As new rush-hour fares rolled out Monday, Metro acknowledged that up to 5 percent of Metro riders paid incorrect fares for at least the last three years.

WASHINGTON — Up to 5 percent of Metro riders paid incorrect fares for at least the last three years, Metro acknowledged as new rush-hour fares rolled out Monday.

A small but significant group of riders were charged more than they should have been for each trip, but a number of fares were also set lower than Metro’s formulas call for. The net impact of the overcharges and undercharges was that Metro has collected about $372,000 less than it should have since July 2014.

There are no plans to attempt to collect additional fares from riders who were undercharged. Riders who were overcharged and who have continuously used a SmarTrip should receive an automatic credit this summer for part of the additional money paid.

The refund will cover any net overcharge over $2 since 2015. Metro did not immediately share additional information on which trips were affected, but suggested that the fare differences were under a quarter, and mostly within five cents of the proper fare.

Asked for clarifications, a Metro spokesman expected to be able to provide additional information Monday afternoon.

How the fares are set

Metro’s rail fares are calculated by adding a minimum base fare to additional charges based on the distance traveled.

The distance-based part of the fare is measured by an average of the distance on the tracks between two stations and the distance between the two stations as the crow flies. The distance calculations used under the previous set of fares were apparently incorrect, and have been updated as part of the new fare hikes.

The base fare covers the first three miles of that composite measure at all times; the next three miles cost 32.6 cents each at rush hour and 24.4 cents at other times, and each mile after that costs 28.8 cents at rush hour and 21.6 cents at other times. That total is then rounded to the nearest nickel to set the actual fare between two stations.

Under the new fare hike that began Sunday, fares are capped at $6 at rush hour and $3.85 at other times. The new base fares are $2.25 at rush hour and $2 at other times.

Before this fare increase, rush-hour fares ranged from $2.15 to $5.90 and off-peak fares ranged from $1.75 to $3.60.