Buffon Needle Calculator
Free online buffon needle 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：布丰投针在线计算器
1777 年布龙克尔（Georges-Louis Leclerc, Comte de Buffon）提出了随机性首次敲开几何大门的问题：把一根针随机丢在画满等距平行线的纸上，针与某条线相交的概率是多少？答案里出现了 π——因为针的随机角度均匀分布，而正弦函数的平均值是 2/π。
短针（L ≤ d）时 P = 2L/(πd)，可反解 π ≈ 2L/(P·d)；长针（L 大于 d）时针可能同时跨两条线，公式切换为带 arccos 的修正版本。本工具同时给出解析概率与随机模拟对照，两者应在千分之一量级内吻合（受模拟次数限制）。
参考值
L = 1、d = 2：P = 1/π = 0.3183098861837907
L = 2、d = 1：P = 0.8372484205582454（长针，约 83.7%）
How to use the Buffon Needle 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 Buffon Needle 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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