Analyze distribution patterns using ranked cumulative proportions today. Supports weights, missing values, and normalization options. See inequality clearly with an accurate Lorenz curve tool.
Try these values to see a clearly curved Lorenz plot.
| Entity | Value | Weight | Comment |
|---|---|---|---|
| A | 1200 | 1 | High share contributor |
| B | 900 | 1 | Upper-middle contributor |
| C | 450 | 1 | Middle contributor |
| D | 300 | 1 | Lower contributor |
| E | 150 | 1 | Small share contributor |
The Lorenz curve is built from ranked values. Let each observation have value vᵢ and weight wᵢ. After sorting by vᵢ in ascending order:
The equality line is y = x. The Gini coefficient is computed from the area A under the Lorenz curve:
A = ∑ₖ (xₖ − xₖ₋₁) · (yₖ + yₖ₋₁)/2, G = 1 − 2A
Many physical systems create uneven distributions. Examples include granular energy dissipation, turbulent intermittency, reaction rates across heterogeneous catalysts, and node loads in transport networks. A Lorenz curve converts these uneven shares into a geometric picture that is easy to compare across experiments.
After ranking observations from smallest to largest, the horizontal axis shows cumulative population share (weighted count), while the vertical axis shows cumulative share of the measured quantity. If 60% of samples account for only 20% of total intensity, the curve bows strongly below the equality line.
The Gini coefficient ranges from 0 to 1. Values near 0 indicate near-uniform allocation, while values near 1 imply concentration in a few observations. In physics datasets, Gini values of 0.2–0.4 are common for mildly heterogeneous fields, whereas 0.6+ suggests heavy-tailed dominance.
The Robin Hood (Pietra) index gives the maximum vertical gap between the Lorenz curve and the equality line. It answers a direct question: what fraction of the total quantity would need to be “reallocated” from high-share observations to low-share observations to make shares equal.
Weights represent repeated measurements, particle counts, exposure time, or spatial cell area. For example, if a detector bins photon counts in pixels of different area, use pixel area as weight so cumulative population share reflects true sampled support rather than just the number of rows.
Standard Lorenz interpretation assumes non-negative values and positive total sum. Negative entries can arise from background subtraction or signed fluxes, but they can invert shares and distort geometry. If needed, analyze signed signals separately or shift the baseline before computing the curve.
Lorenz curves are ideal for comparing conditions: temperature steps, forcing amplitudes, material batches, or network rewiring. Keep measurement units consistent, then compare the Gini and the curve shape. A higher curve (closer to equality) typically indicates more uniform distribution under that condition.
Include the Lorenz plot, the Gini value, and the observation count. Also report how you defined observations (events, nodes, voxels) and weights (counts, area, time). For reproducibility, export the Lorenz table and attach it as supplementary data for reviewers and collaborators.
Any non-negative quantity that sums meaningfully, such as energy dissipation per event, intensity per pixel, node throughput, or particle size contribution. Use weights to reflect repeated counts, area, or time.
At zero population share you have zero accumulated quantity. At full population share you have all observations and the entire total quantity, so cumulative share becomes one by definition.
A stronger bow indicates concentration: a small fraction of observations contributes a large fraction of the total. This often appears with heavy-tailed distributions, intermittency, or strong heterogeneity.
The tool integrates the area under the Lorenz curve using trapezoids. Gini equals one minus twice that area. This approach is stable and works with weighted datasets.
Yes. Paste one value per line, or paste value and weight separated by a comma, tab, or semicolon. The parser ignores empty lines and non-numeric rows.
Negative entries can make total share ambiguous and can push the curve above the equality line. If negatives come from offsets, shift the baseline or analyze positive and negative components separately.
Export the CSV for the Lorenz table and include the Gini and Robin Hood indices. The PDF export bundles a plot, summary, and the table for quick lab documentation.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.