Caliber and calibre are different spellings of the same word, referring to (1) the internal diameter of a gun, or (2), figuratively, the quality or capacity of a person or thing. Caliber is the preferred spelling in the U.S., and calibre is standard in all other main varieties of English.
The word came to English in the 16th century from the French calibre.1 Caliber, though now mainly American, predates the United States and was a common variant even in British writing until the modern spelling was settled in the late 19th century.2 3 Americans mostly went along with the British spelling until the first half of the 20th century.4 Many words traditionally ending in -re went through a similar change in American English around the same time. For example, fibre became fiber, spectre became specter, meagre became meager, and centre became center. There are many others.
American writers use caliber, as in these examples:
Nowadays only a few boys of that caliber ever enter. ["Princeton," by F. Scott Fitzgerald (1927)]
The average caliber of oratory in the Senate … is such that daily readership of its proceedings in the Congressional Record requires a durable conscience. [New York Times (1955)]
In the bag of clothes, officers found a loaded Hi Point .40-caliber semiautomatic handgun. [Boston Globe (2012)]
Outside the U.S., the preferred spelling is the older, French one, as used in these sentences:
This superiority is only natural, as it accompanies work of immeasurably higher calibre. ["Drama and Life," by James Joyce (1900)]
Higher pay for men of the calibre sought is probably only right in this day and age. [Calgary Herald (1960)]
AgResearch chief executive Dr Tom Richardson said improving the number and calibre of graduates entering the dairy industry would pay huge dividends for the industry and New Zealand Inc. [Stuff.co.nz (2012)]
1. Chambers Dictionary of Etymology ↩
2. Caliber/calibre in the OED ↩
3. Ngram graphing both spellings in British books and journals, 1800-2000 ↩
4. Ngram graphing both spellings in American books and journals, 1800-2000 ↩