Divergence Calculator
Calculate the divergence of a two-dimensional or three-dimensional vector field at any point. Enter the vector components and instantly review each partial derivative and the final scalar result.
Select a 2D or 3D vector field.
Provide P, Q, and R functions plus the evaluation point.
See the derivative terms and final scalar value.
Use x, y, and z as variables. Supported functions include sin, cos, tan, asin, acos, atan, sqrt, abs, exp, log, log10, floor, ceil, and round. Use ^ for powers and pi or e for constants. Examples: x*y, sin(x)+y², or exp(z)-x.
The calculator estimates partial derivatives numerically with a central-difference method. Results are most reliable for smooth functions near the selected point. Undefined values, discontinuities, or extremely small step sizes may reduce accuracy.
What is divergence?
Divergence measures the net outward flow of a vector field from an infinitesimally small region around a point.
What does positive divergence mean?
A positive value indicates source-like behavior, while a negative value indicates sink-like behavior.
Can divergence be zero?
Yes. Zero divergence means the field is locally incompressible, with balanced inflow and outflow.
Results are estimates generated locally in your browser using standard mathematical formulas. They are for informational and educational purposes only and are not a substitute for verification in coursework, examinations or professional contexts requiring certified accuracy. VisionVix accepts no liability for decisions based on this tool's output.
This calculator provides numerical estimates for educational and analytical use. Verify critical engineering or scientific results with symbolic software or an independent calculation.
