Metro officials knew in 2012 that some customers were being overcharged as a result of erroneous fare calculations but did not act to correct the problem until last year — and even then reimbursed only those affected after 2015, according to a newly publicized report.

In a fine-print addendum to a news release on fare increases last summer, Metro announced that it was correcting a long-standing problem with its posted fares. The agency had made calculation errors, including incorrectly plotting some platform locations, that led to miscalculated fares in hundreds of the agency’s 16,000 possible fare combinations.

Metro said it would provide SmarTrip credits to any customers who were overcharged more than $2 between 2015 and 2017.

But the inaccurate calculations were known at least as far back as 2012, according to the now-public report that precipitated the changes, originally sought as part of a public records request from WAMU and obtained by The Washington Post on Monday.

The report details how even though the issue was raised with officials multiple times, Metro twice neglected to address it before 2017. The Post first asked the agency’s media relations department about fare calculations from station to station in 2012 in response to a question from a reader, Metro acknowledges in its report. At the time, the transit agency’s planning department acknowledged the problem.

“The Office of Media Relations (MREL) brought to PLAN’s [the Office of Planning’s] attention in 2012 correspondence from the Washington Post inquiring about apparent discrepancies in certain station-to-station fares,” the report says. “. . . PLAN provided intelligence on this matter back to MREL in 2012 and again brought this to the attention of decision-makers in anticipation of the opening of the Silver Line.” The Silver Line’s first phase opened to customers in 2015.

In the end, hundreds of thousands of riders were charged the wrong fare, the agency found. Asked Monday why it took five years to resolve the issue, Metro said it did not understand the extent of the problem.

“What began as an inquiry from the Washington Post regarding a specific fare between two stations was not fully understood until years later,” Metro spokesman Dan Stessel said in a statement.

Asked why refund credits were not offered to customers who were overcharged before 2015, Stessel said, “The credits were based [on] two years of trip data, the longest duration that was technically feasible.”

Metro said “system limitations” prevented it from providing credits for trips before then, given its rail ridership of 190 million trips per year. The agency said it paid $257,355.85 in refund credits from overcharging between 2015 and 2017. The amount was distributed among 37,865 SmarTrip cards, making the average refund about $6.80. Only those overcharged more than $2 total received refunds.

“The only thing I can do as chairman of the board on behalf of Metro is just apologize to everybody,” said Jack Evans, chairman of the Metro board. “We have no way of notifying or identifying everybody who was overcharged.”

Board member Michael Goldman said that while riders were entitled to their money back, compared with the scale of Metro’s operations, the fare glitch was not a major issue.

“It’s an unfortunate situation and obviously Metro should reimburse those individuals, but in an operating budget of $1.8 billion this is, I mean, this is insignificant almost in scope of Metro’s annual operating budget,” said Goldman, who chairs the panel’s finance committee.

Metro relies on distance-based measurements to calculate its fares. Riders pay a flat fare for the first three miles of a trip, an additional charge for each of the next three miles, and a further per-mile charge for every mile exceeding six miles — with a cap of $6, according to the agency’s final report on station distances. Fares also are broken down into peak and off-peak fares.

Following the discovery of the problem, Metro hired an outside engineering firm, Aecom, to recalculate the distances so it could establish the proper fares.

“The minor discrepancies . . . are related to geospatial errors that ultimately impact the points from which distances are calculated,” Metro’s report says. Research “found that the platform locations for several stations were not in their correct geospatial locations in the data [the planning office] used for Metrorail fare calculations, including Eisenhower Ave and the five new Silver Line Phase 1 stations. Additionally the team found that the track centerline was never adjusted to account for the [2004] opening of the NoMa-Gallaudet station.”

The report also notes: “In some cases, customers traveling one additional station experience a noticeable decrease in fare.”

In all, Metro concludes, hundreds of thousands of riders annually had been charged the wrong fare — some paying up to 35 cents too much and others paying up to 55 cents too little per trip, while the majority of fares were off by 5 to 10 cents. Metro lost $124,000 because of the issue during fiscal 2016, when more than 14 million trips were calculated with incorrect fares, according to the report.

“On the whole, these discrepancies were in the customer’s favor,” Stessel said. “Among customers who were overcharged, the amount we’re talking about was [a] nickel in 97.8 percent of cases.”

Metro said the corrected fares affected fewer than 5 percent of its rail trips overall. But the analysis details how widespread the problem was for Green Line riders and those on newer and otherwise newly modified segments.

Seven of the top 10 stations with the most destination-station fare errors were on the Green Line, according to the analysis. For example, from Branch Avenue, travel to 62 of the 90 destination stations resulted in fare calculation errors.

That means during the October 2016 morning rush, 71,000 rush-hour trips were taken with incorrect fares, and in total 13,000 SmarTrip cards were charged an incorrect fare.

Columbia Heights was second, with 35 destinations that had the wrong fares and a total of 26,000 trips and 6,000 SmarTrip cards that were assessed incorrectly.

Greenbelt, Southern Avenue, Silver Spring, Georgia Avenue-Petworth, Glenmont, Fort Totten, Franconia-Springfield and Prince George’s Plaza were the other eight stations most affected. In October 2016, the agency concluded, more than 265,000 SmarTrip users were incorrectly charged.

This story has been updated.