To calculate result you have to disable your ad blocker first.

# Divergence Calculator

Choose divergence or curl, enter the values, and hit the calculate button to find the divergence or curl.

## Divergence Calculator

Divergence calculator is used to finding the divergence of the given vector field with steps in no time.

## What is a divergence of a function?

The divergence of a vector is a method that turns a vector field into a scalar value. We obtain the scalar field by differentiating the given vector field. It is also known as the dot product of a vector field with the nabla operator.

## Formula of divergence:

A vector field F(x, y, z) and the nabla operator ∇=(∂/∂x, ∂/∂y, ∂/∂z). Then the divergence of the vector will be

div. F = ∇.F = ∂/∂x(F(x,y,z)) + ∂/∂y(F(x,y,z)) + ∂/∂z(F(x,y,z))

## Explanation of the divergence:

The divergence of the function may be positive, negative, or zero. Let F is a vector

- If
**∇. F < 0**; it means the divergence is negative which identifies the fluid is denser at the given point. - If
**∇. F > 0**; it means the divergence is positive which identifies the fluid is less dense at the given point. - If
**∇. F = 0**; it means the divergence is zero which identifies the density of the fluid as constant at a given point.

## How do we get the divergence?

To understand the step-by-step solution, we have discussed an example below comprehensively.

**Example:**

Find the divergence of the function (cos(xyz), x^{2}, z^{3}) at the point (2, 3, 4).

**Solution:**

**Step 1:** It is the dot product of ∇=(∂/∂x, ∂/∂y, ∂/∂z) with the function.

∇.(cos(xyz), x^{2}, z^{3})

**Step 2:** Now calculate the partial derivative of the function.

∂/∂x(cos(xyz)) = -yz sin(xyz)

∂/∂y(x^{2}) = 0

∂/∂z(z^{3}) = 3z^{2}

**Step 3:** Combine the terms.

∇.(cos(xyz), x^{2}, z^{3}) = -yzsin(xyz)+ 3z^{2}

**Step 4: **Put the value of the terms in the above function.

= -3(4)sin((2)(3)(4))+ 3(4)^{2}

= 48-12sin(24)