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Curl Calculator

To find the curl through curl calculator, Select the method of your input i.e., with points or without points, enter the functions, and click calculate button

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Curl Calculator

Curl Calculator is used to find the curl of a vector field at the given points of function x, y, and z. This curl finder will take three functions along with their points to find the curl of a vector with steps.

What is the curl of a vector?

The curl of a vector is defined as the cross-product of a vector with nabla . The curl is a vector quantity. Geometrically, the curl of a vector gives us information about the tendency of a field to rotate about a point.

Formula of the curl

∇ × F = ( ∂/∂y [R] - ∂/∂z [Q], ∂/∂z [P] - ∂/∂x [R], ∂/∂x [Q] - ∂/∂y [P])

Where

  • is known as the nabla operator and G is the function.
  • G= G(x1, x2, x3)
  • $$∇=\frac{\partial }{\partial x},\:\frac{\partial }{\partial y},\:\frac{\partial }{\partial z}$$

The determinant is taken as:

$$∇\cdot G=\left[\frac{\partial \:\:}{\partial y}\left(G_3\right)-\frac{\partial \:\:}{\partial z}\left(G_2\right)\right]i\:-\left[\frac{\partial \:\:}{\partial x}\left(G_3\right)-\frac{\partial \:\:}{\partial z}\left(G_1\right)\right]j+\left[\frac{\partial \:\:}{\partial x}\left(G_2\right)-\frac{\partial \:\:}{\partial y}\left(G_1\right)\right]k$$

How we find the curl of a vector:

To find the curl of a vector we have to understand the step-by-step solutions with the help of an example.

Example:

Find the curl of a three-dimensional vector: F = (xy, tan(x), e^z) at the point (2,3,4).

Solution:

Step 1: By definition of curl, we have to take the determinant

$$∇\cdot G=\left[\frac{\partial \:\:}{\partial y}\left(e^z\right)-\frac{\partial \:\:}{\partial z}\left(tan\left(x\right)\right)\right]i\:-\left[\frac{\partial \:\:}{\partial x}\left(e^z\right)-\frac{\partial \:\:}{\partial z}\left(xy\right)\right]j+\left[\frac{\partial \:\:}{\partial x}\left(tan\left(x\right)\right)-\frac{\partial \:\:}{\partial y}\left(xy\right)\right]k$$

Step 2: Now take the partial derivatives

∂/∂y (ez) = 0

∂/∂z (tan(x)) = 0

∂/∂x (ez) = 0

∂/∂z (xy) = 0

∂/∂x (tan(x)) = sec2(x)

∂/∂y (xy) = x

Step 3: Now put the values of partial derivatives in the formula:

(0, 0, -x + sec2(x))

Step 4: Now put the value of the point in the function.

(0, 0, -2 + sec2(2))

Hence we have a curl -2+sec2(2) of the vector.

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