard deviation?
Use population SD when you have the whole cohort. Use sample SD when your list is a sample from a larger group; at least two data points are required for sample SD.
Percentile rank: Below + half of ties
The lower share counts scores below yours plus the selected share of ties. The upper share is its complement; only the at-or-below method excludes all ties from the upper share.
Why can’t I enter 0% or 100% as a target percentile?
0% and 100% would require an infinite z-score in a normal distribution. Use a value slightly above 0 or below 100 (e.g., 0.1% or 99.9%).
Is my score list sent to a server?
Calculations run in your browser. A/C links include the entered numbers. New B links contain no data and open an empty form; copy the result text separately. Old data links still contain data in their URLs and send it in the initial page request.
What should I enter first for deviation score or percentile?
Enter the score, mean, and standard deviation first. Confirm whether the distribution assumption is appropriate before interpreting percentile or standardized score outputs.
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