{"id":9956,"date":"2023-03-19T20:06:42","date_gmt":"2023-03-19T19:06:42","guid":{"rendered":"https:\/\/www.nickzom.org\/blog\/?p=9956"},"modified":"2024-06-19T21:02:51","modified_gmt":"2024-06-19T20:02:51","slug":"how-to-convert-cartesian-to-spherical-coordinate-units","status":"publish","type":"post","link":"https:\/\/www.nickzom.org\/blog\/2023\/03\/19\/how-to-convert-cartesian-to-spherical-coordinate-units\/","title":{"rendered":"How to Convert Cartesian to Spherical | Coordinate Units"},"content":{"rendered":"<p>Three essential parameters are needed to convert cartesian to spherical: the value of x, the value of y, and the value<strong>\u00a0of z<\/strong><strong>.<\/strong><\/p>\n<h3><strong>The formula for converting cartesian to spherical (r, \u03b8, \u03c6):<\/strong><\/h3>\n<p>r = \u221a(x\u00b2 + y\u00b2 + z\u00b2)<\/p>\n<p>\u03c6 = tan<sup>-1<\/sup>(y \/ x)<\/p>\n<p>\u03b8 = tan<sup>-1<\/sup>((\u221a(x\u00b2 + y\u00b2) \/ z)<\/p>\n<p>Let&#8217;s solve an example;<br \/>\nFind 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.<\/p>\n<p>This implies that;<\/p>\n<p>Value of x = 4<br \/>\nValue of y = 3<br \/>\nAnd, Value of z = 6<\/p>\n<p>Finding r:<\/p>\n<p>r = \u221a(4\u00b2 + 3\u00b2 + 6\u00b2)<br \/>\nr = \u221a(16 + 9 + 36)<br \/>\nSo, r = \u221a(61)<br \/>\nr = 7.81<\/p>\n<p>Therefore,\u00a0<strong>r <\/strong>is\u00a0<strong>7.81<\/strong><\/p>\n<p>Finding \u03b8:<\/p>\n<p>\u03b8 = tan<sup>-1<\/sup>((\u221a(4\u00b2 + 3\u00b2)) \/ 6)<br \/>\nThat is, \u03b8 = tan<sup>-1<\/sup>((\u221a(16 + 9)) \/ 6)<br \/>\n\u03b8 = tan<sup>-1<\/sup>((\u221a(25)) \/ 6)<br \/>\n\u03b8 = tan<sup>-1<\/sup>((5) \/ 6)<br \/>\nSo, \u03b8 = tan<sup>-1<\/sup>(0.8333333333333334)<br \/>\n\u03b8 = 39.80\u00b0<\/p>\n<p>Therefore,\u00a0<strong>\u03b8<\/strong>\u00a0is <strong>39.80\u00b0.<\/strong><\/p>\n<p>Finding \u03c6:<\/p>\n<p>\u03c6 = tan<sup>-1<\/sup>(3 \/ 4)<br \/>\nThat is, \u03c6 = tan<sup>-1<\/sup>(0.75)<br \/>\n\u03c6 = 36.86\u00b0<\/p>\n<p>Therefore,\u00a0<strong>\u03c6\u00a0<\/strong>is\u00a0<strong>36.86\u00b0.<\/strong><\/p>\n<p>Therefore, the <strong>spherical coordinates of the Cartesian coordinates (4, 3, 6)<\/strong> is <strong>(7.81, 39.80\u00b0, 36.86\u00b0).<\/strong><\/p>\n<h3><strong>How to Convert Cartesian to Spherical With Nickzom Calculator<\/strong><\/h3>\n<p>Read more:\u00a0<a href=\"https:\/\/www.nickzom.org\/blog\/2023\/03\/19\/how-to-convert-spherical-to-cartesian-coordinate-units\/\">How to Convert Spherical to Cartesian | Coordinate Units<\/a><\/p>\n<p>Nickzom Calculator \u2013 The Calculator Encyclopedia is capable of converting cartesian to spherical.<\/p>\n<div>\n<p>To get the answer and workings of cartesian to spherical using the Nickzom Calculator \u2013 The Calculator Encyclopedia. First, you need to obtain the app.<\/p>\n<p>You can get this app via any of these means:<\/p>\n<p>Web\u00a0\u2013\u00a0<a href=\"https:\/\/www.nickzom.org\/calculator-plus\">https:\/\/www.nickzom.org\/calculator-plus<\/a><\/p>\n<p>To get access to the\u00a0professional\u00a0version via web, you need to\u00a0register\u00a0and\u00a0subscribe\u00a0to have utter access to all functionalities.<br \/>\nYou can also try the\u00a0demo\u00a0version via\u00a0<a href=\"https:\/\/www.nickzom.org\/calculator\">https:\/\/www.nickzom.org\/calculator<\/a><\/p>\n<p>Android (Paid)\u00a0\u2013\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=org.nickzom.nickzomcalculator\">https:\/\/play.google.com\/store\/apps\/details?id=org.nickzom.nickzomcalculator<\/a><br \/>\nAndroid (Free)\u00a0\u2013\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=com.nickzom.nickzomcalculator\">https:\/\/play.google.com\/store\/apps\/details?id=com.nickzom.nickzomcalculator<\/a><\/p>\n<p>Apple (Paid)\u00a0\u2013\u00a0<a href=\"https:\/\/itunes.apple.com\/us\/app\/nickzom-calculator\/id1331162702?mt=8\">https:\/\/itunes.apple.com\/us\/app\/nickzom-calculator\/id1331162702?mt=8<\/a><br \/>\nOnce, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on <b>Coordinate Units <\/b>under <strong>Switches.<\/strong><\/p>\n<\/div>\n<p><img decoding=\"async\" class=\"alignnone wp-image-9955 size-full\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-645.png\" alt=\"\" width=\"1366\" height=\"768\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-645.png 1366w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-645-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-645-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-645-768x432.png 768w\" sizes=\"(max-width: 1366px) 100vw, 1366px\" \/><\/p>\n<p>Now, Click on\u00a0<strong>Cartesian to Spherical <\/strong>under\u00a0<strong>Coordinate Units<\/strong><\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-9976 size-full\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-651.png\" alt=\"\" width=\"1366\" height=\"768\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-651.png 1366w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-651-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-651-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-651-768x432.png 768w\" sizes=\"(max-width: 1366px) 100vw, 1366px\" \/><\/p>\n<p>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 <strong>Value of x, Value of y <\/strong>and <strong>Value of z<\/strong><strong>.<\/strong><\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-9977 size-full\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-652.png\" alt=\"\" width=\"1366\" height=\"768\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-652.png 1366w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-652-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-652-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-652-768x432.png 768w\" sizes=\"(max-width: 1366px) 100vw, 1366px\" \/><\/p>\n<p>Now, enter the values appropriately and accordingly for the parameters as required by the <strong>Value of x<\/strong> is <strong>4<\/strong>,<strong> Value of y<\/strong> is <strong>3 <\/strong>and <strong>Value of z <\/strong>is <strong>6<\/strong><strong>.<\/strong><\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-9978 size-full\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-653.png\" alt=\"How to Convert Cartesian to Spherical | Coordinate Units\" width=\"1366\" height=\"768\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-653.png 1366w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-653-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-653-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-653-768x432.png 768w\" sizes=\"(max-width: 1366px) 100vw, 1366px\" \/><\/p>\n<p>Finally, Click on Calculate<\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-9979 size-full\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-654.png\" alt=\"How to Convert Cartesian to Spherical | Coordinate Units\" width=\"1366\" height=\"768\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-654.png 1366w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-654-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-654-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-654-768x432.png 768w\" sizes=\"(max-width: 1366px) 100vw, 1366px\" \/><br \/>\n<img decoding=\"async\" class=\"alignnone wp-image-9980 size-full\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-655.png\" alt=\"How to Convert Cartesian to Spherical | Coordinate Units\n\" width=\"1366\" height=\"768\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-655.png 1366w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-655-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-655-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2023\/03\/Screenshot-655-768x432.png 768w\" sizes=\"(max-width: 1366px) 100vw, 1366px\" \/><\/p>\n<p>As you can see from the screenshot above, Nickzom Calculator\u2013 The Calculator Encyclopedia solves the conversion of cartesian to spherical and presents the formula, workings, and steps too.<\/p>\n","protected":false},"excerpt":{"rendered":"Three essential parameters are needed to convert cartesian to spherical: the value of x, the value of y,&hellip;","protected":false},"author":5,"featured_media":17497,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_opengraph-title":"","_yoast_wpseo_opengraph-description":"","_yoast_wpseo_twitter-title":"","_yoast_wpseo_twitter-description":"","_lmt_disableupdate":"","_lmt_disable":"","_sitemap_exclude":false,"_sitemap_priority":"","_sitemap_frequency":"","_yoast_wpseo_focuskw_text_input":"","csco_display_header_overlay":false,"csco_singular_sidebar":"","csco_page_header_type":"","footnotes":""},"categories":[119],"tags":[2488,2490,2491,2467,2485,2486,2487],"class_list":["post-9956","post","type-post","status-publish","format-standard","has-post-thumbnail","category-unit-conversions","tag-cartesian","tag-coordinate-units","tag-spherical","tag-units-conversions","tag-value-of-x","tag-value-of-y","tag-value-of-z","cs-entry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.8 - 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