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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

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-dimension 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

$$\frac{\partial \:\:\:}{\partial \:y}\left(e^z\right)=0$$

$$\frac{\partial \:\:\:}{\partial \:z}\left(tan\left(x\right)\right)=0$$

$$\frac{\partial \:\:\:}{\partial x}\left(e^z\right)=0$$

$$\frac{\partial \:\:\:}{\partial \:z}\left(xy\right)=0$$

$$\frac{\partial \:\:\:}{\partial \:x}\left(tan\left(x\right)\right)=sec^2\left(x\right)$$

$$\frac{\partial \:\:\:}{\partial \:y}\left(xy\right)=x$$

**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.**