Vector Divergence Calculator
Easily calculate the divergence of a vector field online. Enter your vector field components and variables to get instant results and understand vector field behavior.
Input Vector Field and Variables
Enter the vector field components and the variables with respect to which you want to calculate the divergence. Use array format for both inputs.
Divergence:
Visual Interpretation of Divergence
Divergence at a point measures the rate at which vector field "flows" or "diverges" away from that point.
Positive Divergence (Source): Vectors point outwards from the red point.
What is Divergence?
In vector calculus, divergence is an operation that measures a vector field's source or sink behavior at a given point. It quantifies the volume density of the outward flux of a vector field from a small volume around a point. Mathematically, for a vector field F = (P, Q, R) in Cartesian coordinates, the divergence is given by:
- A positive divergence at a point indicates a source, where the vector field is expanding or flowing outwards (like water from a source). - A negative divergence indicates a sink, where the vector field is converging or flowing inwards (like water into a drain). - A zero divergence implies that the field is solenoidal or incompressible at that point (flow is neither expanding nor contracting).
Divergence is a scalar quantity and is fundamental in physics and engineering, particularly in fluid dynamics, electromagnetism, and heat transfer to describe the behavior of fields.