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
Percentile is shown as score ≤ x. Top % = 100 − percentile.
How it’s calculated
- z-score: z = (score − mean) / SD. Deviation score (T-score / hensachi) = 50 + 10 × z.
- Percentile (normal approximation): Φ(z) × 100. Φ uses erf-based approximation with |error| ≤ 1e-6.
- Empirical percentile (data mode): choose ties handling — min (below / N), midrank ((below + 0.5×ties)/N), max ((below + ties)/N).
- Target → score: percentile uses the inverse standard normal CDF, searched in z ∈ [−10, 10]; 0 and 100 are clipped away.
- Estimated rank (optional): floor((1 − percentile/100) × N) + 1, clipped to 1..N.
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.
How are ties handled in the percentile?
Choose min (strictly below), midrank (below + half of ties), or max (at or below). Midrank is common and shown by default.
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?
No. Calculations run in your browser. Use the Copy URL button only when you want to share the current inputs.
What should I do first on this page?
Start with the minimum required inputs or the first action shown near the primary button. Keep optional settings at defaults for a baseline run, then change one setting at a time so you can explain what caused each output change.
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