Unit Conversions

How to Convert Cylindrical to Spherical | Coordinate Units

Last Updated on June 19, 2024

To convert cylindrical to spherical, three essential parameters are needed: the Value of ρ, the Value of φ, and the Value of z.

The formula for converting cylindrical to spherical (r, θ, φ):

r = √(φ² + z²)

θ = tan-1(ρ / z)

φ = φ

Let’s solve an example;
Find the conversion of cylindrical to cartesian when the value of ρ is 2, the value of φ is 3 and the value of z is 5.

This implies that;

Value of ρ = 2
Value of φ = 3
And, Value of z = 5

Finding r:

r = √(2² + 5²)
r = √(4 + 25)
That is, r = √(29)
r = 5.38

Therefore, is 5.38

Finding θ:

θ = tan-1(2 / 5)
θ = tan-1(0.4)
So, θ = 21.80°

Therefore, θ is 21.80°.

Finding φ:

φ = 3°

Therefore, the spherical coordinates of the cylindrical coordinates (2, 3°, 5) is (5.38, 21.80°, 3°).

Read more: How to Convert Spherical to Cylindrical | Coordinate Units

How to Convert Cylindrical to Spherical Using Nickzom Calculator

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

To get the answer and workings of cylindrical to spherical 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 Cylindrical to Spherical under Coordinate Units

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

Now, enter the values appropriately and accordingly for the parameters as required by the Value of ρ is 2, Value of φ is 3, and Value of z is 5.

Finally, Click on Calculate

How to Convert Cylindrical to Spherical | Coordinate Units
How to Convert Cylindrical to Spherical | Coordinate Units

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

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