I have some shapefiles which include various points and a corresponding street address, whose lat/lon I've manually found in Google Maps. There is no .prj file.

Google Maps Lat,Lon, unknown coordinate system x, y, city, state 36.7448656,-119.7937943, 6329742.00029, 2155243.06469, Fresno, CA 36.7341137,-119.8126966, 6324144.37016, 2151400.93634, Fresno, CA

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    – PolyGeo
    Jul 19 '18 at 23:59
  • @PolyGeo I don't think its a duplicate question; my question was specific to my data, and it elicited a specific and correct answer referencing a resource (earthpoint.us/StatePlane.aspx) which was not referenced in the question of which this is supposed to be a duplicate. I'll edit to remove the last sentence, asking for general advice, which is actually pretty similar to 7839. Jul 20 '18 at 0:22
  • Even with your edit I still consider your question to be a duplicate because an answer to the duplicate question would provide you the means to answer your question too. Marking your question as a duplicate of that one, which is the fourth most frequently asked question on the site is not a bad thing because the last thing we want is for there to be thousands of near identical questions that vary only in which part of the world and which coordinate system they relate to.
    – PolyGeo
    Jul 20 '18 at 0:43

These look like UTM coordinates, though it's hard to know exactly which coordinate system was used. Perhaps have a look at the California State Plane Coordinate System - Fresno is in Zone 4.

If not, try looking at the Projected EPSG coordinate systems for California.

EDIT: I've confirmed that it is likely the California State Plane Zone 4 on this calculator. It's important to note that the X,Y units are in feet. If I plug in the X,Y coordinates, and choose California State Plane Zone 4 (0404) the results are what you have for lat/long.

Calculated Values - based on Degrees Lat Long to seven decimal places.

Position Type   State Plane - California Zone 4
Degrees Lat Long    36.7448838°, -119.7915918°
Degrees Minutes 36°44.69303', -119°47.49551'
Degrees Minutes Seconds     36°44'41.5816", -119°47'29.7306"
State Plane X Y (Meters)    0404 1929309.220mE 656919.398mN
X Y (US Survey Feet)    0404 6329742.000ftUSE 2155243.059ftUSN
X Y (International Feet)    0404 6329754.660ftE 2155247.370ftN
UTM 11S 250759mE 4070206mN
UTM centimeter  11S 250759.50mE 4070206.23mN
MGRS    11SKA5075970206
Grid North  -1.7°
GARS    121LP33
Maidenhead  DM06CR58AS25
GEOREF  EJAG12504469

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