Nilakantha Series Calculator
Free online nilakantha series 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：尼拉坎塔级数在线计算器
原理：尼拉坎塔约 1500 年给出 π = 3 + 4/(2·3·4) − 4/(4·5·6) + 4/(6·7·8) − ⋯，通项分母是三个连续整数的乘积，衰减速度比莱布尼茨级数的 1/k 快得多。
步骤：① 输入求和项数 n；② 累加符号交替、分母为 (2k)(2k+1)(2k+2) 的项；③ 与 π 对比。
示例：仅 10 项就有 3.141406718467（误差约 1.9×10^−4）；100 项达 3.141592410846（误差 2.4×10^−7），比莱布尼茨级数同项数精确约 4 万倍。
注意事项：该级数同样源自 arctan 展开与恒等变换，数值求和时先算符号再累加可避免大数吃小数；当 n 超过约 10^7 时双精度误差已与截断误差相当。
相关：格雷戈里-莱布尼茨级数是同一思想更早的形态；韦达公式与阿基米德割圆术代表几何路径的 π 逼近。
How to use the Nilakantha Series 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 Nilakantha Series 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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