Equals is more idiomatic in American English, but either is acceptable.
To determine whether "three feet" is treated as singular or plural, try using it in other contexts. In American English, and I believe in UK English as well, you would say:
Three feet is pretty long for a garter snake
Three feet are too many for a human being to have.
When expressing a distance, rather than describing the things your socks go on, "three feet" is treated as singular. Think of it as shorthand for "a distance of three feet" rather than "three of the items known as feet."
The trick with your phrase is that it can be interpreted in either way. Because it is a distance, you could think of it as:
A distance of three feet is equivalent to a distance of one yard.
in which case you use "equals." Or you could think of it as:
Three of the items known as feet are equivalent to one of the items known as yard.
in which case you use "equal."
Because either reading is possible, it's grammatically ambiguous. In my experience, though, "equals" is more common, following the way "three feet" would be treated in other sentences.