SAN FRANCISCO—During the first day's closing session of Vanity Fair's New Establishment Summit, Uber CEO Travis Kalanick said that his app has 40 million monthly riders paying an average of $50 for the company's ride-sharing services.

That's approximately $6 billion per quarter, which is roughly $1 billion more in bookings than Uber reported to shareholders for the second quarter. What's more, Uber's growth this year has been staggering: A late August story in Bloomberg stated the technology company had $3.8 billion in bookings during Q1. So in two quarters, ride bookings have jumped 58 percent.

At any rate, Kalanick revealed the latest stats during an interview with Vanity Fair's editor in chief Graydon Carter. In addition to the monthly riders, the CEO said that Uber drivers have made between $1.5 billion and $2 billion in the past month and 20 percent of all rides globally now come from UberPool—the app's feature that lets riders share and split the cost of a cab.

In terms of Uber's growing investments in autonomous vehicles, the app has a few pilots going on in San Francisco and Pittsburgh and called self-driving technology "existential" as it faces new competition from Apple, Google and other companies building similar technology.

"When you start to automate, you start to do the self-driving thing on our roads, the roads in many ways are the cardiovascular system for a city, you make it a much more efficient cardiovascular system," Kalanick said. "These cars, when they go into self-driving, you're now starting to become a robotics company. So, I think we're at the very beginning stages of becoming a robotics company."

Kalanick also talked about changing the brand's logo from a U-shaped icon earlier this year to a circle with a square in it to make it look like a button that Carter quipped "looks like a pharmaceutical" logo.

"We got so much hate," Kalanick explained. "We went from this launching new services in two cities [company] to being in 400, 500 cities around the world in 70-plus countries. [The new logo is] something that was more populous, more of-the-people, for-the-people thing."

Carter also asked Kalanick about what car he drives. In true pitchman mode, Kalanick doesn't have a car.

"I have a car in my garage and two things have happened: One, the alternator belt was broken and two, my driver's license is expired."