The　analytical　geometry　of　a　face　gear　and　the　mathematical　model　for　face　gear　error　analysis　are　established　based　on　the　face　gear　generation　process.　The　normal　vector　of　each　point　on　the　surface　of　the　face　gear　is　also　obtained.　The　error　caused　by　the　coordinate　disunity　of　the　face　gear　and　the　CMM　is　analyzed.　The　datum　of　the　point　measured　on　the　surface　of　the　face　gear　is　not　the　inspection　datum　of　the　center　of　the　probe.　A　corresponding　equation　is　put　forward　to　compensate　for　the　error　caused　by　the　disunity　of　the　measured　point　and　the　center　of　the　probe.