5. Gear Ratio Calculations and Effects of Tire Diameter

Let’s start this with a simple gear computation. To determine gear ratio, simply divide the ring gear teeth by the number of teeth on the pinion. If we have 40 teeth on the ring gear and 10 teeth on the pinion: 40 / 10 = 4.10:1 ratio. This also works for any gear or even a blower drive. Merely divide the driven pulley tooth count by the drive tooth. This also works for belt pulleys – just use diameters instead of a tooth count.

When we look into the effect of tire size on the gear ratio, it gets a little more complicated. Let’s start by finding engine RPM from a given vehicle speed. We’ll need to know the rear gear ratio, the rear tire diameter, and the vehicle speed. Let’s use a Camaro with a Muncie four-speed and 4.10 gears running a 28-inch tall tire at 70 mph. This equation assumes no slippage as with a manual transmission. With a torque converter not in lockup, there will be some slippage in the converter.

Engine RPM = (MPH x Gear Ratio x 336) / Tire Diameter

Engine RPM = (70 x 4.10 x 336) / 28

Engine RPM = (96,432) / 28

Engine RPM = 3,444

Now let’s use that same Camaro, but we’ll plug in a TKO five-speed with a 0.64:1-overdrive ratio. This requires the same formula but we have to first determine something called Final Drive Ratio.

With the Muncie four-speed, Fourth gear is 1:1 with the output shaft turning the same as the input. But with an overdrive, this uses a gear inside the transmission to increase the speed of the output shaft compared to the input. The formula for Final Drive is simple:

Final Drive Ratio = Rear Gear Ratio x Overdrive Ratio

Final Drive Ratio = 4.10:1 x 0.64:1

Final Drive Ratio = 2.62:1

Now, our numbers for cruising engine speed at 70 mph will be drastically reduced with the overdrive ratio:

Engine RPM = (70 x 2.62 x 336) / 28

Engine RPM = 61622 / 28

Engine RPM = 2,200

There are three variations on the RPM equation that solve for the other variables. To keep this story brief, we won’t offer examples for each since they all execute similarly.

MPH = (RPM x Tire Diameter) / (Gear Ratio x 336)

Gear Ratio = (RPM x Tire Diameter) / (MPH x 336)

Tire Diameter = (MPH x Gear Ratio x 336) / RPM

One variable that is fun to look at is solving for the effect of tire diameter on gear ratio. So, using our same Camaro, let’s say we want to know the Effective Gear Ratio if we changed from a 28-inch tall tire to a shorter 26-inch-tall rear tire.

Effective Gear Ratio = (Old Tire Diameter / New Tire Diameter) x Gear Ratio

Effective Gear Ratio = (28 / 26) x 4.10

Effective Gear Ratio = 1.0769 x 4.10

Effective Gear Ratio = 4.41:1

Conversely, if the Camaro initially ran a 26-inch-tall rear tire and we wanted to add a 28-inch-tall tire, logic tells us that the taller tire will reduce the effective gear ratio.

Effective Gear Ratio = (26 / 2 x Gear Ratio

Effective Gear Ratio = 0.9285 x 4.10

Effective Gear Ratio = 3.80:1
Not sure of the ratio of that set of gears sitting on the shelf? Dividing the ring gear teeth by the pinion count will offer an immediate answer.

Many of the equations used in this story can be found in the John Lawlor Auto Math Handbook. As you can see, ours is well-used. It has recently updated material with input from our friend and former Chrysler engineer, Bill Hancock. It’s a great reference manual located on the quick-access side of our library.