How this calculation works
Count reference values below and equal to the target. Report three empirical percentile-rank conventions so ties are explicit. The target need not occur in the reference data, and the reference observations are not changed.
Strict below = L/n; at or below = (L+E)/n; midpoint ties = (L+E/2)/nA worked example
For 10,20,20,30 and target 20, one value is below and two equal. The three percentile ranks are 25%, 75% and 50%.
Good to know
Unweighted descriptive calculations for up to 1,000 observations within ±1 trillion. Floating-point arithmetic and rounded display are used. No missing values are silently removed, no population distribution is inferred, and no confidence intervals are supplied.
Reference: NIST: percentile conventions (opens in a new tab) ↗
Ties create an interval of reasonable rank conventions
For reference values 10,20,20,30 and target 20, one observation is below the target and two equal it. Strict-below rank is 25%, at-or-below rank is 75%, and midpoint-tie rank is 50%. All three come from the same counts.
The at-or-below version is the empirical cumulative distribution function at the target. The strict-below version excludes ties. The midpoint convention places a tied group halfway through the jump between those two values.
A target need not occur in the sample. If no observation equals it, all three conventions agree. Below the minimum they give zero; above the maximum they give 100%. A target at the minimum or maximum can still have ties that separate the results.
A rank is relative to a particular reference group
Changing the reference observations changes the percentile rank even when the target value stays fixed. A score ranked within one class cannot automatically be interpreted as its rank within a national population.
A sample percentile reverses the direction of inquiry by taking a proportion and returning a value. Interpolated percentiles and empirical ranks need not round-trip exactly, so do not treat one operation as a universal inverse of the other.
This calculator uses exact equality of the parsed numbers for ties. Measurements that should be treated as equal after rounding must be rounded explicitly before analysis. Competition ranks such as first, second and joint third use another convention and are not the displayed percentages.
A few questions, answered
Why are there three answers?
They differ in how equal observations contribute. Choose the convention required for your task and retain that label with the result.
Is midpoint rank the middle observation?
No. It allocates half the tied count below the target for a percentage calculation; it does not select a sample median.
Should I add the target to the reference list?
Only if the task defines the reference group that way. The calculator does not insert it automatically.