A 4k run is 4 kilometers long. Four kilometers is the equivalent of 4,000 meters and is approximately 2.49 miles in the U.S. measuring system.
A 4k run is not a common length for competitive running; the 5k and 10k are more common. One mile is 1.61 kilometers, so 1 kilometer is about 0.62 mile. One kilometer is also 1,000 meters. In the Olympics, there is not a 4,000-meter run.
The men's world record for the 3,000-meter or 3k run is seven minutes and 20.67 seconds, while the record for the 5,000-meter or 5k run is 12 minutes and 37.35 seconds.