Hessian Matrix Calculator

What the Hessian tells you

The Hessian matrix collects every second-order partial derivative of $f$ .

Diagonal entries measure curvature along each axis, while off-diagonal entries measure how variables interact through mixed partial derivatives.

In optimization, the Hessian helps classify critical points and understand whether a surface bends upward, downward, or in mixed directions.

Separate variables with commas, such as x, y or x, y, z.
Use math syntax like x^2*y + y^3 or exp(x*y).
If the function is twice continuously differentiable, the Hessian is typically symmetric.

Easily compute the Jacobian matrix of a multivariable function online.

Find critical points of multivariable functions easily.

Calculate the Laplacian of a scalar function with variable toggles, second-derivative breakdowns, and a compact operator-expansion board.