Can someone explain gear ratios on a 21 speed bicycle to me?

Easiest: Smallest # of teeth on the front and largest amount on the back (Think climbing hills)
Hardest: Largest # of teeth on the front and smallest amount on the back. (Think flat sprints and descending fast)

@ARE_you_kidding_me I am pretty sure on my 18 speed the hardest gear ratio is large on front (3 on the shifter) and large on rear (6 on the other shifter).

the hardest gear ratio is large on front (3 on the shifter) and large on rear (6 on the other shifter).

It might be a larger number label on the shifter, but it’s the small cog on the rear wheel.

Two examples:

1)
Front chainwheel 28
Rear cog 28
If you push the pedals around one time (28 teeth) the rear wheel spins once (28 teeth)

2)
Front chainwheel 28
Rear cog 14
If you push the pedals around one time (28 teeth) the rear wheel spins twice (28 teeth)

The second example takes exactly twice as much force but carries you twice as far.

Here’s the whole progression below. Notice there is overlap – you can sometimes get nearly the same effect by changing to a different front chainwheel and different rear cog.

But I can tell you from decades of riding, nobody maniacally shifts around to these combinations in order.

IN GENERAL, people ride long periods shifting only the back.
1)
On flat ground, you probably stay with the middle chainring in front.
2)
Up hills or into a strong headwinds, switch to the small chainring in front
3)
Trying to break speed records or racing, you use the big chainring in front

Front….................Rear….........Rear wheel turns per chainwheel turn
28….................27….................1.04
28….................25….................1.12
28….................23….................1.22
28….................21….................1.33
38….................27….................1.41
38….................25….................1.52
28….................18….................1.56
38….................23….................1.65
28….................16….................1.75
48….................27….................1.78
38….................21….................1.81
48….................25….................1.92
48….................23….................2.09
38….................18….................2.11
28….................13….................2.15
48….................21….................2.29
38….................16….................2.38
48….................18….................2.67
38….................13….................2.92
48….................16….................3.00
48….................13….................3.69

@Cruiser Nope but it’s an easy mistake to make. Think of it this way: you are putting more energy into the system when you need to spin the rear wheel the most. My largest front cog and the smallest rear usually net around 200W when riding normal. This only goes down when reducing to the smaller front cog or larger rear. I mountain bike regularly and also build my bikes. I actually ditched all but one cog on the front chain ring, you can save a bunch of weight by eliminating the shifter, selector, extra cogs and cable.

Thanks for all the help. I understand how the ratios are calculated now! And while it probably won’t adjust my riding style greatly it at least gives me something to think about on the uphills.

Please bear in mind that the bicycle is not designed for using all the combinations front changing and rear gearing. To do so results in chain crossing, which puts a great deal of excess tension on the chain and reduces efficiency. It also speeds up wear on the components.

Chain crossing is using the largest front chain ring (which is to the outside of the ring cluster) with the largest rear gear (which is the most leftward on the gear cassette).The chain is as far as possible from being parallel with the frame and wheels.

@zenvelo Good point.

For example, 48/27 is an extreme cross, far-right front chain ring to far-left cog in back – don’t do that.

38/21 is good, the chain goes straight down the middle.

The gear ratio, and the pedaling would be virtually the same.
48….................27….................1.78
38….................21….................1.81

So 48/27 is pointless.