Here are two articles by the late Sheldon Brown. The first shows how to measure the width of the rim. The second one has a table (in bright green and red) that shows what width of tire can be used on the rim you have. The table is quite far down on the page. It is measured in mm so just divide by 25.4 to get the inch equivalent.

Measuring Bicycle Rims and Hub Flanges Tire Sizing Systems

It's actually a fair bit of leeway. My Catrike 700 came with 1" Schwalbe tires that were totally unsuitable for my use so I replaced them with 1.4" wide BMX tires. That was thousands of miles ago with no problem since.