Percentile Rank and Sample Quantile Calculator
Compare strict, inclusive and midpoint empirical percentile ranks for a score and calculate an entered sample percentile under two explicit conventions.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Sort observations, count strict-below and equal values for rank variants, then calculate the requested quantile by the selected convention.
Midpoint rank=100×(below+equal/2)/n; linear quantile uses index p(n−1)
Worked example
For 10, 20, 20, 30, 40, score 20 has 20% strict-below rank, 60% inclusive rank and 40% midpoint rank. The linear 75th percentile is 30.
Assumptions and input details
1–1000 finite values. Ties are counted explicitly and values outside the sample give boundary ranks. Nearest-rank percentile zero returns the minimum. These are empirical conventions, not distribution probabilities, population quantile guarantees or a judgment of performance. Different software methods may disagree.
References: NumPy: sample quantile conventions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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