A built-in feature of IP, Address Resolution Protocol (ARP) translates IP addresses to MAC addresses. ARP was not designed to translate addresses in the other direction, however. There is no universal mechanism to determine an IP address given a known MAC address, although it can be done in certain specific situations.
ARP maintains a list of both IP addresses and matching MAC addresses called the "ARP cache." These caches are available on individual network adapters and also on IP routers.
This is one way to derive an IP address from a MAC address; however, the mechanism is limited in many respects.
On Windows and some other operating systems, the "arp" command provides access to the local ARP cache. In Windows, for example, typing "arp -a" at the command (DOS) prompt will display all of the entries in that computer's ARP cache. Depending on how that local network is configured, however, this cache will often remain empty. At best, a client device's ARP cache only contains entries for other computers on the LAN.