Developers in Montgomery County will pay a higher tax to build in farther-out, auto-dependent areas and contribute more to expand sidewalks, bike lanes and transit as part of a new growth policy aimed at curbing the suburb’s car-centric sprawl.

Under new rules approved Tuesday, the council also will require residential developers countywide to pay more toward building new or expanded schools to ease crowding.

The changes come as part of an updated and simplified Subdivision Staging Policy intended to ensure that public infrastructure keeps pace with private development. The policy specifies how developers must estimate, and pay for, the impacts of their projects.

Crippling congestion and crowded schools have become growing concerns as the Washington suburb of 1 million people has continued to develop. With another 200,000 residents anticipated over the next 30 years, county officials say, Montgomery’s transportation network and school system can keep up only if the county continues to focus growth around transit and requires developers to pay more to help expand schools and build new ones.

“I think it’s smart to continue to prioritize smart growth and transit-oriented development over sprawl,” said Council member Tom Hucker (D-Silver Spring).

Among the biggest changes approved Tuesday is a higher transportation impact tax for building in rural areas and ­farther-out suburbs, such as Damascus and Colesville, where planners say data shows people are more likely to drive and to travel farther, both for commuting and errands. The different tax rates are designed to encourage development near job centers and Metro stations, where the tax is lower. Someone building a new single-family home in North Potomac, for example, will pay a transportation impact tax of almost $22,000, compared with about $7,000 for a new single-family home near a Metro station, such as in downtown Silver Spring or Rockville Town Center.

The new policy also adds financial incentives for developers to limit the amount of parking they build, which is considered key to limiting new traffic.

How developers help offset the impacts of their projects will vary in different parts of the county. A developer proposing a high-rise apartment building in downtown Bethesda might be required to contribute money toward new bike lanes or sidewalks, while those in farther-out areas such as Olney or Potomac might have to pay for an additional turn lane at a nearby intersection.

Densely developed areas such as Bethesda, Silver Spring and Friendship Heights don’t have room to build new roads or widen existing ones, officials say.

“We all recognize that the improvements we need [in urban areas] aren’t intersection improvements for the most part,” Council member Roger Berliner (D-Potomac-Bethesda) said during a recent work session on the policy.

Council member Marc Elrich (D-At Large) cast the lone vote against the policy, saying it won’t do enough to prevent already horrendous traffic from worsening, particularly near rapidly growing areas such as downtown Bethesda.

“You basically have no protections for communities for how congested traffic can get, and there’s no requirement to fix things,” Elrich said after the vote. “This is just a green light to developers.”

The council rejected an idea by county planners to scrap traffic tests for new buildings proposed near Metro stations. Planners had said the tests weren’t helpful because individual building proposals rarely were found to generate enough additional traffic to violate local limits. The county generally permits more traffic congestion in areas that are well-served by Metro and other transit.

Council members said they heard from residents who said it didn’t make sense to forgo intersection studies when approving additional growth in areas already swamped with traffic. The council also voted to require developers to conduct more sophisticated traffic analysis in more urban and heavily developed areas.

Montgomery planning officials rejected criticisms from some longtime residents who have said the changing focus is unfair to people who want to live in farther-out suburbs where there can be few reliable transit options.

“It’s your choice where you live, but not all development has the same impact on the use of roads and other transportation services, and you should pay for what you use,” said Casey Anderson, chair of the Montgomery planning board. “Why would people living next to Metro who don’t own a car have to subsidize people who are using the roads? . . . You can make whatever choice you want and pay accordingly.”

The higher school impact tax, which will be the same across the county, is based on 120 percent of the cost to build a new seat, up from the current tax based on 90 percent of that cost.

Parent advocates also celebrated the council’s decision to impose a building moratorium in any area where the local elementary or middle school is over­capacity by 20 percent and a certain number of seats. The current policy applies only to an entire high school cluster, leading to building bans only when the cluster’s elementary or middle schools collectively are 20 percent over capacity.