Unit Conversions

How to Convert Cartesian to Spherical | Coordinate Units

Last Updated on March 20, 2023

The image below represents cartesian to spherical.

To convert cartesian to spherical, three essential parameters are needed and these parameters are the Value of x, the Value of y, and the Value of z.

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

r = √(x² + y² + z²)

φ = tan-1(y / x)

θ = tan-1((√(x² + y²) / z)

Let’s solve an example;
Find the conversion of cartesian to spherical when the value of x is 4, the value of y is 3 and the value of z is 6.

This implies that;

Value of x = 4
Value of y = 3
Value of z = 6

Finding r:

r = √(4² + 3² + 6²)
r = √(16 + 9 + 36)
r = √(61)
r = 7.81

Therefore, r is 7.81

Finding θ:

θ = tan-1((√(4² + 3²)) / 6)
θ = tan-1((√(16 + 9)) / 6)
θ = tan-1((√(25)) / 6)
θ = tan-1((5) / 6)
θ = tan-1(0.8333333333333334)
θ = 39.80°

Therefore, θ is 39.80°.

Finding φ:

φ = tan-1(3 / 4)
φ = tan-1(0.75)
φ = 36.86°

Therefore, φ is 36.86°.

Therefore, the spherical coordinates of the Cartesian coordinates (4, 3, 6) is (7.81, 39.80°, 36.86°).

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

To get the answer and workings of cartesian 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 Cartesian 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 cartesian to spherical according to the respective parameters which are the Value of x, Value of y and Value of z.

Now, enter the values appropriately and accordingly for the parameters as required by the Value of x is 4, Value of y is 3 and Value of z is 6.

Finally, Click on Calculate

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

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