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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

## 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(x**_{1}, x_{2}, x_{3})- $$∇=\frac{\partial }{\partial x},\:\frac{\partial }{\partial y},\:\frac{\partial }{\partial z}$$

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 (e^{z}) = 0

∂/∂z (tan(x)) = 0

∂/∂x (e^{z}) = 0

∂/∂z (xy) = 0

∂/∂x (tan(x)) = sec^{2}(x)

∂/∂y (xy) = x

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

`(0, 0, -x + sec`

^{2}(x))

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

`(0, 0, -2 + sec`

^{2}(2))

Hence we have a curl **-2+sec ^{2}(2)** of the vector.