## Introduction to Spherical Coordinates Calculator:

Spherical Coordinates Calculator is an online tool that is used to find the **solution of spherical coordinates** in three-dimensional space. It helps you to get a simplified process for evaluating the symmetry spherical coordinates values.

Spherical to rectangular coordinates calculator is a useful tool for students, teachers, and researchers to solve these coordinate value problem solutions without any error because it has various applications in physics, engineering, and mathematics.

## What are Spherical Coordinates?

Spherical coordinates is a that is used to describe the one distant point and two angles in three-dimensional space in coordinate geometry.

It is used to find the coordinates of the objects which are present in three-dimensional space. The **spherical coordinates** conversion are (ρ,θ,φ) that is given as:

- ρ measures how far a point is at the origin.
- θ specifies the high or low point which is relative to the z-axis.
- φ determines the direction around a point around the z-axis in the XY-plane.

## How to Find Spherical Coordinates?

To **find the spherical coordinates** (ρ,θ,φ) from Cartesian coordinates (x,y,z), you need to know about the other coordinates like rectangular or cartesian coordinates which are used for the conversion into spherical coordinates. Here is the calculation steps for spherical coordinates.

**Step 1**:

First, determine the type of the coordinates that you convert into spherical coordinates value.

**Step 2**:

Find the radial distance (ρ) which is the distance from the origin to the point.

**Step 3**:

Then determine the polar angle θ which is the angle between the positive z-axis and the line that intersects the origin to the point.

**Step 4**:

Lastly, to find the azimuthal angle φ which is the angle between the positive x-axis and the projection of the point onto the xy-plane. Follow these steps to get an idea about the spherical coordinates value problem solution.

## Example of Spherical Coordinates:

An **example of spherical coordinates** value gives you complete detail about the working process spherical coordinates calculator

### Example: Convert the rectangular coordinates to spherical coordinates,

$$ (-1, 1, \sqrt{6}) $$

**Solution**:

The given rectangle coordinates are (x,y,z) as (-1,1,√6)

First, find the radial distance,

$$ ρ^2 \;=\; x^2 + y^2 + z^2 $$

Put these values in the above expression,

$$ ρ^2 \;=\; x^2 + y^2 + z^2 \;=\; (-1)^2 + 1^2 + (\sqrt{6})^2 \;=\; 8 $$

$$ ρ \;=\; 2 \sqrt{2} $$

To find the angle θ,

$$ tan \theta \;=\; \frac{y}{x} $$

Put the value in it,

$$ tan \theta \;=\; \frac{1}{-1} $$

$$ \theta \;=\; arctan(-1) \;=\; \frac{3 \pi}{4} $$

To find the azimuthal angle φ,

$$ φ \;=\; arccos \left( \frac{z}{\sqrt{x^2 + y^2 + z^2}} \right) $$

After simplification you get,

$$ \sqrt{6} \;=\; 2\sqrt{2} cos\; φ $$

$$ cos\; φ \;=\; \frac{\sqrt{6}}{2\sqrt{2}} \;=\; \frac{\sqrt{3}}{2} $$

$$ φ \;=\; \frac{\pi}{6} $$

Therefore the spherical coordinates are,

$$ \left( 2\sqrt{2},\; \frac{3 \pi}{4},\; \frac{\pi}{6} \right) $$

## How to Use Spherical Coordinate Converter?

Spherical coordinate calculator has a simple design that enables you to use it to calculate the spherical coordinates questions easily. Before adding the coordinates value as an input for spherical coordinates in solutions, you must follow some of our guidelines. These guidelines are:

- Enter your coordinates value problem for spherical coordinates in the input field.
- Recheck your spherical coordinates problem before hitting the calculate button to start the calculation process in the spherical to rectangular coordinates calculator.
- Click on the “
**Calculate**” button to get the desired result of your given coordinates value question. - If you want to try out our spherical graphing calculator for the first time then you can use the load example.
- Click on the “Recalculate” button to get a new page for solving more spherical coordinates value problems to get solutions.

## Output From the Spherical Coordinate Calculator:

The spherical to rectangular coordinates calculator gives you the **solution** to a given spherical coordinate value problem when you add the input into it. It provides you with solutions to the spherical coordinates value problem. It may contain the following:

**Result Option**:

You can click on the result option and it provides you with a solution for the spherical coordinates value questions.

**Possible Step**:

When you click on the possible steps option it provides you with the solution of spherical coordinates value problems in detail.

## Benefits of Rectangular to Spherical Coordinates Calculator:

The spherical to rectangular coordinates calculator has many **benefits** that you obtain whenever you use it to calculate spherical coordinates problems to find the solutions. These benefits are:

- Spherical graphing calculator is an easy tool that can be operated through any electronic devices like laptops, computers, mobile, tablets, etc.
- Spherical coordinate calculator is a free tool so you can use it to find the spherical coordinates value problems.
- Our tool saves the time and effort that you consume in doing lengthy calculations of spherical coordinates value problems in a few seconds.
- You can use the cartesian to spherical coordinates calculator for practice because of which you get in-depth knowledge about this method.
- It is a trustworthy tool that provides you with accurate solutions of spherical coordinates problems whenever you use it.
- The spherical coordinate converter provides you solutions to spherical coordinates questions with a complete process for a better understanding.