⭕ 韦恩图计算器Venn Diagram Calculator
按集合大小和交集数量（两个或三个集合），用容斥原理算出韦恩图每个区域的数量、并集和「都不属于」的个数；也可以直接列出各集合的元素，自动求交集、并集和差集。Work out every region of a two- or three-set Venn diagram from the set sizes and overlaps with inclusion–exclusion, including the union and the number in none of the sets — or list each set's items and get the intersections, union and differences automatically.
使用说明与常见问题How-to & FAQ
「韦恩图计算器」是什么？What is the Venn Diagram Calculator tool?
按集合大小和交集数量（两个或三个集合），用容斥原理算出韦恩图每个区域的数量、并集和「都不属于」的个数；也可以直接列出各集合的元素，自动求交集、并集和差集。Work out every region of a two- or three-set Venn diagram from the set sizes and overlaps with inclusion–exclusion, including the union and the number in none of the sets — or list each set's items and get the intersections, union and differences automatically.
如何使用「韦恩图计算器」？How do I use the Venn Diagram Calculator tool?
在「韦恩图计算器」中，填写「输入方式」、「n(A)」、「n(B)」、「n(C)」、「n(A∩B)」等参数，结果会随输入实时计算并显示在下方。In the Venn Diagram Calculator: Fill in "Input", "n(A)", "n(B)", "n(C)", "n(A∩B)"; results are recalculated instantly as you type.
区域数量怎么算？How are the region counts worked out?
从中间往外算：三者交集 |A∩B∩C| 直接给出；「只属于 A 和 B」= |A∩B| − |A∩B∩C|；「只属于 A」= |A| − |A∩B| − |A∩C| + |A∩B∩C|，其余同理。并集用容斥原理：|A∪B∪C| = |A| + |B| + |C| − |A∩B| − |A∩C| − |B∩C| + |A∩B∩C|。Work from the middle out: the triple overlap |A∩B∩C| is given; 'A and B only' = |A∩B| − |A∩B∩C|; 'A only' = |A| − |A∩B| − |A∩C| + |A∩B∩C|, and likewise for the rest. The union uses inclusion–exclusion: |A∪B∪C| = |A| + |B| + |C| − |A∩B| − |A∩C| − |B∩C| + |A∩B∩C|.
为什么提示数量矛盾？Why does it say the numbers contradict each other?
如果某个区域算出来是负数，说明输入不可能同时成立，例如交集比集合本身还大，或三者交集大于某个两两交集。If any region comes out negative the inputs can't all be true — for example an overlap bigger than one of its sets, or a triple overlap bigger than a pairwise overlap.
列出元素时怎么分隔？How do I separate listed items?
用逗号、分号、顿号或换行分隔，重复的元素只计一次，首尾空格会被去掉。默认区分大小写，可选择忽略大小写（结果以小写显示）。只填 A 和 B 时按两个集合计算。Separate items with commas, semicolons or new lines; duplicates count once and surrounding spaces are trimmed. Matching is case-sensitive unless you choose Ignore case (results then appear in lower case). Fill in only A and B for two sets.
计算精度如何？How precise are the results?
「韦恩图计算器」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Venn Diagram Calculator uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「韦恩图计算器」免费吗？需要注册吗？Is the Venn Diagram Calculator free? Do I need an account?
「韦恩图计算器」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 Venn Diagram 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.