Vieta Formula Calculator
Free online vieta formula 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：韦达无穷乘积 π 计算器
原理：韦达 1593 年给出 2/π = cos(π/4) · cos(π/8) · cos(π/16) ⋯，每一项都是用半角公式从单位圆反复二分得到的无穷乘积，是人类历史上第一个精确的 π 无穷表达式。
步骤：① 选乘积项数 n；② 计算前 n 项部分积；③ 与 2/π ≈ 0.636619772368 对比误差。
示例：n = 10 时 P(10) ≈ 0.636620022039，与 2/π 相差约 2.5×10^−7；n = 20 时误差已缩小到 10^−12 量级。
注意事项：该乘积每增加一项误差约缩小一半的对数尺度，20 项之后双精度浮点已无法继续改善；若用普通浮点逐项相乘，注意从大项往小项乘以减少舍入累积。
相关：阿基米德割圆术同样用二分多边形逼近 π；无穷乘积工具给出 Π(1+c/k^p) 型乘积的敛散判定。
How to use the Vieta Formula 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 Vieta Formula 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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