How can you tell what speed gearing a bicycle has eighteen speed twentyone speed?

Answer 1

You count and multiply the number of sprockets at the rear wheel with the number of sprockets by the pedals. 3x6 = 18, 3x7 = 21. By the pedals you can have 2 or 3, or even 4 with some modification. At the wheel you can have anything between 5 and 11. But the number of different gears isn't the same as the number of useable gear ratios. Typically if you have 27 different gears it'll give you 15-18 usefully different gear ratios. You'll also want to avoid those gears that set the chain off at an extreme angle(called cross-chaining). Don't run the chain on big-big, or small-small.

Answer 2

If you have 3 chainwheels/chain rings up by the pedals, and 7 sprockets by the rear wheel, then you have what's called a 21-speed bike (3x7=21)

In reality this isn't true though. What you have is 21 possible gear combinations, but due to the nature of the setup you will get several repeated gear ratios.

In practical terms you'll have about 15-17 usefully different gears.

You also need to think about cross-chaining. It's bad for the bike to run the chain from smallest sprocket to smallest chainwheel/chainring and biggest sprocket to biggest chainwheel/chain ring - so out of the 21 you've lost two there straight off. Running small/small or big/big doesn't do anything for you in term of ratios either, so stay away from there.