Some models you can especially before 1921 after that the barrels are date code stamped and it's more accurate then the serial list surprisingly which one early models (1900's) can be off a year or so from the list. Barrel codes are available on the Remington Society of America here: http://remingtonsociety.com/rsa/questions/barrelcodes
Serial number 3273324 regards an early war (1941) built Remington Model 1903 Service Rifle, in caliber 30-06. Remington 1903A3 productions did not begin until 1942 dated to serial number 3348086 and higher.
Post a serial or call Remington.
April 1942.
July 1943
1920 (pre barrel date code stamp)
SPRINGFIELD ARMORY US MODEL 1903 RIFLE SERIAL NUMBER RANGES(Including Rock Island Arsenal, Remington, and Smith-Corona production)[Dated by calendar year: January - December]1909 - 358085 - 398275
Quick serial number guide:No serial number, pre 1967 riflesSerial number range 400-419K 1967 rifleSerial number range 419-473K 1968 rifleSerial number range 2.1 million-2.59 million December 1968- January 1977 rifleSerial number range with an "A" prefix-post Feb 1977 rifle.
The serial number can be used to determine which year it was built. Ask again with the serial number.
Need to know if it is a derringer or rifle.
By checking the serial number against published data.
With the serial number that you have supplied;your Winchester model 1894 rifle was made in the year 1974.
Wow that's close to the last one made in 1935 it's date code stamped I would be interested to know what code it has. Please see the related links for a pointer to the Remington Society of America website with details.