If you go to my useful links you will see a link to Sheldon Brown's Gear Calculator. For those of you who aren't bike geeks you might be wondering what that is all about. The simplest explanation I can give is; it is a device used to help one figure out what type of gearing to use on a bicycle. Why would you want to know this? You may not if you are entirely happy with how your bike performs and you aren't planning on getting a new bike. But if you're having trouble getting up the hills or you want to be able to pedal down hills you may want to calculate the gear ratio on your bike. If you are buying a new bike or building up a new bike you may find the gear calculator useful.
To use the bike calculator you just input tire size, crankarm length, Chainring size (chainrings are the sprockets next to your pedals) and the cassette size ( the cassette is the cluster of sprockets attached to your rear wheel) Sprocket sizes are usually written on them or you can count the number of teeth. Once you input all the data the calculator will give you a chart with the gear inches for each chainring/sprocket combination.
But what do gear inches tell you? A 50 x 12 combo equals 105.1 gear inches and a 30 x 26 combo equals 30.3 gear inches, right off the bat you can see that a higher # occurs in the higher gears and the lower # occurs in the lower gears. Gear Inches represent the amount of chain that is moved with one complete pedal revolution while in each gear combination. So the higher gears move more chain and the lower gears move less chain. That makes sense since you go slower in the lower gears and faster in the higher gears. It logically follows that moving more chain requires more effort than moving less chain.
If you want to pedal up those big hills more easily you may want to change your cassette to one that has some larger sprockets, anything from 28-36 tooth sprockets. You could also change the chainrings probably by changing your entire crankset, to include chainrings that have something less than 30 teeth.
That should give you an idea what gear calculators are all about. It is possible to calculate this without the calculator but the calculator is much faster. There are a lot of gear calculators on the internet but I like Sheldon's calculator because it allows you to choose common cassette clusters or manually plug in the sprocket sizes. Sheldon also lets you measure your gear combos in other increments such as MPH/KMH per RPMs or gear ratios,which is Sheldon's thing so I'll let you read about that on his website.
Please note this post is not meant to be an exclusive guide to changing a bikes gearing. In addition to changing cassettes and cranksets you may also have to change the rear derailleur and lengthen the chain.