<?xml version="1.0" encoding="US-ASCII"?>
<!--XBRL Document Created with Wdesk from Workiva-->
<!-- -->
<link:linkbase xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd" xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
  <link:roleRef roleURI="http://www.westpharma.com/role/DocumentAndEntityInformationDocumentAndEntityInformation" xlink:href="wst-20191002.xsd#DocumentAndEntityInformationDocumentAndEntityInformation" xlink:type="simple" />
  <link:calculationLink xlink:role="http://www.westpharma.com/role/DocumentAndEntityInformationDocumentAndEntityInformation" xlink:type="extended" />
</link:linkbase>