The velocity needed to escape from Earth's gravity is called Escape Velocity, and it is sixteen kilometers per second (16 Km/sec), which is about eleven miles per second (11 miles/sec), or about 40,000 miles per hour. A rocket must be going at least this fast in order to escape Earth's gravity.

Now, that said, if the place you are going is the space station, you aren't out of Earth's gravity yet. You only need to be going half that fast to put yourself into orbit.

The speed required to escape the atmosphere is called the escape velocity, and it depends where you're located! It can be different if you're at the equator, or if you're on the ground or high up in the sky. However, this doesn't take air resistance into account, which will slow you down, especially at higher speeds! At the surface of the Earth, escape velocity is about 11 km/s, or 7 miles per second