Gov. David Paterson signed a measure Wednesday allowing out-of-work New Yorkers to collect another 13 weeks worth of unemployment insurance, extending the possible benefit to 72 weeks.

The extension taps $645 million in federal funds through the American Recovery and Reinvestment Act.

“These benefits allow unemployed New Yorkers to pay for their homes and buy food for their families while also searching for jobs,” Paterson said.

About 56,000 jobless people would lose their benefits this week if the extension was not approved by the Legislature on Tuesday and signed by the governor.

The extension is based on the use of a new yardstick: The “Total Unemployment Rate” is calculated by dividing the overall number of unemployed workers by the total civilian labor force in the state; if that rate exceeds 6.5 percent over a three-month period, the extended benefits are triggered.

Prior to the legislation, the state used the higher standard of the “Insured Unemployment Rate,” which is calculated by dividing the average number of workers receiving state unemployment benefits in the past 13 weeks by the total number of employed workers in the state.

Unemployment in New York stood at 7.7 percent in April, Paterson said. That’s down a tenth of a percent from March, but up 3 percent from April 2008.

More than 500,000 people are currently on unemployment in New York, said Leo Rosales, spokesman for the state Labor Department. The last time that many people drew on the insurance was just after the 9/11 attacks, when 450,000 New Yorkers were collecting benefits.

The stress of rising unemployment is clear to people like John Evers, executive director of the state Food Bank Association, who called the extension “very good news.”

“What we’ve seen lately is at least a third more increased demand,” Evers said.

Evers volunteers at Albany’s St. Maximilian Kolbe soup kitchen on Central Avenue, which is open for lunch on Mondays and Thursdays. He’s seen the organization’s numbers rise from about 75 to 80 people per week to more than 120.

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