ENG FLAMED OUT AT CRUISE ALT DUE TO FUEL STARVATION. FUEL QUANTITY GAUGE ERROR CAUSED UNDER FUELING 1 WING TANK.

Narrative

WHEN THE ENG FAILED; I WAS AT FL190 IN CRUISE FLT PREPARING FOR MY DSCNT INTO ZZZ1. INITIAL INDICATIONS WERE A LOSS OF TORQUE; FOLLOWED BY YAW AND A LOSS OF ALL R ENG GAUGES. THERE WERE NO ANNUNCIATORS INDICATING ANYTHING MAJOR. NOT A FUEL PRESSURE LIGHT OR ANYTHING. I SHUT DOWN THE R ENG. I HAD MY COPLT PULL OUT THE EMER CHKLIST AND WE DID A COMPLETE SHUTDOWN. BECAUSE I NEVER SAW ANY MAJOR PROB; WE WENT THROUGH THE ENG STARTER ASSISTED RESTART. WITH NO SUCCESS; I WENT THROUGH THE SHUTDOWN PROCESS AGAIN. AT THIS POINT WE HAD ABOUT 400 LBS A SIDE INDICATED ON EACH FUEL GAUGE. WE DECLARED AN EMER BECAUSE WE WERE PART 135 WITH 3 PAX. WE TOLD THEM THAT EVERYTHING WAS UNDER CTL AND THERE WAS NO NEED FOR EMER VEHICLES STANDING BY. WE WERE GIVEN DIRECT TO ZZZ1 WHICH OUR GPS TOLD US WAS THE NEAREST SUITABLE ARPT. WE BEGAN OUR DSCNT AND APCH TO ZZZ1. I COMPLETED A SINGLE ENG APCH AS MY COPLT WENT THROUGH THE CHKLIST. WE LANDED SAFELY AT ZZZ1. IT WAS LATER FOUND THAT THERE WAS A FAULTY R FUEL GAUGE. PRIOR TO DEPARTING; WE HAD THE PROPER AMOUNT OF FUEL INDICATING ON THE GAUGES FOR THE FLT. WE HAD THE 45 MIN VFR NIGHT REGRESS AS FIGURED THROUGH EXTENSIVE FLT PLANNING. WE STARTED WITH 850 LBS A SIDE FOR ACTUAL OF 1700 LBS. DUE TO UNFORECAST HEADWINDS; WE WENT INTO OUR RESERVES. BUT DUE TO THE MISFUEL GAUGE THAT FAILED; WE THOUGHT WE HAD MORE FUEL THAN WAS ACTUALLY ON BOARD. I DID EXTENSIVE FLT PLANNING TO TRY TO BUY MINIMAL FUEL AT THE EXPENSIVE RATE. THROUGH ALL OF MY CALCULATIONS I FIGURED THAT FOR THE 1 HR 18 MIN FLT; 1700 LBS OF FUEL WOULD BE PLENTY TO NOT ONLY GET US THERE; BUT ALSO MEET THE FARS FOR VFR NIGHT TIME FUEL RESERVES OF 45 MINS WITH A LITTLE EXTRA CUSHION. THE UNFORECAST HEADWINDS; ALONG WITH FLYING THE LAST 10-15 MINS WITH 1 ENG; CUT INTO MY RESERVES. THE FAULTY FUEL GAUGE; WHICH I USED ITS READING TO CALCULATE MY FUEL; WAS THE CAUSE OF THE PROB ON THE R ENG. ON THE GND; IT WAS FOUND THAT THE R ENG WAS OUT OF FUEL. THE GAUGE WAS STILL READING AROUND 350-400 LBS OF FUEL; WHEN DRAINED; THE L ENG HAD ABOUT 35 GALLONS OF FUEL REMAINING. THIS WAS AFTER FLYING THE REMAINING FLT ON THAT ENG. THE ONLY EXPLANATION IS THE FAULTY FUEL GAUGE ON THE R SIDE.