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🎂 随机生日生成器（指定年龄范围）Random Birthday Generator (by age range)
按年龄范围随机生成生日：例如生成 10 个 18–65 岁的人的出生日期，并显示每个人的年龄、出生星期、星座和距下一次生日的天数；还会统计这些生日里有没有同月同日，并给出“生日悖论”概率。适合测试数据、表单填写演示、课堂概率实验和角色设定。Generate random birthdays for people in an age range — say 10 people aged 18 to 65 — with each person's age, day of the week they were born, star sign and days until their next birthday. It also flags shared birthdays (same month and day) and gives the birthday-paradox probability. Useful for test data, form demos, probability lessons and character backstories.
使用说明与常见问题How-to & FAQ
「随机生日生成器（指定年龄范围）」是什么？What is the Random Birthday Generator (by age range) tool?
按年龄范围随机生成生日：例如生成 10 个 18–65 岁的人的出生日期，并显示每个人的年龄、出生星期、星座和距下一次生日的天数；还会统计这些生日里有没有同月同日，并给出“生日悖论”概率。适合测试数据、表单填写演示、课堂概率实验和角色设定。Generate random birthdays for people in an age range — say 10 people aged 18 to 65 — with each person's age, day of the week they were born, star sign and days until their next birthday. It also flags shared birthdays (same month and day) and gives the birthday-paradox probability. Useful for test data, form demos, probability lessons and character backstories.
如何使用「随机生日生成器（指定年龄范围）」？How do I use the Random Birthday Generator (by age range) tool?
在「随机生日生成器（指定年龄范围）」中，按需设置「人数」、「最小年龄」、「最大年龄」、「参考日期（按此日计算年龄）」、「日期格式」等选项，然后点击「生成」、「复制」按钮即可。In the Random Birthday Generator (by age range): Set "Count", "Minimum age", "Maximum age", "Reference date (ages are as of this day)", "Date format", then click "Generate", "Copy".
年龄是怎么计算的？How is age worked out?
按参考日期计算周岁：过了当年生日才加一岁。2 月 29 日出生的人在平年按 3 月 1 日过生日（例如 2000-02-29 出生，2023-02-28 为 22 岁，2023-03-01 满 23 岁）。Age is completed years as of the reference date: it goes up only once that year's birthday has passed. People born on 29 February are treated as having their birthday on 1 March in common years (born 2000-02-29: 22 on 2023-02-28, 23 on 2023-03-01).
生日是怎么随机生成的？How are the birthdays drawn?
在“年龄刚好在范围内”的所有出生日期中等概率抽取（使用 crypto.getRandomValues），所以每个年龄、每一天被抽到的机会相同；它不反映真实人口的年龄或出生季节分布。Every birth date that gives an age inside the range is equally likely (using crypto.getRandomValues), so each age and each day has the same chance. It does not reflect real population age structure or birth seasons.
什么是生日悖论？What is the birthday paradox?
只要有 23 个人，至少两人同一天生日的概率就超过 50%（约 50.73%），远高于直觉。计算公式为 1 − (365/365 × 364/365 × … × (365−n+1)/365)，假设 365 天等可能并忽略 2 月 29 日。With just 23 people, the chance that at least two share a birthday is over 50% (about 50.73%) — far higher than most people expect. It is 1 − (365/365 × 364/365 × … × (365−n+1)/365), assuming 365 equally likely days and ignoring 29 February.
星座按什么日期划分？Which star-sign dates are used?
与本站“生肖星座查询”一致，例如摩羯座 12 月 22 日–1 月 19 日、水瓶座 1 月 20 日–2 月 18 日。不同资料的交界日期可能相差一天。The same dates as this site's Chinese Zodiac & Star Sign Calculator — for example Capricorn 22 December to 19 January and Aquarius 20 January to 18 February. Sources can differ by a day at the boundaries.
随机结果真的随机吗？Is the randomness truly random?
「随机生日生成器（指定年龄范围）」使用浏览器的 crypto.getRandomValues（密码学安全随机数）生成结果，并做了无偏处理，每个结果出现的概率相同。The Random Birthday Generator (by age range) uses crypto.getRandomValues (cryptographically secure randomness) with unbiased sampling, so every outcome is equally likely.
「随机生日生成器（指定年龄范围）」免费吗？需要注册吗？Is the Random Birthday Generator (by age range) free? Do I need an account?
「随机生日生成器（指定年龄范围）」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 Random Birthday Generator (by age range) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.