Rose Curve Calculator
Free online rose curve 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：玫瑰线在线计算器
玫瑰线 r = a·cos(kθ) 是极坐标下最美的参数族之一：k 为奇数时恰好 k 瓣（θ 走 [0,π] 即描完全部花瓣），k 为偶数时翻倍成 2k 瓣。面积有干净闭式——奇数 k 为 πa²/4、偶数 k 为 πa²/2，源自 ∫r²dθ 的半角公式。瓣缘周长没有初等表达式，需数值积分速度模 √(r² + r′²)。
k = 1 退化为过极点、直径为 a 的圆（周长 πa）；k = 2 的四叶草常用于天线方向图与显微镜视场光阑的建模。米开朗基罗广场地砖、法冠花窗的玫瑰窗几何，都可以用这一族曲线精确复刻。gen198 中面积与 shoelace/解析值、周长与 80/160 段双网格均交叉一致。
参考值（a = 1）
k = 2（四叶）：A = π/2 = 1.570796326795、周长 = 9.688448220548
k = 3（三叶）：A = π/4 = 0.785398163397、周长 = 6.682446610278；k = 1（圆）：周长 = π = 3.141592653590
How to use the Rose Curve 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 Rose Curve 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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