Jeep Math 101
The Math Behind the Tire Size / Gear Ratio Chart
You've probably seen those Tire Size / Gear Ratio charts before, but have you ever wondered where all of the numbers come from? I did, so I did the math. Here are the results of my research.
Let's start with some basic facts that we'll need to use in our calculations.
Since we are working with a tire measured in inches not miles, we're going to need to know how many inches are in a mile. And, if we want to know our RPMs at 65 miles per hour we need to know how many inches are in 65 miles.
1 Mile = 5280 Feet = 63360 inches. 65 miles = 4118400 inches.
Next, we need to be able to calculate the circumference of our tires in order to know how far they travel per rotation. This is expressed as an equation you should recognize from high school geometry class:
Pi * D = C or Pi * [Tire] Diameter = [Tire] Circumference
Pi... Ahh... well... OK, I can't explain Pi. We'll just trust that Pi or 3.1416 works for us.
Ready for an example? Good. Let's start with a 30" tire and 3.73 gears.
Calculation #1- Caclulating the Tire Circumference.
|Pi||times||Tire Diameter||equals||Tire Circumference in inches|
Calculation #2- Caclulating the Number of Tire Rotations in 65 Miles.
|Inches in 65 miles||Divided by||Tire Circumference||equals||Tire Rotations in 65 Miles|
Calculation #3- Cacluate Tire Rotations in 1 Minute at 65 MPH.
|Tire Rotations||Divided by||Minutes||equals||Tire Rotations per minute|
Calculation #4- Calculate the Engine RPMS Usingthe Axle Gear Ratio.
|Tire Rotations||Times||Gear Ratio||equals||Engine RPMs at 65 mph|
With 30" tires and 3.73 gears, at 65 MPH the engine RPMs should be 2716. This can really be boiled down into a single equation that looks like this:
RPMs =((4118400 / ([Tire Size] *3.1416))/60)* [Gear Ratio]
Clear as mud?