The revelation comes as the operator is being stretched to the limit by having to switch carriages from other routes to run longer trains between Fife and Edinburgh because of the Forth Road Bridge closure.
The dearth of trains means some commuters elsewhere in Scotland have had their rail service replaced with buses, while trains on other lines are running less frequently.
These include trains on the Falkirk Grahamston-Glasgow line being cancelled until January.
The rolling-stock crisis comes hard on the heels of the opening of the Borders Railway in September, whose popularity caused overcrowding that forced ScotRail to add carriages from elsewhere. Weary commuters will have to wait two years for the first of two new ScotRail train fleets to arrive, and it expects to get only seven more trains in the interim.
The 08:29 from Milngavie to Edinburgh is ScotRail’s busiest service, with 380 passengers crammed onto the 183-seat train between Westerton and Glasgow Queen Street.
However, the crush may now be even greater, because the figures were compiled nearly a year ago and passenger numbers are growing at around 3 per cent a year. ScotRail is carries 93 million passengers annually, with the total nearly doubling over the last two decades.
The figures, provided by the Scottish Government’s Transport Scotland agency under freedom of information laws, showed the busiest service in the east is the 07:09 from Dundee to Edinburgh, with the 272-seat train carrying 398 passengers between Inverkeithing and Edinburgh Haymarket.
In East Lothian, 266 people are jammed into a 198-seat train from Wallyford to Edinburgh, which starts in Prestonpans at 08:05.
Lothian Green MSP Alison Johnstone last week criticised ministers for their lack of urgency in easing the crush on that line.
She said some trains were so full that commuters had been unable to board at Musselburgh.
Johnstone said: “There’s growing frustration as trains are so full they don’t stop at Musselburgh, leaving people on the platform, disrupting their entire day.”
Rail watchdog Transport Focus said nearly one in four passengers said they had insufficient space on trains.
Passenger director David Sidebottom said: “Overcrowding has become a daily struggle for some commuters. In our latest survey, 78 per cent of ScotRail passengers were satisfied with the amount of space they had to sit or stand on their train.”
ScotRail has ordered more than 100 new and refurbished trains, but the first are not due to arrive until late 2017.
Its spokesman said: “To support communities, businesses and the national economy during the Forth Road Bridge closure, we have managed to hire two trains from other operators.
“This is helping us add thousands of extra seats to Fife services every day.
“Starting from next spring, we look forward to permanently introducing seven more electric trains to Scotland’s railways. These will be fully refurbished with better cycle storage, free wi-fi and at-seat power sockets.”
A Transport Scotland spokesman said: “The Scottish Government wants to see more people choose to leave their car at home and make use of public transport.
“That is why we are investing a record £5 billion in our rail network to 2019, including significant improvements to rolling stock.”