How divergence is calculated
- Write the vector field as \(\langle P,Q,R\rangle\).
- Compute \(P_x+Q_y+R_z\).
- Interpret the scalar result as source or sink tendency.
Divergence Calculator
Calculate divergence for vector fields.
Use this calculator as a study checker
Enter the problem carefully, review the interpreted input, and compare each step with your own work. Calculus results can depend on notation, variables, bounds, domains, and assumptions.
- Check the method before copying the answer.
- Use the examples below to test nearby problems.
- Read the calculus guides for worked explanations.
Solution
50 study checks todayEnter an expression or choose an example to calculate.
Divergence Examples
What this calculator is for
Divergence measures how much a vector field spreads out from a point. Positive divergence suggests a source and negative divergence suggests a sink. Use it to check your setup, compare steps with your own work, and review the meaning of the final expression before copying it into homework.
Manual example
- Problem: \(\mathbf{F}=\langle x,y,z\rangle\).
- Differentiate matching components: \(\partial x/\partial x=1\), \(\partial y/\partial y=1\), \(\partial z/\partial z=1\).
- Divergence is \(3\).
Common mistakes to avoid
- Differentiating every component with respect to every variable.
- Confusing divergence with curl.
- Entering vector components in the wrong order.
When to double-check the result
Divergence requires a vector field, not a scalar function. Use commas or clear component notation in the input.