Multiple sprocket gear ratio??

[brosgoboom]

So, my go-kart has an interesting drivetrain setup. I've been trying to figure out my gearing ratio(which came with the frame when I bought it) although I cannot use a calculator as it has multiple sprockets throughout the drivetrain. I am using a 420cc Predator Engine(Governed but I may change that) with a torque converter. There is a total of 4 sprockets including the axle and torque converter. The sprocket on the torque converter is a 12 tooth, which connects to a 24 tooth sprocket on the end of a shaft mounted horizontally under the engine mount. On the middle of the shaft, there is a 10 tooth sprocket that connects to a 60 tooth sprocket mounted on the middle of the axle(which has a differential). I am using 18-inch wheels. I have tried calculating the ratio manually but I am not sure if I am doing it correctly, so I was hoping someone could explain how you go about doing so. I will post the specs below for convenience. Any help is appreciated!
(Sprockets in order from torque converter to axle)
12 tooth
24 tooth
10 tooth
60 tooth
18 Inch rear wheel diameter
420cc Governed Stock Predator Engine (Approx 3600 RPM)

Thanks

 

[MTNSleder]

You got any pictures of your kart?

http://app.kartcalc.net/#home Here this site calculates What you want.

Heres what I got 12:1

You wanting to go faster or slower?

 

[mckutzy]

Here's another, it'll calculate jackshaft ratios...

http://www.affordablegokarts.com/GearCalc.php

 

[Bbqjoe]

I'm going to venture to say, in the end you're still delivering 6:1 to the wheels.
I don't know from what the wheels are seeing.

 

[brosgoboom]

Got it figured out

I am not very acquainted with jackshafts, I'm more of an engine internals guy, but I did manage to find the jackshaft calculator a little after that. I don't know if the previous owners were fixing to pull stumps or what, but I have another 10 tooth sprocket to replace the 24 tooth, which gives me the good ole 5:1 12-60 tooth reduction. Anyhow, thank you guys for your help, I appreciate it.
I would post pictures but my phone is broken right now so I cant, although I'm most likely going to chop the entire frame and mount the axle on the top of the floor pan so I can get it real low, along with putting a Harley muffler on it. I reckon itll look pretty cool with the big 18's in the back and maybe some 15's in the front, give it that tilted dragster look. Ill post pictures when I get a new phone anyhow because I also have no clue who produced this go kart, I havent seen a chassis like it before personally.

UPDATE: Scratch that, I was able to find an older pic of the kart
http://www.diygokarts.com/vb/showthread.php?p=464935#post464935

 

[itsid]

12:1 chain ratio plus ~2:1 for the TC.. 24:1 max ratio (wow that's some serious torque )

chain ratio is actually simple: divide the toothcount of the driven axle by the toothcount of the sprocket driving it:
(60/10 ... -> 6:1)

and repeat this step in this direction until you meet the engine multiplying all steps...
6:1 carry over... next step 24/12 (2:1)

sprockets that run on the same shaft rotate at the exact same speed can be ignored during calculation
(they'd run 1:1 so you'd multiply by one.. which is rather pointless )

6*2 =12 12:1 chain ratio.
12:1 internal TC ratio can be looked up... assume 2 for now:
12 * 2 ->> 24:1 overall ratio

'sid

PS I don't know what weight this thing has to push around,
but yes, I'd say you could easily double the speed by just replacing the 24T sprocket with another 12T one (making it effecitvely a 6:1 chain ratio.. which should be more than good for an engine that size)