Unit Conversions

How to Convert Spherical to Cartesian | Coordinate Units

Last Updated on March 19, 2023

The image below represents spherical to cartesian.

To convert spherical to cartesian, three essential parameters are needed and these parameters are the Value of r, the Value of θ, and the Value of φ.

The formula for converting spherical to cartesian (x, y, z):

x = rsinθcosφ

y = rsinθsinφ

z = rcosθ

Let’s solve an example;
Find the conversion of spherical to cartesian when the value of r is 2, the value of θ is 8 and the value of φ is 4.

This implies that;

Value of r = 2
Value of θ = 8
Value of φ = 4

Finding x:

x = 2 x sin(8°) x cos(4°)
x = 2 x 0.139 x 0.997
x = 0.277

Therefore, is 0.277.

Finding y:

y = 2 x sin(8°) x sin(4°)
y = 2 x 0.139 x 0.069
y = 0.019

Therefore, is 0.0019.

Finding z:

z = 2 x cos(8°)
z = 2 x 0.9902680687415704
z = 1.98

Therefore, z is 1.98.

Therefore, the Cartesian coordinates of the spherical coordinates (2, 8°, 4°) is (0.27, 0.019, 1.98).

Nickzom Calculator – The Calculator Encyclopedia is capable of converting spherical to cartesian.

To get the answer and workings of spherical to cartesian using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

You can get this app via any of these means:

Web – https://www.nickzom.org/calculator-plus

To get access to the professional version via web, you need to register and subscribe to have utter access to all functionalities.
You can also try the demo version via https://www.nickzom.org/calculator

Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator
Android (Free) – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator

Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Coordinate Units under Switches.

Now, Click on Spherical to Cartesian under Coordinate Units

The screenshot below displays the page or activity to enter your values, to get the answer for the conversion of spherical to cartesian according to the respective parameters which are the Value of r, the Value of θ, and the Value of φ.

Now, enter the values appropriately and accordingly for the parameters as required by the Value of r is 2, the Value of θ is 8, and the Value of φ is 4.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves the conversion of spherical to cartesian and presents the formula, workings, and steps too.

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