Create a shared calendar in Microsoft 365, then share it with someone outside your organization.
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Open your Outlook calendar. Under the list of calendars on the left, select New Calendar.
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Name the calendar.
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Right click the calendar name and select Sharing & Permissions.
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Add the email address of the external person you want to share with. You share your calendar (the room calendar) with a person outside your organization, so you cannot give them edit permissions.
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Select the permission level for the shared calendar. Can view when I'm busy lets people outside your organization see only event times. To share more, Can view titles & locations details shows free/busy time, titles, and location.
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Repeat these steps for each of your room calendars in Microsoft 365.
If the person you shared the calendar with uses Microsoft365, Outlook, or another Exchange app, they get an invitation and can add your calendar to their list.
Cross-platform permission issues
These steps have some limits. They work only for people who also use Exchange or Microsoft 365.
Google users can view the calendar via a link emailed from Outlook. But they cannot access your shared calendar invitation without a 3rd party app, because the calendar formats are different.
Google (and other non-Outlook) users get an email like this: