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📊 基尼系数计算器Gini Coefficient Calculator
输入一组收入、财富或任意非负数值，计算基尼系数 G（0 = 完全平等，1 = 极度不平等）及小样本修正值，并画出洛伦兹曲线、给出累计份额。Enter a list of incomes, wealth or any non-negative values to get the Gini coefficient G (0 = perfect equality, 1 = maximal inequality) and its small-sample corrected value, with a Lorenz curve and cumulative shares.
使用说明与常见问题How-to & FAQ
「基尼系数计算器」是什么？What is the Gini Coefficient Calculator tool?
输入一组收入、财富或任意非负数值，计算基尼系数 G（0 = 完全平等，1 = 极度不平等）及小样本修正值，并画出洛伦兹曲线、给出累计份额。Enter a list of incomes, wealth or any non-negative values to get the Gini coefficient G (0 = perfect equality, 1 = maximal inequality) and its small-sample corrected value, with a Lorenz curve and cumulative shares.
如何使用「基尼系数计算器」？How do I use the Gini Coefficient Calculator tool?
在「基尼系数计算器」中，填写上方字段等参数，结果会随输入实时计算并显示在下方。In the Gini Coefficient Calculator: Fill in the fields above; results are recalculated instantly as you type.
基尼系数怎么算？How is the Gini coefficient calculated?
G = Σᵢ Σⱼ |xᵢ − xⱼ| ÷ (2n²μ)，即所有两两差值的平均值除以平均数的两倍。等价地，把数据从小到大排序后 G = Σ(2i − n − 1)·xᵢ ÷ (n·Σx)。它也等于洛伦兹曲线与完全平等线之间面积的两倍。G = Σᵢ Σⱼ |xᵢ − xⱼ| ÷ (2n²μ) — the mean absolute difference between all pairs divided by twice the mean. Equivalently, with the values sorted from smallest to largest, G = Σ(2i − n − 1)·xᵢ ÷ (n·Σx). It also equals twice the area between the Lorenz curve and the line of perfect equality.
为什么有修正值？Why is there a corrected value?
对 n 个数据，上面的公式最大只能到 (n − 1)/n（一人拥有全部），所以样本很小时偏低。乘以 n/(n − 1) 后，一人独占时正好为 1，常用于把数据当作样本来估计总体时。With n values the formula can reach at most (n − 1)/n (one person holding everything), so it runs low for small samples. Multiplying by n/(n − 1) makes the one-holds-all case exactly 1, which is commonly used when the data are a sample from a larger population.
可以输入什么数据？What data can I enter?
任意非负数值，例如每个人或每户的收入、财富，至少 2 个、最多 100,000 个；总和须大于 0。这里每个数代表一个个体，不支持分组（频数）数据。默认数据只是示例。Any non-negative values — such as each person's or household's income or wealth — from 2 up to 100,000 of them, with a sum above 0. Each number stands for one individual; grouped (frequency) data isn't supported. The default data are only an example.
计算结果可以用于作业或工程吗？Can I use the results for homework or engineering?
「基尼系数计算器」使用教科书标准公式（公式写在说明和常见问题中），适合学习和估算核对；涉及安全的工程设计请以规范和实测为准。The Gini Coefficient Calculator uses standard textbook formulas (given in the description and FAQ), which is good for learning and checking estimates; for safety-critical engineering follow codes and measured values.
「基尼系数计算器」免费吗？需要注册吗？Is the Gini Coefficient Calculator free? Do I need an account?
「基尼系数计算器」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Gini Coefficient Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.