How can you find out how much you owe the IRS without calling?

You can go to your local IRS office and ask some one if they can give you the information that you need to know.

Go to the IRS gov website and look at top right side of the page above the search box and choose Contact IRS or use the search box for Contact Your Local IRS Office

IRS Taxpayer Assistance Centers for when you believe your issue is best handled face-to-face. Hours of service and other local information is provided on a per state basis.