Gradient Vector Calculator

Calculate the gradient vector of f(x,y) = ax² + by² + cxy at any point. Shows magnitude and direction of steepest ascent.

Coefficient of x² (a)

Coefficient of y² (b)

Coefficient of xy (c)

x Point

y Point

Tab to move between fields

∂f/∂x

∂f/∂y

Magnitude |∇f|7.2111

Direction56.31°

How to Use This Calculator

Enter the partial derivative values ∂f/∂x and ∂f/∂y (and optionally ∂f/∂z for 3D functions) at the evaluation point.
The gradient ∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z) is a vector pointing in the direction of steepest ascent of f.
Gradient magnitude |∇f| = √((∂f/∂x)² + (∂f/∂y)² + (∂f/∂z)²) tells you how steep the ascent is.
The unit gradient vector (∇f / |∇f|) gives the direction of steepest ascent with magnitude normalized to 1.
In optimization, the gradient is zero at critical points; gradient descent moves opposite to ∇f to minimize f.
The bar chart displays each component's magnitude to visualize which variable drives the most change.

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