π 圆周率 π 位数计算器（最多 10000 位）Pi Digits Calculator (up to 10,000 digits)
在浏览器里用梅钦公式（π = 16·arctan(1/5) − 4·arctan(1/239)）和大整数精确算出 π 小数点后 1–10000 位，可分组显示、复制，统计各数字出现次数，并查找生日等数字串第一次出现的位置。Compute π to 1–10,000 decimal places right in your browser with Machin's formula (π = 16·arctan(1/5) − 4·arctan(1/239)) and exact big-integer arithmetic. Group and copy the digits, count how often each digit appears, and find where a digit string such as a birthday first shows up.
使用说明与常见问题How-to & FAQ
「圆周率 π 位数计算器（最多 10000 位）」是什么？What is the Pi Digits Calculator (up to 10,000 digits) tool?
在浏览器里用梅钦公式（π = 16·arctan(1/5) − 4·arctan(1/239)）和大整数精确算出 π 小数点后 1–10000 位，可分组显示、复制，统计各数字出现次数，并查找生日等数字串第一次出现的位置。Compute π to 1–10,000 decimal places right in your browser with Machin's formula (π = 16·arctan(1/5) − 4·arctan(1/239)) and exact big-integer arithmetic. Group and copy the digits, count how often each digit appears, and find where a digit string such as a birthday first shows up.
如何使用「圆周率 π 位数计算器（最多 10000 位）」？How do I use the Pi Digits Calculator (up to 10,000 digits) tool?
在「圆周率 π 位数计算器（最多 10000 位）」中，填写「小数位数（1–10000）」、「分组」、「查找数字串（可选）」等参数，结果会随输入实时计算并显示在下方。In the Pi Digits Calculator (up to 10,000 digits): Fill in "Decimal places (1–10000)", "Grouping", "Find digits (optional)"; results are recalculated instantly as you type.
这些位数是查表得来的吗？Are the digits looked up from a table?
不是，每次都在你的浏览器里现场计算：用梅钦公式 π = 16·arctan(1/5) − 4·arctan(1/239)，把 arctan 的级数用 JavaScript 大整数（BigInt）精确求和，并多算 10 位保护位后截断，所以显示的每一位都是准确的（截断而不是四舍五入）。我们用 mpmath 核对过 1、10、50、1000 和 10000 位的结果。No — they are computed live in your browser with Machin's formula π = 16·arctan(1/5) − 4·arctan(1/239), summing the arctan series exactly with JavaScript big integers (BigInt) plus 10 guard digits and then truncating, so every digit shown is correct (truncated, not rounded). Results at 1, 10, 50, 1,000 and 10,000 places were checked against mpmath.
为什么最多 10000 位？Why stop at 10,000 digits?
梅钦公式的计算量大约随位数的平方增长。10000 位在普通电脑上通常一秒内算完，再多就会让页面明显卡顿。日常背诵、教学或测试用 10000 位已经足够。The work for Machin's formula grows roughly with the square of the number of digits. 10,000 places usually take under a second on an ordinary computer; beyond that the page would stall noticeably. It is plenty for memorising, teaching or testing.
“查找数字串”怎么用？How does 'Find digits' work?
填 1–20 位数字（比如生日 0314），工具会在当前算出的小数位里找它第一次出现的位置，从小数点后第 1 位算起。找不到时可以把“小数位数”调大。著名的“费曼点”999999 出现在第 762 位。Enter 1 to 20 digits (a birthday such as 0314, say) and the tool finds where they first appear among the computed decimals, counting from the first place after the point. If they aren't found, raise 'Decimal places'. The famous Feynman point, 999999, starts at place 762.
「圆周率 π 位数计算器（最多 10000 位）」免费吗？需要注册吗？Is the Pi Digits Calculator (up to 10,000 digits) free? Do I need an account?
「圆周率 π 位数计算器（最多 10000 位）」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 Pi Digits Calculator (up to 10,000 digits) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.