Staff Sergeant Ryan Austin was "very drunk" when he ventured on to the tracks at Maidstone East station and fell backwards on to the 750-voltage line.
The 25-year-old's widow Jessica was eight months pregnant when he died on August 6.
Ryan Martin was based at Ramstein air base in Germany
She gave birth to their first child, Brayden, just a month after her husband's funeral in their hometown of Corbin, Kentucky.
S/Sgt Austin was staying at the Hilton Hotel, in Ashford Road, Bearsted, for one night with three other servicemen.
They were travelling from Ramstein Air Base, Germany, to a military airfield in Suffolk.
Ryan Austin, pictured with widow Jessica, was killed when he was electrocuted on a railway line. Picture: LEX18 News
The inquest heard three of the men, including S/Sgt Austin, went into the town centre after a pub meal and several drinks at the hotel bar.
They spent a couple of hours drinking at Bar Chocolate, in Market Buildings.
They called a taxi just before 2.30am when S/Sgt Austin, who friends say was in good spirits, ran off in search of food.
Ryan Austin's widow Jessica has since given birth to the couple's son. Picture: LEX18 News
His two colleagues searched the area and were directed towards the station, where they were met by police.
S/Sgt Austin's body had been discovered by two passers-by shortly after he had left his friends.
CCTV showed him standing on a wall outside the station, looking towards the opposite platform.
S/Sgt Austin's baby at his grave in America
He was then seen walking towards a slope that leads on to the track.
Sgt Mark Dron, from British Transport Police, said it is believed the airman was trying to cross the railway and lost his balance when passing a patch of undergrowth.
He told the inquest: "As he edged around that bush, he grabbed it, trying to keep himself upright and fell backwards."
The platform at Maidstone East station where Staff Sergeant Ryan Austin died
Mid Kent coroner Patricia Harding recorded that the death was accidental. The cause was given as electrocution.
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