What is Multivariable Gradient Div Curl Calculator and Why it Matters?
Gradient, divergence, and curl are fundamental operators in vector calculus used in electromagnetism and fluid dynamics.
Mathematical Formula and Theory
∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z). div F = ∂Fₓ/∂x + ∂Fᵧ/∂y + ∂F_z/∂z. curl F is the usual determinant formula.
How to Use This Calculator - Step by Step
- Select Gradient, Divergence, or Curl.
- Enter the scalar or vector components.
- Click Compute.
Solved Example with Full Calculation
f = x²+y²+z² ⇒ ∇f = (2x,2y,2z). F=(−y,x,0) ⇒ curl F = (0,0,2).