Congress and the Department of Housing and Urban Development are in a little $100 million race to see who can be the first to rewrite federal rent subsidy standards for poor people.

The race is being run before a grandstand packed with public housing authorities, rooting, for the most part, for Congress.

HUD broke on top last year with a proposal to rewrite the formula by which it calculates "fair market rents" in its Section 8 program for existing buildings.

These FMRs, as they are called in governmental jargon, are household words only in low-income households, but they are important. They determine how much the department will shell out to help a low-income family rent a place to live.

HUD figures out what the fair market rent ought to be for a certain size dwelling in a particular area. The tenant family puts up 30 percent of its income, and HUD pays the difference between that and the FMR.

Consequently, how HUD arrives at the fair market rent is of more than passing interest to tenants and public housing authorities, who oversee the program and try to find landlords who will rent for the price the department offers.

At the moment, HUD figures the fair market rent in a given area is equal to what is paid by the 50th percentile of families who have recently moved into houses or apartments.

The department would like to change that to the 40th percentile of rents in an area, excluding housing built in the past two years, and including people who live in assisted housing.

The effect would be a substantial lowering of most FMRs, saving about $100 million on a program that costs taxpayers $2.2 billion in fiscal 1983, HUD figures.

But the plan has provoked an outcry from many public housing authorities, real estate dealers and even the National Association of Home Builders. HUD has received volumes of comments, almost none favorable.

Housing officials from Birmingham to Juneau and from Winooski, Vt., to Santa Cruz, Calif., have written to complain.

HUD, for its part, thinks the plan is anything but shameful. It believes that its program has been an engine for driving up rents and that there is an adequate supply of housing in the marketplace at the new standard.

"What we're saying by 50th percentile of all rents . . . is that 50 percent of the units out in the marketplace are available" at that price, said Janet Hale, deputy assistant secretary for policy and budget in HUD's Office of Housing. "They're standard units, and all we're just saying is that we're lowering the standard to say that 40 percent of the units out in the marketplace are available.

"Part of the problem has been that when HUD sets a fair market rent, what has been the ceiling becomes the floor. We know that automatically people raise the rent to whatever" the federal government will pay, she said. And "what we're trying to do is really look at what level does support a program.

"I think we're pretty committed to" the view that 40 percent "is in fact the right percentage," she said, but "there may be some compromise" on whether to use all movers, recent ones, or perhaps "a dual track system."

Congress, meantime, seems committed to the view that the proposed standard is too low. The House Banking Committee has voted to go back to the 50th percentile of recent movers, and the Senate panel has opted for the 45th percentile.

HUD's target date for the final regulation is next month, which seems likely to put it across the finish line first.

The catch is that since Congress' word is law, it does not have to get there first to win. All it has to do is get there.

But that's something it did not do last year, when it could not manage to enact a housing bill. This year's bills are far enough apart to raise the possibility again, and that would put HUD in the winner's circle.