Divergence Theorem Calculator
Free online divergence theorem 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：散度定理验证计算器
散度定理（高斯公式）验证：∯ F·n dS = ∭ div F dV。对半径 R 的球面，分别用球面网格数值计算通量与体积解析积分，两侧对照。
径向场解析：∯ (x,y,z)·n dS = 3·(4/3)πR³ = 4πR³。旋转场 div = 0，两侧均为 0（流入等于流出，无净通量）。散度定理把闭曲面面积分转化为体积积分，是电磁学高斯定律 ∮ E·dA = Q/ε₀ 的数学基础。
How to use the Divergence Theorem 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 Divergence Theorem 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 2026-09-12
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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