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.
How to use this calculator effectively
This guide helps you use Deviation Score (T-score) & Percentile Calculator in a repeatable way: define a baseline, change one variable at a time, and interpret outputs with explicit assumptions before you share or act on results.
How it works
The page applies deterministic logic to your inputs and shows rounded output for readability. Treat it as a comparison workflow: run one baseline case, adjust a single parameter, and measure both absolute and percentage deltas. If a result seems off, verify units, time basis, and sign conventions before drawing conclusions. This approach keeps your analysis reproducible across teammates and sessions.
When to use
Use this page when you need a fast estimate, a classroom check, or a practical what-if comparison. It works best for planning and prioritization steps where you need direction and magnitude quickly before investing in deeper modeling, manual spreadsheets, or formal external review.
Common mistakes to avoid
- Changing multiple parameters at once, which hides the true cause of output movement.
- Mixing units (percent vs decimal, monthly vs yearly, gross vs net) across scenarios.
- Comparing with another tool without aligning defaults, constants, and rounding rules.
- Using rounded display values as exact downstream inputs without re-checking precision.
Interpretation and worked example
Run a baseline scenario and keep that result visible. Next, modify one assumption to reflect your realistic alternative and compare direction plus size of change. If the direction matches your domain expectation and the size is plausible, your setup is usually coherent. If not, check hidden defaults, boundary conditions, and interpretation notes before deciding which scenario to adopt.
See also
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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