LaTeX
\nabla\times\mathbf FVariables
- F: vector field
How to use this formula
Measures local rotation of a three-dimensional vector field.
Important notes
- In two dimensions, curl is often represented by a scalar component.
Quick example
For F=(−y,x,0), curl=(0,0,2).
Applicability, worked calculation, and verification
Assumptions and domain checks
- In two dimensions, curl is often represented by a scalar component.
- Preserve matrix order and verify dimension compatibility; multiplication and inversion are not generally commutative or always defined.
- The function must satisfy the differentiability, continuity, or integrability conditions required by the operation being used.
Worked example
For F=(−y,x,0), curl=(0,0,2).
Common mistakes
- Before substituting values into Curl, map each variable to its definition and preserve every sign, exponent, subscript, and grouping mark.
- Do not apply a differentiation or integration rule outside its domain or omit endpoint, continuity, or constant-of-integration checks.
Continue the workflow
Use Curl in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
\nabla\times\mathbf F. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Calculus Volume 1OpenStax, Rice University — Reviewed limits, derivatives, integrals, and foundational calculus formulas.
Frequently asked questions
What is the Curl used for?
Measures local rotation of a three-dimensional vector field.
Can I copy this formula as LaTeX?
Yes. Copy \nabla\times\mathbf F or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.