http://www.wolframalpha.com/Wolfram Alpha is an online service from developed by Wolfram Research, who are also the creators of the well known computational software program known as Mathematica.
Unlike a search engine which merely matches words, it answers a question directly by computing an answer using the information stored in its database.
Sounds cool but how do I use it?
First of all Wolfram Alpha
IS NOT A SEARCH ENGINE and will not work very well if you try to use it as one. It's not going to tell you about the latest episode of Top Gear or whether [insert actors name here] is pregnant, that is not its purpose.
What Wolfram Alpha does well is answer questions that can be answered using widely available information but require more processing than other sources like search engines can provide.
To use a bit of a metaphore, while a search engine is like really stupid person who memorized everything, Wolfram Alpha is like a really smart person who only memorized what is necessary.
Say for example you wanted to know "density of water at highest temperature on earth".
If you try to use Google you have to hope that someone somewhere in the world even bothered to find that specific number and posted it on the internet, which is unlikely. At the time of the post Google doesn't give any good answers.
This is where Wolfram Alpha comes in. Instead of looking for the answer elsewhere, Wolfram Alpha can use the information it already has to get the information that you want. Wolfram Alpha already has information and equations regarding the density of water at different temperatures, knows the highest recorded surface temperature on earth, and by default will assume a pressure of about 1 atmosphere. Using these three seperate pieces of information Wolfram Alpha then calculates the answer you want, which in this case is 984.2 kg/m^3.
Another example, say you want to know how many calories you will burn if you run for a given amount of time. You could type something like "running for 45min at 5mph 5'11" 130lb 19 years old male". Wolfram Alpha has access to several medical studies on how rapidly people of different weights, heights, and ages can burn calories while running and will use several of these studies to obtain an answer. It then lists how many calories will be burned, how much fat will be burned, maximum heart rate, and several other semi-relevant bits of information like how quickly you would finish the marathon if you kept up that speed.
