A mathematical error caused city engineers to underestimate by about 200,000 gallons the size of a massive sewage spill that closed Waikiki Beach and Ala Moana Beach Park last month.

The spill, now estimated at 587,150 gallons, with 462,050 gallons reaching the ocean, occurred Aug. 24 during heavy rainfall. City officials previously said the spill was about 393,000 gallons and of that, only 129,000 gallons reached the ocean.

Lori Kahikina, director of the city Department of Environmental Services, said Tuesday that the mistake was tied to the pumping of sewage that had not spilled on the ground. That sewage — pumped to reduce overflow at manholes — was returned to the system.

Crews also sucked up sewage that overflowed from manholes and estimated about 500,000 gallons of sewage spilled based on the rate of overflow from manholes.

Engineers subtracted the amount of sewage that cesspool trucks pumped from pipes, which was sewage that was never considered part of the spill. Instead, they should have subtracted only the amount crews recovered from the ground to determine how much sewage had reached the ocean.

Kahikina said the mistake was probably caused by engineers asking field crews how much they pumped, rather than how much of the spilled sewage they recovered.

“This does not happen very often,” she said. “We want the public to know that we weren’t trying to hide anything.”

In a spill report submitted to the Department of Health on Sept. 4, the city revised the spill estimate to about 587,150 gallons of sewage mixed with rainwater.

Crews recovered 125,100 gallons, and the remaining 462,050 gallons entered storm drains leading to the ocean, the report said.

According to the report, the spill began at about 5 a.m. Aug. 24 at Atkinson Drive and Ala Moana Boulevard and continued until 2:30 that afternoon.

The city posted warning signs along the water stretching from Kakaako into Waikiki and closed Ala Moana Beach Park for two days. The city conducted bacteria tests the day of the spill and continued testing in some areas until the last warning signs were removed Aug. 29.

City officials blamed the spill on a miscommunication that left a key pump down at a pumping station on Keawe Street during heavy rainfall.

The remaining pump could not handle the influx of storm runoff entering the sewage system, and a mixture of sewage and rainwater backed up into the streets from seven manholes in parts of Ala Moana and Kakaako.

Kahikina said she has put in place new procedures to prevent similar incidents, such as requiring division chiefs to provide hourly updates on facilities to department directors during heavy rain events.

Keith Kawaoka, deputy director of environmental health at the state Department of Health, said the state is reviewing the city’s spill report and is investigating the incident.