Hessian Calculator
Free online hessian 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：海森矩阵计算器
求二元二次函数 f(x,y) = a·x² + b·y² + c·xy + d·x + e·y 的海森矩阵、驻点与极值分类。判定规则：det H > 0 且 a > 0 为极小，det H > 0 且 a < 0 为极大，det H < 0 为鞍点。
驻点由 ∇f = 0 解出：2ax + cy + d = 0 与 cx + 2by + e = 0 联立。特征值 λ₁₂ = (a+b) ± √((a−b)² + c²)，两特征值同正为正定（极小），同负为负定（极大），异号为鞍点。
How to use the Hessian 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 Hessian 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.
Related calculators
More in this category: Math calculators
About math calculators
Free online math calculators for algebra, statistics, number theory and everyday arithmetic — from quadratic equations and matrices to percentages, fractions and prime factorization, each with step-by-step formulas.