Brouncker Calculator
Free online brouncker calculator. Enter your values and get instant results with the formula, step-by-step working, a worked example and FAQs — everything runs locally in your browser on Calcton, no signup required.
中文版：布龙克尔连分数在线计算器
布龙克尔连分数是 π 最早的无理表示之一：4/π = 1 + 1²/(2 + 3²/(2 + 5²/(2 + 7²/(2 + ⋯))))。它由沃利斯时代的皇家学会主席布龙克尔勋爵给出，分子是奇数平方、分母全是 2，形式整齐得像一句咒语。
它的缺点是收敛极慢：误差约按 1/ln N 的量级衰减，N = 10000 才准到小数点后 4 位。本工具自底向上折叠连分数（从最深处的 2 开始往回套），比递归展开数值上稳定得多。
收敛过程（对照 4/π = 1.273239545）
N = 100 → 1.269239529；N = 500 → 1.272431108
N = 2000 → 1.273037036；N = 10000 → 1.273199022
How to use the Brouncker Calculator
- Fill in the inputs with your own numbers — every field shows what it expects.
- The result updates instantly as you type; no "Calculate" click needed.
- Read the result card for the main figure, the step-by-step formula, and practical notes.
Frequently asked questions
Is the Brouncker Calculator free?
Yes — all math calculators on Calcton are free, with no sign-up required. Your inputs are processed in your browser and never sent to a server.
Is there a Chinese version of this tool?
Yes. Use the Chinese version link above — it is the same calculator with the interface in Simplified Chinese.
References
Formulas and benchmarks used by this calculator follow these published sources.
KevinContent LeadCalcton Editorial Team · Last updated 2026-09-28
Kevin maintains Calcton's formula verification and content: every calculator cites the standard it implements, worked examples are recomputed programmatically, and health benchmarks follow WHO and international guidelines.
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