Archimedes Pi Calculator
Free online archimedes pi 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：阿基米德割圆术在线计算器
原理：单位圆内接正 n 边形周长为 2n·sin(π/n)、外切为 2n·tan(π/n)，两者分别夹住圆周长 2π；因此 π 被夹在 n·sin(π/n) 与 n·tan(π/n) 之间，边数翻倍区间大约缩小 4 倍。
步骤：① 输入边数 n（阿基米德用 96 边形）；② 计算上下界；③ 查看区间宽度评估精度。
示例：n = 96 时得 3.141031950891 < π < 3.142714599645，区间宽约 0.00168，正是阿基米德「3 又 10/71 与 3 又 1/7 之间」的来源。
注意事项：n 很大时 tan(π/n) 的浮点计算稳定，但外切界对舍入更敏感；本方法收敛速度与韦达公式相当（每翻倍约多得一位十进制数字）。
相关：韦达公式可视为割圆术的解析极限；尼拉坎塔与格雷戈里-莱布尼茨级数则用解析级数路径逼近 π。
How to use the Archimedes Pi 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 Archimedes Pi 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 2026-10-03
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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