<?xml version="1.0" encoding="UTF-8"?>

<!--XBRL Document Created with Wdesk from Workiva-->
<!--Copyright 2021 Workiva-->
<!--r:03200d82-d40e-4124-ad18-9a451cdde4d4,g:76f2c337-9321-40f0-b4af-53eb34b84c97-->
<link:linkbase 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" xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd">
  <link:roleRef roleURI="http://www.unitedcontinentalholdings.com/role/DocumentandEntityInformation" xlink:type="simple" xlink:href="ual-20210115.xsd#DocumentandEntityInformation"/>
  <link:calculationLink xlink:role="http://www.unitedcontinentalholdings.com/role/DocumentandEntityInformation" xlink:type="extended"/>
</link:linkbase>