We already know ride-sharing has the potential to drastically cut the number of the cars on the road. But it turns out that impact could be way more than anyone has previously estimated.

A new study from researchers at Cornell University and the Massachusetts Institute of Technology found that shared rides — whether through Uber and Lyft or a traditional taxi — could fulfill demand with just 15 percent of the current taxi fleet in New York City.

"Ride-sharing services are transforming urban mobility by providing timely and convenient transportation to anybody, anywhere and anytime. These services present enormous potential for positive societal impacts with respect to pollution, energy consumption, congestion, etc. Current mathematical models, however, do not fully address the potential of ride-sharing," the study's authors wrote.

This study, released Monday, used a mathematical model to figure out exactly how vehicles could best meet demand through ride-sharing. Previous studies were generally limited to vehicles shared between only two passengers, rather than a full Uber Pool car, the authors said.

The study, called "On-demand high-capacity ride-sharing via dynamic trip-vehicle assignment," also accounted for variables like vehicle capacity, waiting time, travel delays and operational costs using 3 million points of ride data from New York City.

The study found that 2,000 vehicles with a 10-person capacity could serve 98 percent of ride demand. With that model comes a mean wait time of 2.8 minutes and a mean trip delay of 3.5 minutes. Two-thousand vehicles is just 15 percent of New York's current taxi fleet.

Reducing that capacity from 10 people to four brings the number of vehicles up to 3,000.

A ride-sharing model like this would work particularly well with autonomous vehicles, the authors concluded.

Now the autonomous future has a mathematical model to follow.