What an axle ratio is and why every other number depends on it
An axle ratio is a count, not a measurement. The ring gear inside your differential has a fixed number of teeth and the pinion that the driveshaft turns has a fixed number of teeth, and the ratio between them is simply the first divided by the second. A 41-tooth ring driven by an 11-tooth pinion is 41 ÷ 11 = 3.7273, which the catalogue sells as a “3.73”. That number tells you the driveshaft turns 3.7273 times for every single turn of the wheels.
Because it is a tooth count, it never drifts. Everything else in a driveline calculation carries uncertainty — tire diameter changes with pressure and wear, torque converters slip, speedometers are calibrated at the factory for a tire you may no longer own — but the axle ratio is exact for the life of the gear set.
The axle ratio is also the last multiplication in the chain. Engine crankshaft to transmission output is the transmission ratio; transmission output to the axle is the transfer case ratio, if you have one; axle input to wheel is the axle ratio. Multiply the three and you have the overall ratio, the number of engine revolutions per wheel revolution. That single figure sets your acceleration, your cruise rpm, your effective torque at the tire and how hard the drivetrain works to hold a given speed.
Fitting taller tires changes the same arithmetic from the other end. A larger diameter covers more ground per wheel revolution, so at any road speed the wheels turn more slowly, the engine turns more slowly, and the torque multiplication at the contact patch falls. Regearing to a numerically higher axle ratio is how you put back what a tire upsize took away. The tire diameter calculator gives you the diameter figure this page needs.
The formula, and where the constant comes from
Start with the axle ratio itself:
A = N_ring ÷ N_pinion
Then the overall ratio in any gear:
R_overall = G × A × T
where G is the transmission ratio in that gear and T is the transfer case ratio, which is 1.000 in two-wheel drive or high range.
The speed relationship is where most people reach for a memorised constant. Build it instead. A mile is 63,360 inches. At MPH miles per hour you travel MPH × 63,360 ÷ 60 = MPH × 1056 inches every minute. One turn of a tire of diameter D covers πD inches, so the wheels turn
wheel rpm = MPH × 1056 ÷ (π × D)
and the engine turns R_overall times faster:
RPM = wheel rpm × G × A × T
Collapse the constants and you get the familiar shop formula MPH = RPM × D ÷ (336 × ratio). That 336 is really 63,360 ÷ (60π) = 336.135, so the rounded version reads about 0.04% optimistic. This calculator keeps π explicit rather than rounding it, which is why its answers sit a couple of rpm away from a 336-based slide rule at highway speed.
Rearranging for the ratio you need is one line of algebra. Fix the target rpm and the road speed, and the axle ratio that delivers them is
A_req = RPM_target × πD ÷ (1056 × MPH × G × T)
You then buy the nearest ratio the manufacturer actually makes, because tooth counts are integers and the catalogue is a short list.
Worked example: a 41/11 axle, a 31-inch tire and 70 mph
Take a truck with a four-speed automatic whose ratios are 3.06, 1.63, 1.00 and 0.70, a 41-tooth ring with an 11-tooth pinion, no transfer case reduction, and 31-inch tires. You want to know the cruise rpm at 70 mph, and what ratio would put you at 2,000 rpm instead.
- Axle ratio. 41 ÷ 11 = 3.7273.
- Overall ratio in top gear. 0.70 × 3.7273 × 1.000 = 2.6091.
- Tire circumference. π × 31 = 97.389 in.
- Inches travelled per minute. 70 × 1056 = 73,920 in/min.
- Wheel rpm. 73,920 ÷ 97.389 = 759.02 rpm.
- Engine rpm. 759.02 × 2.6091 = 1,980 rpm.
- Revolutions per mile. 63,360 ÷ 97.389 = 650.6.
Now solve the other direction. You want 2,000 rpm at the same 70 mph in the same 0.70 overdrive. The wheels still turn 759.02 rpm, so the overall ratio must be 2,000 ÷ 759.02 = 2.6350, and the axle ratio must be 2.6350 ÷ 0.70 = 3.7643. (As a check: 41/11 × 3.7643 ÷ 3.7273 reproduces the same figure, and 2,000 ÷ 1,980.35 = 1.0099 is exactly the ratio between the two axle ratios.) That is 0.037 away from what you already have — roughly a 1% change — which is far inside the granularity of the catalogue. The honest answer is that a regear is not worth doing for that difference; you already have the right gear.
Change one input and the conclusion changes completely. Fit 35-inch tires and leave the 3.73 axle alone: circumference becomes 109.956 in, wheel rpm at 70 mph falls to 672.27, and engine rpm drops to 1,754. To get back to the original 1,980 rpm you need an axle ratio of 3.7273 × 35 ÷ 31 = 4.2082, and the nearest catalogue set is a 4.10 or a 4.30. That is the calculation that sells ring-and-pinion sets.
How to read the result
Match the cruise rpm to where the engine makes its power, not to a number you like. A modern turbo-diesel pulls a highway grade happily at 1,600 rpm because peak torque arrives just above idle. A small naturally aspirated gasoline engine with peak torque at 4,400 rpm has nothing left at 1,600 and will hunt between overdrive and direct on every rise. Look up where your engine makes torque and put your habitual cruising speed somewhere it can respond without a downshift.
Judge a regear by the ratio of ratios, not by the difference. Going from 3.73 to 4.10 multiplies overall ratio by 4.10 ÷ 3.73 = 1.099, so torque at the tire rises about 10% and cruise rpm rises about 10% at any fixed speed. Going from 4.10 to 4.56 is another 11%. As a shop rule of thumb, a change under about 5% is comparable to what tread wear alone takes out of a tire's diameter over its life, so it is rarely worth the labour of pulling an axle.
Restore the ratio a tire upsize consumed. If you go from a 31-inch to a 35-inch tire, multiply your old axle ratio by 35 ÷ 31 = 1.129 to keep the drivetrain where it was. This is the single most common reason a truck feels sluggish and shifts poorly after a lift kit.
Check the crawl ratio separately. First gear × low range × axle ratio is the number that matters off-road, and this calculator gives it directly if you set the transfer case field to your low-range ratio and read the first-gear row of the table. A 3.06 first, a 2.72 low range and a 3.73 axle give 31.0:1.
Non-hunting sets. If the ring and pinion tooth counts share a common factor, each pinion tooth only ever contacts a fixed subset of ring teeth. Gear manufacturers normally pick counts that are coprime so wear spreads over every tooth pair. The calculator flags a shared factor for you.
Common ring-and-pinion tooth counts and the cruise rpm each gives
| Ring / pinion | Exact ratio | Sold as | RPM at 65 mph |
|---|---|---|---|
| 40 / 13 | 3.0769 | 3.08 | 1,518 |
| 42 / 13 | 3.2308 | 3.23 | 1,594 |
| 41 / 12 | 3.4167 | 3.42 | 1,686 |
| 41 / 11 | 3.7273 | 3.73 | 1,839 |
| 37 / 9 | 4.1111 | 4.10 | 2,028 |
| 41 / 9 | 4.5556 | 4.56 | 2,248 |
| 39 / 8 | 4.8750 | 4.88 | 2,405 |
| 41 / 8 | 5.1250 | 5.13 | 2,528 |
| 43 / 8 | 5.3750 | 5.38 | 2,652 |
The advertised ratio is always rounded. Order by tooth count where you can, because two sets sold as the same number can differ in the third decimal place.
Mistakes that make a gearing calculation wrong
- Using the advertised tire size instead of a measured diameter. A tire marked 285/75R16 has a geometric diameter of 32.83 in, but the loaded rolling diameter under vehicle weight is smaller and the manufacturer's published revolutions per mile reflects that. Where the two disagree, the published revs-per-mile figure is the better input.
- Forgetting the transfer case. A part-time four-wheel-drive case is 1.000 in high range, but a full-time case may not be. Read the tag before assuming.
- Reading the differential tag as gospel. Tags survive rebuilds that the gears did not. Count driveshaft turns per wheel turn, or count teeth with the cover off.
- Comparing overall ratios across different tire sizes. Ratio alone is meaningless without diameter. The pair that matters is ratio divided by tire diameter, which is why a 4.10 on 35s pulls like a 3.63 on 31s.
- Ignoring torque converter slip at cruise. In a locked converter there is none, which is why every figure here assumes lockup. Unlocked, the engine turns several percent faster than this calculation says; the speed from rpm calculator has a slip input for that case.
- Regearing on rpm alone. The ratios available are limited by the ring gear diameter the housing was designed around, and the deepest sets in the catalogue exist only for the larger housings. Check your axle model's ratio list against the ratio the arithmetic asks for before you order anything.
Where this sits among the other driveline calculations
Gear ratio is one of three inputs that decide how a vehicle feels, and the other two live on neighbouring pages. Tire diameter comes from the size code and is handled by the tire size to diameter calculator. The rpm-to-speed conversion in every individual gear, including converter slip and speed at redline, is on the rpm to mph calculator. This page is the piece that gets you the ratio itself and the overall ratio through the whole box.
On the performance side, gearing decides how much of the engine's usable band you spend inside on a run, which is why drag racers pick an axle ratio to cross the finish line at peak power rpm rather than for cruise comfort; the quarter mile ET calculator handles the power-to-weight half of that question. Engine airflow, and therefore where the torque peak sits at all, is the domain of the volumetric efficiency calculator.
Two limits are worth naming. First, this is a kinematic calculation: it says nothing about whether the axle can carry the torque, and a numerically higher ratio raises pinion tooth loading. Second, on a vehicle with a locking or limited-slip differential, the ratio you compute is unchanged, but the traction consequences of the extra torque multiplication are not. Neither shows up in tooth counts, and both should shape the ratio you order.
Finally, remember that changing the axle ratio changes speedometer and odometer calibration on any vehicle that takes its speed signal from the transmission output shaft rather than from the wheels. Vehicles with ABS wheel-speed-based speedometers are unaffected by an axle change but are affected by a tire diameter change. Which of the two applies to you determines whether a regear needs a recalibration.
Key terms
- Ring and pinion
- The hypoid gear pair inside the differential. The pinion is turned by the driveshaft; the ring gear is bolted to the differential carrier and turns the axle shafts.
- Final drive ratio
- Used loosely for the axle ratio alone, and loosely again for the overall ratio in top gear. On this page the axle ratio is stated separately from the overall ratio so there is no ambiguity.
- Overdrive
- Any transmission gear with a ratio below 1.000, in which the output shaft turns faster than the input shaft.
- Crawl ratio
- First gear ratio multiplied by low-range transfer case ratio multiplied by axle ratio. It is the deepest torque multiplication available to the vehicle.
- Hunting gear set
- A ring and pinion whose tooth counts share no common factor, so every pinion tooth eventually meets every ring tooth and wear is distributed evenly.