Curl Calculator
Calculate the curl (nabla x F) of a vector field in 3D space.
Vector Field F(x, y, z)
Use: x, y, z, ^, sin, cos, tan, exp, log, sqrt, pi
Point of Evaluation
Curl Formula
curl F = nabla x F
= (dFz/dy - dFy/dz)i + (dFx/dz - dFz/dx)j + (dFy/dx - dFx/dy)k
Curl nabla x F
(0.0000, 0.0000, -2.0000)
|curl F| = 2.000000
iCurl x
0.000000
jCurl y
0.000000
kCurl z
-2.000000
|C||curl F|
2.000000
Field Properties
Rotational Field
curl F != 0: Field has nonzero rotation/circulation
Vector Field at Point
F = (1.0000, -1.0000, 0.0000)
About Curl
Physical Interpretation
The curl measures the rotation or circulation of a vector field. It points along the axis of rotation, with magnitude proportional to the rotation speed. For fluids, it represents the vorticity.
Applications
- Electromagnetic induction (Faraday's law)
- Fluid vorticity and turbulence
- Angular momentum in physics
- Conservative force detection