Pareto Principle Calculator (80/20 Rule, Pareto Index and Gini)
Fit a Pareto distribution to a rule like 'the top 20 % hold 80 %' and read off the Pareto index, the Gini coefficient and the shares held by the top 1 %, top 10 % and bottom half.
Results
The dashed line marks the value you entered.
What this tool does
The 80/20 rule is the best-known case of a Pareto distribution, where a small top group holds most of the total — sales, wealth, bugs, complaints. If the top fraction x holds a share y, the exponent follows from ln y ÷ ln x, and the same curve then tells you what any other top slice holds: 80/20 is a Pareto index of about 1.16 and a Gini coefficient of about 0.76, and the top 1 % would hold roughly 53 %. The rule is a rough heuristic, not a law of nature: real shares vary, and extreme tails rarely follow one curve exactly.
Formula
top fraction t holds t^(1 − 1/α) · α = 1 ÷ (1 − ln y ÷ ln x) · Gini = 1 ÷ (2α − 1)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
xt | The top group — share of people, customers or items | % |
yt | …together hold this share of the total | % |
AL | Pareto index α | — |
GI | Gini coefficient of that distribution | — |
T1 | Share held by the top 1 % | % |
T10 | Share held by the top 10 % | % |
B50 | Share held by the bottom 50 % | % |
Worked example
- The top group — share of people, customers or items20 %
- …together hold this share of the total80 %
- Pareto index α1.1610
- Gini coefficient of that distribution0.756
- Share held by the top 1 %52.8 %
- Share held by the top 10 %72.7 %
- Share held by the bottom 50 %9.2 %
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.