Curl Calculator

Compute the curl of a 3D vector field F = (P, Q, R) symbolically and evaluate it at a specific point.

Use the Curl Calculator

Vector Field F = (P, Q, R)

Enter expressions using x, y, z. Operators: ^ * / + -, functions: sin cos tan exp ln sqrt.

Evaluate at point (optional)

curl F = ∇ × F

Enter field components and click Compute Curl.

Summary

The curl of a vector field measures how much the field rotates or circulates around a point. Given F = (P, Q, R), its curl is the cross product of the del operator with F, producing a new vector whose components are partial-derivative differences. This tool evaluates those partial derivatives using your input expressions, shows the full symbolic step, then substitutes a point (x, y, z) for the numeric result.

How it works

  1. Enter expressions for the three components P, Q, and R of your vector field.
  2. Optionally enter a point (x, y, z) where the curl should be evaluated numerically.
  3. Click "Compute Curl" to run the symbolic differentiation.
  4. The tool displays the curl formula breakdown, the resulting curl vector, and the magnitude at the given point.
  5. Use the step-by-step panel to review each partial derivative computation.

Use cases

  • Verify curl calculations for homework or exams in multivariable calculus.
  • Check whether a vector field is irrotational (curl = 0) before assuming a potential function exists.
  • Visualize rotation in electromagnetic fields (Faraday's law involves curl E).
  • Quickly evaluate curl at a specific point in fluid dynamics problems.
  • Validate hand computations before submitting assignments.

Frequently Asked Questions

Last updated: 2026-06-18 · Reviewed by Nham Vu