Single Engine Pilot reported an engine failure due to fuel starvation. The pilot landed off airport and found the fuel tanks were dry. The pilot later landed at the nearby airport to refuel and continued to the original destination.

Narrative

Miss Calculation of On Board Usable Fuel.Inaccurate Gauge Reading Along with Additional Flight Time.Estimated Time En-Route 2 Hours 20 Minutes. Flight Time At Low Fuel Was 3 hours into flight. 40 Gallons of Gas Was Estimated Onboard at Take off. After Reviewing the situation; its likely more accurate that 35-37 Gallons of Fuel Were On Board. it Was also noted that a 'Sump Valve' Had fallen off during flight (though no evidence of leaking fuel was found). At approx 2.5 hours into the flight we cancelled Flight Following to descend and land at ZZZ to get fuel. At which time we noted approx. 8 gallons of fuel on board. 15 minutes later; we ran out of fuel and the engine began to 'sputter'. Assuming we were in fact running out of fuel it was my decision to land on a county road just south of ZZZ. There was no visual fuel inside of the tanks upon inspection.After retrieving 15 gallons of fuel from ZZZ ; we put 10 gallons in the left side and 5 gallons in the right side so i could take off and fly to ZZZ were i would pick up 20 more gallons of fuel. After putting in the 15 gallons on the county road is when i noticed the 'sump valve' was missing (but no noticeable leaks were found).After landing at ZZZ. Again no noticeable leaks were found. And yet again after our final landing at ZZZ1; no dripping leaks were found; but the valve body and bottom of wing were damp from fuel moisture; but its not noted at the a 'large' amount of fuel had been lost. The local mechanic is scheduled to inspect and fix the Valve before any further flying.Myself; [the] Pilot in command has a learned a hefty lesson that watching the 'flight time' needs to be more of a priority; rather than assumptions time; and indicated fuel in the tank gauges. Moving forward; flight planning will be better done and executed to avoid such an incident from happening again.No Bodily Injuries.No Aircraft Damage.No Property Damage.There were no other incidents. All other factors contributing to the flight went as expected.It is noted that flying at 8;500 Feet we experience 32-35 knot heads winds for the duration of our flight.