Koch Snowflake Calculator
Free online koch snowflake 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：Koch 雪花在线计算器
Koch 雪花是最著名的分形之一：每次迭代把每条边三等分、中段换成向外凸的等边三角形。周长每轮乘 4/3 发散到无穷，面积却每轮只增加有限份额、收敛到初始三角形的 8/5 倍——「无限长边界围住有限面积」的经典悖论，也是海岸线测度悖论（Richardson 效应）的玩具模型。
闭式全套可写：P_n = 3s(4/3)ⁿ；A_n = A₀ + Σₖ 3·4^(k−1)·(√3/4)(s/3ᵏ)²，求和收敛到 A∞ = 2√3/5·s²。分形维数 log4/log3 ≈ 1.2619，介于 1 维曲线与 2 维面之间。本工具已验证 A_n 的递推、闭式与极限值逐位一致。
参考值（s = 1）
A₁ = √3/3 = 0.577350269190、P₃ = 64/9 = 7.111111111111
A∞ = 2√3/5 = 0.6928203230275509；n = 10 时 P₁₀ = 3(4/3)¹⁰ = 53.273179901438
How to use the Koch Snowflake 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 Koch Snowflake 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 2026-09-29
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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