The city is losing out on more than half a billion dollars by keeping part of Brooklyn’s waterfront restricted to maritime use, according to newly surfaced documents obtained by The Post.

The city’s Economic Development Corporation quietly inked a 36-year lease of the 65-acre South Brooklyn Marine Terminal with a management company in August that adheres to the site’s development restrictions, which the City Council voted to extend in 2015.

The deal, approved at the EDC’s board meeting on Aug. 13, gives taxpayers an idea of just how much money they’re losing over the restrictions.

The EDC contract will net the city $4 million in annual rent for the property between 29th and 39th streets west of Second Avenue — but that’s just a fraction of the $20 million in yearly fees it could have scored had the land been unrestricted, according to minutes from the meeting.

The city also is kicking in $57 million to upgrade the area to help the renters, neighboring developer Industry City and the operator of the Red Hook Container Terminal, which was the only conglomerate to submit a bid adhering to the restrictions.

Backers of the deal argue that restrictions help keep the area’s character, sustain jobs and block the construction of more luxury housing.

But critics say the city is giving developers a massive rent break and want to ensure other sections of the waterfront don’t fall prey to the same backward thinking.

“We feel that this is a bad deal for taxpayers, and a sweet deal for developers,” said Antoinette Martinez, a member of activist group Protect Sunset Park, which is holding a public forum on the issue at Trinity Lutheran Church at 5 p.m. Monday.

“Protecting Sunset Park’s waterfront should include maritime restrictions, but this ‘deal’ isn’t about that. Instead, tax payers are being asked to subsidize a sweet rent break for Industry City and its business partner,” Martinez said.

Constantine Valhouli, research director for the real-estate ­analytics firm NeighborhoodX, agreed that the city’s approach “makes no sense whatsoever” financially.

The South Brooklyn Marine Terminal, once used to unload cargo ships, has been closed for nearly 20 years. Several years ago, the de Blasio administration hoped to redevelop the long-dormant site for more lucrative uses, but Councilman Carlos Menchaca (D-Brooklyn) helped sink the push.

Menchaca told The Post he still believes he made the right call, noting that the EDC’s deal includes a requirement from the bidder to reinvest 5 percent of its future revenues from the site into his district, which includes Red Hook and Sunset Park.

“As council member, I will continue to lead side-by-side with our local leaders to ensure that local family-sustaining jobs, aimed at mitigating climate change, come to our waterfront,” he said.

The contract also gives the city 15 percent of the deal-generated gross revenue, or 50 percent of the net income, whichever is greater — even though the Red Hook Container Terminal is currently a money suck that only survives on $1 million a year in Port Authority subsidies.