What is divergence?
A scalar measuring source/sink strength of a vector field.
Divergence Calculator
Enter linear coefficients to obtain the constant divergence of the field.
Choose dimension and coefficients
Select 2D or 3D, then enter the linear coefficients of each component.
About this calculator
How to use Divergence Calculator, plus the formulas and logic behind the results.
Tool description
Divergence measures the net outward flux density of a vector field at a point.
How to use
- Select 2D or 3D mode.
- Enter the linear coefficients.
- Select Calculate to view ∇ · F.
- Positive divergence suggests a local source.
Formulas & reference
2D: div F = ∂P/∂x + ∂Q/∂y = a + d3D diagonal: div F = a + b + c
Divergence tips
- div curl F = 0
- Incompressible flow often has div v = 0
- 2D: off-diagonal b and c do not affect divergence
- Compare with the curl calculator
Calculation logic
Sums the diagonal partial derivatives of the linear field model.
3D mode uses F=(ax, by, cz) for a clear educational example.
Divergence Calculator FAQ
Common questions about this calculator and how to use the results.
Why is div constant here?
Linear fields have constant first partials.
Do b and c matter in 2D?
Not for divergence—only a and d appear.
What is the 3D model?
F = (ax, by, cz) so div = a+b+c.
Zero divergence meaning?
Locally volume-preserving / incompressible (in fluid contexts).
Is this free?
Yes.