Is the iphone 5s as fast as a mac computer?

I have a macbook but not a iphone. Just curious if the iphone 5s is close to the speed of a mac computer. Loading from page to page on the web, uploading pictures on facebook, watching youtube videos stuff like that.

Loading pages and videos has nothing at all to do with the computer/phone in use, and everything to do with how you are connected to the Internet. The phone could be faster, or not, depending on how the Mac (or any other sort of PC) is connected.

If you've got Google Fiber to the Mac and 3G service on the iPhone, the Mac wins. If the Mac is connected via 56k dialup and the iPhone is using 4G, the phone wins.

The activities you describe are limited by the speed of your network connection, not by the iPhone or the Mac. Even the slowest Mac or iPhone is generally more than fast enough to keep up with most network connections.