Philadelphia’s new payroll computer system has been miscalculating paychecks for a month, inconveniencing and frustrating employees across all city government departments.

Officials on Thursday acknowledged that the city has had to issue at least 5,121 supplemental paychecks in the last month to correct mistakes that left workers getting less than they had earned. One prison worker got a $0 check for 80 hours’ work. Some Police Department employees haven’t received a paycheck at all.

The shortages in pay have mostly centered on overtime calculations. One union that represents 3,000 workers said employees were improperly shorted in their overtime rate by 33 percent.

But an untold number have also received more money than they were entitled to — some twice their normal pay.

City officials have been slow to publicly identify and quantify the problem, let alone fix it.

After four weeks of continuous problems, employees and labor unions are saying, “Enough.” Labor representatives for about 10,000 city employees — more than a third of the workforce, including sanitation workers, corrections officers, parking enforcement officers, court employees, and supervisors in various departments — confirmed Thursday they are planning a joint lawsuit against the city over the “egregious” payroll discrepancies.

One Philly is a $40 million IT project — in the works since the Nutter administration — to link timekeeping, payroll, pensions, and benefits under one system. It’s been delayed for years and gone over budget. The roll-out of the payroll part in late March drew criticism from the unions and workers confused about a change in the number of work hours used to calculate pay and an increase in overtime rates.

When the first One Philly paychecks came out in early April, the disarray escalated as employees started seeing lower wages.

“We have people who have been missing pay since the beginning of April,” said one employee within the Prison Department, who asked not be identified because he was not authorized to speak with the media.

It’s unclear what is causing the inaccurate paychecks. City officials are mostly staying mum. And the executive vice president of HTC/Ciber Global, the vendor charged with implementing One Philly, declined to comment.

City spokesperson Mike Dunn initially said a total of 2,192 paychecks citywide — 3 percent of all issued — had been short “in varying degrees” and had been adjusted with supplemental checks. Nearly 80 percent of those shortages were in the prisons department, he said.

But at 5 p.m. Thursday, Dunn clarified that the total was more than 5,100 and that the previous count didn’t include overtime mistakes.

That total accounts for about 9 percent of all checks issued so far through One Philly.

Dunn wouldn’t say how many employees received double paychecks or too much pay and how the city is remedying those issues, among other issues.

“The One Philly team is focused on both this week’s payroll cycle, fixing remaining issues, and instituting some systemic tweaks to ensure the integrity of future payroll cycles,” Dunn said in an email Wednesday. “So we won’t be able to provide answers this week.”

Employees complain that they aren’t getting answers either.

“This new payroll system is nothing but chaos, and all [supervisors] are acting like they don’t know how to fix the issues or even explain the problems,” said one Water Department employee, who spoke on condition of anonymity because he is not authorized to speak with the media. “There was no training on it supposedly for them, and they are getting mad at you when you ask questions.”

One source familiar with the One Philly project said that training was rushed and that the system wasn’t thoroughly tested before it was rolled out. So now, the source said, issues are coming up among the various modules, such as benefits and time entry, that are affecting payroll.

On Monday, AFSCME District Council 33 Local 159, which represents 3,000 employees in prisons, the Juvenile Justice Center, municipal guards, the Office of Supportive Housing, the Office of Homeless Services, and some employees of the Sheriff’s Office, sent a three-page complaint to the Office of Labor Relations demanding compensation for workers whom the city has “financially harmed” through implementation of the new system.

The city’s “promise of compensatory checks to affected represented employees to complement the undelivered earned wages … did not transpire,” Eric Hill, business agent for Local 159, said in the letter.

On Tuesday, the local asked to join a lawsuit already in the works by other locals within D.C. 33 and District Council 47.

But D.C. 33 president Pete Matthew is not on board with the plans to file suit against the city.

“I was highly upset” about the inaccurate paychecks, Matthews said Thursday. “The city admitted 100 percent this is their fault, any losses will be recovered, and our members are receiving supplemental checks.”

Matthews said he has contract negotiations coming up and doesn’t want to file a lawsuit.

Hill’s and some other locals within D.C. 33 are nevertheless moving forward with court action.

“A suit is being submitted to the courts,” Hill said, adding that he was not sure in which court the lawsuit will be filed. “We are waiting on our attorney to advise us.”

Bob Coyle, president of D.C. 47 Local 2187, which represents administrative and technical staff across all departments, said union leaders are being careful with how they respond to the One Philly issue.

“It’s politics,” he said, adding that he also had to weigh whether to sign onto the lawsuit (he is as of now). “I don’t want to piss off the mayor, but my obligation is to my members. It’s nothing personal.”

John McGrody, vice president of Fraternal Order of Police Lodge 5, said police and firefighters have also been having issues with pay. He said he thinks the number is much higher than the city is releasing publicly.

“Our phones have been lighting up all week,” he said, with officers complaining about missed paychecks or inaccurate wages. “It’s a mess. That’s for sure.”

Police Department workers are still using the legacy timekeeping system and not yet entering time into One Philly. But because the paychecks are issued by OnePhilly, some information did not transfer, and some police employees who are not signed up for direct deposit and get paper checks in the mail have not been receiving their pay, McGrody said.

Overtime pay has also been problematic. For prisons, overtime has been paid at straight time instead of time and a half, according to the Local 159 complaint letter.

In other cases, overtime pay — which for employees working at the city’s 24/7 facilities is mandatory — has been delayed as city officials try to fix the system. Some did not receive their holiday pay for working Good Friday.

One prison employee shared with The Inquirer a copy of a paycheck showing the employee worked 80 hours during the two-week period ending April 26. And the deposit amount was $0.

The city is supposed to send supplemental paychecks to any employee who was shorted pay. Dunn would not provide the number of supplemental checks that have been issued.

City Controller Rebecca Rhynhart said through a spokesperson that her office will audit the new One Philly system in July.

“Specifics about the number of short paychecks or overpayments will happen as part of the audit process,” Rhynhart said.

Hill, the business agent for Local 159, said that many of his members have suffered consequences of inaccurate pay, such as having trouble paying rent and mortgages. Others have been hit with insufficient-funds fees at their bank.

Some members have also received additional paychecks in one pay period.

“We’ve been advising them to put that extra money in an escrow account,” until the city asks for the money back, Hill said.

For employees who have received inaccurate paychecks or no paycheck at all, Dunn said employees should contact their department’s human resources office in person or via email for adjustments.

Staff writer Chris Palmer contributed to this article.

Correction: A previous version of this story incorrectly said D.C. 47 Local 2187 represents supervisors.