# How to Determine Your Axle Gear Ratio

People who are buying a used vehicle, or shopping for an axle from a junk yard, frequently need to know what the ring and pinion gear ratio is in the axle's differential, as well as whether or not the axle has some sort of traction control device like a limited slip, locker, or spool.

One way is to look at the little metal tag that's bolted to the
differential cover. This will have stamped in it, among other things,
either the gear ratio or the ring/pinion tooth counts that the axle came
with from the factory. Tooth counts will be something like
"`37 9`

" for 4.11 gears (37 / 9 = 4.11). The problem
is that sometimes these tags are missing or unreadable, and sometimes
(especially common on off-road vehicles) a previous owner will have
changed the gears and not bothered to change the tag.

Another way is to remove the differential cover or the 3rd member and count the number of teeth on the gears. Unfortunately, this can get messy. However, it does tell you without a doubt what kind of traction control device you may have.

One somewhat easy yet very reliable way is to jack up the wheels, disconnect the driveshaft, rotate one wheel, and count how many revolutions the pinion yoke/flange makes. Those instructions gloss over some important details, so rather than simply reciting the exact instructions, I'll first explain why things are the way they are. If you're impatient, skip to the bottom.

Let's pretend through this example that you have 3.73 gears.

If you have a locker or good traction (or even a limited slip with equal resistance on either wheel), then when you turn the driveshaft 3.73 full turns, both wheels will rotate one full turn. That's the gear reduction at work.

Now, pretend you're making a tight turn, where the outer wheel has to turn more times than the inner wheel to complete the turn. Because of the way an open differential works, when one wheel turns slower than the ring gear, the other wheel has to compensate by turning faster than the ring gear. In this situation, for every 3.73 turns of your driveshaft, the inner wheel may only make half a revolution, while the outer wheel makes 1.5 revolutions.

Basically, for each 3.73 turns of the driveshaft, there must be two full wheel turns for the two wheels combined. When driving a straight line, each wheel makes one full turn. When turning, one wheel may make 0.8 turns while the other makes 1.2 turns. The tighter the turn, the more dramatic the difference between how fast the two wheels turn.

This situation is exaggerated when you jack up only one rear wheel while leaving the other on the ground. One wheel cannot rotate at all, so the other wheel (the one you're turning) must make two full turns in order to get one full rotation of the ring gear in the differential. One rotation of the ring gear will generate 3.73 rotations of the pinion gear.

If you jack up both tires and leave the tranny in gear, the ring gear won't be allowed to rotate at all. Therefore, if you jack up both wheels and try to rotate one of them (with an open diff), the opposite wheel will have to rotate the same number of times, but in the opposite direction. If you try this trick with a good limited slip, you'll have to really wrestle the tire in order to get it to turn, since you're trying to overcome the slip-limiting force of your LSD. If you try this trick with a locker, you'll pop a blood vessel before you get the tire to turn, since a locker won't let either wheel rotate without the driveshaft turning. That's the whole point of a locker.

So, assuming you've got an axle up in the air with the driveshaft disconnected & neither wheel on the ground:

- If you turn one tire & the other one either stays still while the
pinion rotates, or the other one rotates backward while the pinion
stays still, or something in between, then you've got an open diff
or a very weak LSD (like a Trac-Lok with too many miles on it).
In this case, you need to secure one wheel (perhaps by lowering
the tire onto the ground), then you can figure your gear ratio by
rotating the airborne tire
**TWO**full rotations and counting the number of times the pinion rotates. 3.73 turns means 3.73 gears. If you only rotate the tire once, then 1.865 turns means 3.73 gears. - If you turn one tire & the other one turns the same number of turns
in the same direction, then you've got a good LSD or locker. In this
case, you can just rotate the tires
**ONE**full rotation and figure your gear ratio by counting the number of times your pinion rotates. 3.73 turns means 3.73 gears.

If you've never opened up an open differential and rotated the various parts to see how it all interacts, I highly recommend doing so. That's what really made all this make sense for me when I was first learning about Jeeps.

One good site for learning about this stuff is How Stuff Works. If you click on the "Spinning at different speeds" link and pay attention to the animations, you'll see what I was talking about with the outside wheel spinning faster than the ring gear while the inside wheel spins slower. When determining your gear ratio, the key is that you need to make your ring gear (not necessarily your tire) make one full rotation.

### Calculating your engine RPM

I'll expand the following into a page of its own eventually, but if you're curious how to find what your engine RPM will be with different tire sizes, gear ratios, and cruising speeds, use this formula:

Divide 336.1355 by the height of your tire in inches. Call this number P. Next, to determine your engine RPM at a certain speed (in MPH) with a certain gear ratio, you just multiply P times the gear ratio times the speed. If your tranny has overdrive, multiply that result times your overdrive ratio. If you've got an auto tranny without a lockup torque converter (which means anything prior to the early 1980's), then you can add about 5 or 10% to that number to allow for torque converter slippage.

For example, say you've got 31" tires, 3.73 gears, an auto tranny with 0.79 overdrive but no lockup converter, and you want to check your engine RPM at 70 mph:

336.1355 / 31 | = | 10.843 | |

10.843 * 3.73 * 70 | = | 2831.101 rpm | (direct drive, no slippage) |

2831.101 * 0.79 | = | 2236.570 rpm | (overdrive, no slippage) |

2236.57 * 1.05 | = | 2348.398 rpm | (overdrive, minimal slippage) |

2236.57 * 1.1 | = | 2460.227 rpm | (overdrive, maximum slippage) |

So you'd be cruising down the interstate at roughly 2400 rpm.

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created 19 Feb 2004 last updated 1 Dec 2005 Obi-Wan (obiwan@jedi.com)