My bike, which I love dearly, has 21 gears, which appears to now be standard among mountain bikes. Is that truly better with a bike that has, say, 7 gears? And why is it that the amount of gears a bike has always a multiple of 7?
There's a good article here which explains it pretty well - although there are 21 gears there are only effectively about 11 distinct useful gears on a typical 3x7 gear setup:
That is to say, some of the gear combinations overlap (or near enough) and this means you don't really get any extra function from them, but having them can make gear changing up/down a range smoother because it means you have to change the front sprocket less often. The exact number of "useful" gears will change based on the number of teeth you have in your particular setup, but the principle is the same.
As you can see from the graph, you do gain extra range from having an extra front sprocket - if you only had 28t on the front then adding a 38t gear gives you 3 extra useful gears, then adding a 48t gear gives you another 2 on top of that. This is good but it's not really the same as adding an extra 7 useful gears each time.
Also as some others have mentioned, gears don't always come in multiples of 7, this just seems to be the most common number of gears in the rear cassette of most mass-market bikes.
The total number of gears is the product of the number of chainrings you have and the number of cogs on your cassette. If you have 21 gears you have a triple chainring and a 7-speed cassette in the rear. If you have two or three chainrings some of your gears overlap, so they don't give you more capability.
There are two things of interest. The first is the range of your gears. One is what is the highest, what is the lowest. Do they satisfy your needs?
The second is how fine is the spacing, so do you feel you want a gear in between?
I'm a roadie and it doesn't take a very high end bike to be geared 2x11, often a 50/34 front and 11/28 rear. This gives 22 speeds. I ride a 2x10 giving 20. Many mountain bikers seem to have moved to 1x11 with a wide range cassette like 11-42. I suspect (not being a mountain biker) that their terrain is so quickly variable that they want to be in about the right gear but the wider spacing is not a problem for them. For me it would be, I notice the big gaps in the 15/17 and 21/24 shifts in the cassette, and they have much larger gaps than that.
You need to look at your riding and find a gear set that fits your needs.
On a mountain bike, you typically want to be able to go up steep hills, which requires some very low gears, and to go down hills fast, which requires some reasonably high gears. That means you either need quite a lot of gears in between, or big jumps between adjacent gears.
The advantage of having plenty of gears in between is that it allows you to pedal in a fairly narrow RPM range where you're most efficient, neither whirling your legs like crazy nor having to press really hard on the pedals. That cadence range will vary from person to person but it's typically some part of the 75 100RPM range. Note that, even if you used that whole range, it's only a 33% increase in cadence from the bottom to the top of the range, but your range of possible speeds is much greater, because of the gears.
However, there aren't really 21 different gears, since various combinations of front and back will be so close together that they may as well be the same. However, the overlaps allow more options for changing gears. For example, you can use the big chainring for "going fast", the small chainring for "going up steep hills" and the middle chainring for stuff in between. In each case, you have a choice of roughly seven gears at the back for finer-grained adjustments. (I say "roughly" because big-at-the-front, big-at-the-back and small-small combinations put the chain at quite an angle, which is noisy and causes wear; that's known as "cross-chaining". It's best not to do that too much, but do it if you need to.)
The number of gears doesn't have to be a multiple of seven. For derailleur systems, you'll have one, two or three gears on the front (I think I've even seen four) and between five and eleven on the back. 3x7 seems to be a common place for the engineering and marketing teams to meet for lower end commuter and mountain bikes. If you spend a bit more money, 3x8 becomes more common. Road bikes tend to be 2x9/10/11.
Gears don't make a bike "better" or "worse." The quality of a bike is always a function of how well it suits your needs. You might be better off with a bike with 21 gears, or just 1! It all depends on how you plan on using it.
The number of gears isn't always a multiple of 7, as others have pointed out. The total number of gears is the number of chainrings (big gears near the pedals) multiplied by the cogs on the rear wheel. The number is a little misleading, since there's a good amount of overlap between them, so the actual number of truly different gears will be smaller.
Between bikes with many gears, and bikes with few, there are certain trade-offs and mechanical differences. I'd be happy to get into those if you'd like, but practically speaking they probably won't affect you much. Just make sure to never use the smallest cog on the front unless you're climbing a steep hill!
On paper you have 3x7 = 21 gears, in reality much less.
- "twisting" the chain to have for example the front big gear and the rear big gear affects the yield of your pedaling and also the life of the chain, so you won't do it too often (I am sure there is a better explanation for this somewhere)
- some of the combination front-back are so close that they are practically redundant
you end up having 6 to 8 actual speeds (2 or 3 rear on each front gear).
Then there is the point if you would ever use all of them. You probably will if you use your bike in a hilly region or on challenging surfaces.
I now cycle in the Netherlands and I see fellow cyclists switching to a lower gear when they stop at a traffic light, like they would do with a car or a motorbike. IMHO that's really nonsense, as I catch them without changing gear before they are even done crossing the road.
Mine (which is a "hybrid", not a mountain bike) has gears like that.
On a long downhill I can use the top gear (so I "need" the top gear).
On a very steep uphill I need the bottom gear.
So I need a wide range of gears.
Now, you ask, why so many within that range: why not just 3 gears (minimum, maximum, and medium)?
It's because there's a cadence (RPM) that's the most efficient: if I spin too fast (too easily) then I want a higher gear; and if I spin too slowly then I want a lower gear. When I'm cycling at speed I want to make small changes to the gear (e.g. if the gradient changes slightly).
QED: because being able to make small changes over a wide range requires many gears.
The way I use them that I set the front gear first (e.g. the big ring for flat, or downhill, or slight uphill) and use the fine rear gears for small adjustments within that range.
I use the smaller or smallest front gear for uphill.
BTW I found now that I'm stronger that I no longer need the smallest ring (e.g. on gradients of 13% or less); I might do with only two rings on the front. But "mountain" bikes are made for steep hills.
Oh, also you will never (or you should never) use half the gear combinations: avoid using a highest gear in front with a lowest gear behind, and vice versa -- it's called cross-chaining.
Also I don't think it is always 7: mine's 3 on the front and 9 on the back.
By itself, the number of gears a bike has, is not very helpful in determining usefulness or quality of the bike. Generally, a large number of gears means the rider can tackle a wide range of terrain and more precisely match the gearing to his/her ability. If you ride totally flat terrain, you could very likely use a single gear. Riding more varied terrain, especially off-road, a rider will use many gears. How many will depend on just how varied the terrain is and the ability of the rider. An overly tired rider will appreciate having more lower gears from which to choose. A beginning rider will use a lower range of gears than he/she will, once fitness has improved. A bike with many gears allows the bike to be used over many different types of terrain and by a variety of riders with varying abilities and needs, even though any single rider may use only a small number of gears available.