Sami, the size is 1.5346". Tolerance is SAE 'Class 2'- 0.0005" to 0.0008" PRESS fit on an axle, and yes- that 5th digit is important. The bearing's inner race will expand a bit when pressed onto a shaft, and is designed to do so. The slightest looseness at running temps will result in the extremely hard bearing fretting on the softer mild steel axle, with very bad results for the axle. Some stock axles were made too loose at the factory to survive, but failures are rare today, 50-years on. ANY noticeable looseness is cause for axle replacement. The bearings rarely fail.
Current replacement axles from the vendors are M-300 steel (a type of heat-treated, age-hardened chrome/moly/nickel tool steel and are not hollow, so are strong enough for pro racing with modified engines. 2nd version axle nuts are replaceable from the vendors, too. In spite of using the proper press fit and the proper nut torque (350-450 ft-lbs), stock hollow axles will eventually break thru the fillet between wheel flange and shaft, if used in competition with oversized sticky modern tires. I used to repair worn Pantera axles with Stellite-C hard-face weld and precision grinding, but that didn't fix flange cracking. The stress damage is cumulative over years, too.
To check an axle, you'll need a 1-1/2" 5-digit micrometer measured at 70 F, because a normal 4-digit mic' simply isn't precise enough. Such mic's are sometimes rentable. Note that brand new bearings also have tolerances so ideally you should check both the shaft OD and the bearing ID at the same time for the needed interference fit. Good bearing supply houses know all this but you won't hear this at Autozone. Good luck.