How curl is calculated
- Write the field as \(\langle P,Q,R\rangle\).
- Use \(\nabla\times\mathbf{F}=\langle R_y-Q_z, P_z-R_x, Q_x-P_y\rangle\).
- Keep component order and signs consistent.
Curl Calculator
Calculate curl for three-dimensional 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.
Curl Examples
What this calculator is for
Curl measures local rotation in a three-dimensional vector field. It is important in fluid flow and electromagnetism. 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: \(\mathbf{F}=\langle -y,x,0\rangle\).
- Curl is \(\langle0-0,0-0,1-(-1)\rangle\).
- Final result: \(\langle0,0,2\rangle\).
Common mistakes to avoid
- Swapping components in the determinant.
- Losing the minus sign in the middle component.
- Using curl on a two-dimensional scalar function.
When to double-check the result
Curl is normally a three-dimensional vector-field operation. For 2D fields, check whether your course expects scalar curl or a 3D embedding.