Actually, the "38c" part really only refers to the width of a tyre. The cross-section profile of a tyre isn't always perfectly round. You can have a wide squat tyre, like the Tioga CitySlickers which are modeled after a motorcycle tyre. It is roughly 1.5 times as wide as it is tall. On the other extreme, you can have narrow-profile time-trial type tyres that are about 0.8 times as wide as they are tall.
Pull out the calipers and measure the actual casing-width. The rubber part doesn't count. May be tough on some tyres due to the knobbies, but you can usually wedge the calipers in between them.