Divergence Calculator
Calculate the divergence (nabla dot F) of a vector field in 3D space.
Vector Field F(x, y, z)
Use: x, y, z, ^, sin, cos, tan, exp, log, sqrt, pi
Point of Evaluation
Divergence Formula
div F = nabla dot F = dFx/dx + dFy/dy + dFz/dz
Divergence nabla dot F
12.000000
at point (1, 2, 3)
dxdFx/dx
2.000000
dydFy/dy
4.000000
dzdFz/dz
6.000000
|F||F|
9.899495
Field Classification
Source (div F > 0): Yes
Sink (div F < 0): No
Solenoidal (div F = 0): No
Vector Field at Point
F = (1.0000, 4.0000, 9.0000)
About Divergence
Physical Interpretation
Divergence measures the net outward flux per unit volume at a point. A positive divergence indicates a source (fluid expanding), while negative indicates a sink (fluid contracting).
Applications
- Fluid dynamics and flow analysis
- Electromagnetic theory (Maxwell's equations)
- Heat transfer problems
- Continuity equations in physics