how do you calculate internet speed using pings?

From the speedtest.net support page,

The ping is the reaction time of your coection–how fast you get a response after you've sent out a request. A fast ping means a more responsive coection, especially in applications where timing is everything (like video games). Ping is measured in milliseconds (ms).

There are other frequently asked questions with answer in their support section, including How does Speedtest.net know where I am?. More on ping can be found by reading about the utility, as well as the ICMP.