What is curl?
A vector measuring the infinitesimal rotation of a vector field.
Curl Calculator
Enter linear coefficients for P, Q, R to obtain the constant curl vector.
Enter linear field coefficients
For P=a₁x+b₁y+c₁z, Q=a₂x+b₂y+c₂z, R=a₃x+b₃y+c₃z enter the nine coefficients.
About this calculator
How to use Curl Calculator, plus the formulas and logic behind the results.
Tool description
Curl measures local rotation of a vector field. For linear fields the curl is a constant vector.
How to use
- Enter the nine linear coefficients of P, Q, and R.
- Select Calculate to view ∇ × F.
- Interpret a zero curl as an irrotational field (in simply connected domains).
- Compare with the divergence tool for ∇ · F.
Formulas & reference
curl F = (∂R/∂y − ∂Q/∂z, ∂P/∂z − ∂R/∂x, ∂Q/∂x − ∂P/∂y)For linear fields, partials are the corresponding coefficients
Curl tips
- curl grad f = 0 for smooth f
- 2D field (P,Q,0): curl reduces to (0,0, Qₓ − Pᵧ)
- Positive z-curl suggests counterclockwise spin in xy
- Units depend on the field quantity
Calculation logic
Reads constant partial derivatives from the linear coefficients and assembles the curl components.
Constants and nonlinear terms are omitted—linear homogeneous model only.
Curl Calculator FAQ
Common questions about this calculator and how to use the results.
Why linear fields?
Partials are constants, so curl is easy to compute by hand and by machine.
What if curl is zero?
The field is irrotational (locally conservative under mild conditions).
Is 2D supported?
Set all R coefficients and z-coeffs of P,Q to 0.
Does position matter?
Not for this linear model—curl is constant everywhere.
Is this free?
Yes.