Laplacian Calculator
Free online laplacian 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：拉普拉斯算子计算器
计算三维二次场 f(x, y, z) = a·x² + b·y² + c·z² 的拉普拉斯算子 Δf = ∂²f/∂x² + ∂²f/∂y² + ∂²f/∂z²，并用中心差分数值验证。Δf = 0 的函数称为调和函数，描述静电场无源区与稳态温度分布。
经典调和函数：f = x² + y² − 2z²（默认参数，Δf = 0）；f = ln r 在二维、1/r 在三维中除原点外处处调和。物理上静电学满足 ΔV = −ρ/ε₀（泊松方程），无电荷区域 ρ = 0 退化为拉普拉斯方程；稳态热传导中 ΔT = 0。
How to use the Laplacian 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 Laplacian 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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