Most of you "seasoned" folks most likely know all this, but I stumbled upon this and thought I'd pass it on for someone new, FWIW. 
A common 4x4 application is an upgrade to larger-than-stock tires (duh ).
Once completed, this change immediately alters vehicle speed at a given rpm, rpm at a given speed, and effective gear ratio, which in turn affect both acceleration and fuel economy (I know, big news flash here). Tire size, drive ratio, mph, and rpm weave an intricate pattern of performance. Change one and all four are affected.; knowing any of the three, the fourth can be easily determined. The following four formulas illustrate the point:
-Tire diameter = mph x drive ratio x 336/Rpm
-Gear ratio = rpm x tire diameter /Mph x 336
-Mph = rpm x tire diameter /Gear ratio x 336
-Rpm = mph x gear ratio x 336 /Tire diameter
If you are contemplating a tire size upgrade and know your rearend gear ratio, the table below will offer a quick reference guide for figuring your engine rpm at 60 mph cruising speed. Likewise, if you measure your tire size and observe rpm and mph, you can calculate what gears are in your axles.
How To Calculate Actual Speed:
With the change to taller tires, your speedometer will read "slower" than the actual vehicle speed. To determine the percentage of speedometer error, the formula is a simple relationship between old and new tire diameters.
-Actual Speed = new tire diameter x indicated speed /Old tire diameter
Example: You have replaced your 28-inch OEM rubber "wimpys" with a new set of 35-inch all-terrain "mud-gobbler ultra x-tremes" and you want to know your actual speed when the speedo reads 60 mph--well read on
-35 inch (new tire) x 60 mph (what speedo reads) /28 (old tire)=75 mph (actual speed)
See...simple :smoke:
----------------------------------------------
Now...
Speedometer ratio adjustment calculation.
Ever wonder how far off your speedometer is with your new bigger tires? By using a simple ratio calculation, this info will only approximate your corrected speed and depends on the accuracy of tire size diameters (assumimg nothing but tire size has changed). If you know specific information about your vehicle (gear ratios, RPM, etc.) then use the Gear Ratio calculator, it's probably a little more accurate.
Formula used (slight variation of above...I love math!!)
(New Tire Diameter / Old Tire Diameter) x Speedometer MPH = Actual MPH
Now, another way of looking at this relationship would be to figure what the indicated speed would be if you were actually going 60 mph. In this case, the tire diameter relationship is flip-flopped to:
Indicated Speed = old tire diameter x actual speed /New tire diameter
Using the previous example, your speedometer reading at an actual 60 mph is:
-28 inch x 60 MPH /35 inch = 48 MPH
See, easy!!! OK class, on to GEARS!!!!
-------------------------------------------------
Gearing up:
Using the above tire change as an example, lets say that your vehicle is currently running a 3.40:1 final-drive gear set. Now that you have changed to a taller tire, you want to determine the actual, or effective, final ratio. This can be figured by dividing the old tire diameter by the new, and multiplying by the current gear ratio1):
-28 inch (old tire) x 3.40 (your actual stock gear ratio) /35 inch (new tire) = 2.72:1 (final effective drive ratio)
Whoa big fella
Dropping from a 3.40:1 to a 2.72:1 ratio will seriously reduce off-the-line responsiveness and severely affect slow-speed trail capabilities. 
So, Mr. Trail-Monster, if your new 35-inch all-terrain "mud-gobbler ultra x-tremes" rubber is just what you want, but you now need to restore your vehicle’s low-end, the following formula will allow you to determine what gear set (equivalent) ratio should be installed to compensate:
-Equivalent ratio = new tire diameter x original ratio /Old tire diameter
As in my example:
-35 inch (new tire) x 3.40 (your actual stock gear ratio) /28 inch (old tire) = 4.25:1 (what you need to restore your vehicle’s low-end responsiveness to previous 3.40)
By installing a gear set in the range of 4.25:1, you will not only restore your vehicle’s low-end grunt, you will likewise restore your speedometer’s accuracy. Cool!!
Ahhh....just a little more...
Figuring gear ratio:
Knowing what gears are in a given axle is a must when considering that axle for a swap. The actual ratio or reference code, will normally be found on either a tag attached to a bolt, or will be stamped into the axle housing. If it cannot be found, there is a simple method for manually (and mathematically ) determining the ratio for any axle installed on a vehicle.
Raise both wheels of the axle, with the transmission in Neutral. (Make sure you support the vehicle with safety stands and block the front tires.) Make a reference mark on the driveshaft and on the differential housing. Next, without rotating them, make a mark on both tires and their respective fender wells. With a friend watching the driveshaft, carefully rotate both tires at the same time exactly one revolution. The number of turns the driveshaft makes will indicate the ratio. If the driveshaft rotates 4 ½ turns, for instance, the axle ratio is roughly 4.5:1.
Almost done...
METRIC TIRE TO DIAMETER (INCHES) CALCULATION
Most of the formulas dealing with gear ratios will want a tire diameter (measured in inches). This formula is a quick way to get the tire diameter of those metric tires that are common on just about everything stock. For example a LT265/75R16 would be around 31.6 inches tall and 10 inches wide. Enter any three of the numbers into this form to solve for the fourth. "LT" means Light Truck and "P" means Passenger tire. The bigger number (on the left) is the Section Width. The number to the right of the slash ("/") is the Aspect Ratio (percent of width). The "R" means Radial tire and the last number, far right, is the rim diameter in inches.
Formula used :
-(Section Width x Aspect Ratio x 2) /25.4 + Rim Diameter = Tire Diameter
Width in inches = section width / 25.4
Section Height in inches = Width in inches X Aspect Ratio (%)
Finally...
GEAR RATIO CALCULATION
If your tires are bigger than stock you either guess at the actual MPH or do something like count the seconds between mile markers on the highway while maintaining 60 on the speedometer. If you know your gear ratios and tire size you can get a fairly close number using this calculating tool. Fill in all entries except the one you want an answer to in green section only. If you'd like to find your overall crawl ratio, enter the Diff/Trans/TransfCase ratios.
Formulas used :
-(RPM x Tire Diameter) / (Diff Ratio x Trans Ratio x Transf Case Ratio x 336) = MPH)
and
(Trans Ratio x Transf Case Ratio x Axle Ratio) = Crawl Ratio
Well, that's it...hope this helps someone, especially some of the new folks...enjoy!
A common 4x4 application is an upgrade to larger-than-stock tires (duh
).Once completed, this change immediately alters vehicle speed at a given rpm, rpm at a given speed, and effective gear ratio, which in turn affect both acceleration and fuel economy (I know, big news flash here). Tire size, drive ratio, mph, and rpm weave an intricate pattern of performance. Change one and all four are affected.; knowing any of the three, the fourth can be easily determined. The following four formulas illustrate the point:
-Tire diameter = mph x drive ratio x 336/Rpm
-Gear ratio = rpm x tire diameter /Mph x 336
-Mph = rpm x tire diameter /Gear ratio x 336
-Rpm = mph x gear ratio x 336 /Tire diameter
If you are contemplating a tire size upgrade and know your rearend gear ratio, the table below will offer a quick reference guide for figuring your engine rpm at 60 mph cruising speed. Likewise, if you measure your tire size and observe rpm and mph, you can calculate what gears are in your axles.
How To Calculate Actual Speed:
With the change to taller tires, your speedometer will read "slower" than the actual vehicle speed. To determine the percentage of speedometer error, the formula is a simple relationship between old and new tire diameters.
-Actual Speed = new tire diameter x indicated speed /Old tire diameter
Example: You have replaced your 28-inch OEM rubber "wimpys" with a new set of 35-inch all-terrain "mud-gobbler ultra x-tremes" and you want to know your actual speed when the speedo reads 60 mph--well read on
-35 inch (new tire) x 60 mph (what speedo reads) /28 (old tire)=75 mph (actual speed)
See...simple :smoke:
----------------------------------------------
Now...
Speedometer ratio adjustment calculation.
Ever wonder how far off your speedometer is with your new bigger tires? By using a simple ratio calculation, this info will only approximate your corrected speed and depends on the accuracy of tire size diameters (assumimg nothing but tire size has changed). If you know specific information about your vehicle (gear ratios, RPM, etc.) then use the Gear Ratio calculator, it's probably a little more accurate.
Formula used (slight variation of above...I love math!!)
(New Tire Diameter / Old Tire Diameter) x Speedometer MPH = Actual MPH
Now, another way of looking at this relationship would be to figure what the indicated speed would be if you were actually going 60 mph. In this case, the tire diameter relationship is flip-flopped to:
Indicated Speed = old tire diameter x actual speed /New tire diameter
Using the previous example, your speedometer reading at an actual 60 mph is:
-28 inch x 60 MPH /35 inch = 48 MPH
See, easy!!! OK class, on to GEARS!!!!
-------------------------------------------------
Gearing up:
Using the above tire change as an example, lets say that your vehicle is currently running a 3.40:1 final-drive gear set. Now that you have changed to a taller tire, you want to determine the actual, or effective, final ratio. This can be figured by dividing the old tire diameter by the new, and multiplying by the current gear ratio
1):-28 inch (old tire) x 3.40 (your actual stock gear ratio) /35 inch (new tire) = 2.72:1 (final effective drive ratio)
Whoa big fella
Dropping from a 3.40:1 to a 2.72:1 ratio will seriously reduce off-the-line responsiveness and severely affect slow-speed trail capabilities. So, Mr. Trail-Monster, if your new 35-inch all-terrain "mud-gobbler ultra x-tremes" rubber is just what you want, but you now need to restore your vehicle’s low-end, the following formula will allow you to determine what gear set (equivalent) ratio should be installed to compensate:
-Equivalent ratio = new tire diameter x original ratio /Old tire diameter
As in my example:
-35 inch (new tire) x 3.40 (your actual stock gear ratio) /28 inch (old tire) = 4.25:1 (what you need to restore your vehicle’s low-end responsiveness to previous 3.40)
By installing a gear set in the range of 4.25:1, you will not only restore your vehicle’s low-end grunt, you will likewise restore your speedometer’s accuracy. Cool!!
Ahhh....just a little more...
Figuring gear ratio:
Knowing what gears are in a given axle is a must when considering that axle for a swap. The actual ratio or reference code, will normally be found on either a tag attached to a bolt, or will be stamped into the axle housing. If it cannot be found, there is a simple method for manually (and mathematically
) determining the ratio for any axle installed on a vehicle. Raise both wheels of the axle, with the transmission in Neutral. (Make sure you support the vehicle with safety stands and block the front tires.) Make a reference mark on the driveshaft and on the differential housing. Next, without rotating them, make a mark on both tires and their respective fender wells. With a friend watching the driveshaft, carefully rotate both tires at the same time exactly one revolution. The number of turns the driveshaft makes will indicate the ratio. If the driveshaft rotates 4 ½ turns, for instance, the axle ratio is roughly 4.5:1.
Almost done...
METRIC TIRE TO DIAMETER (INCHES) CALCULATION
Most of the formulas dealing with gear ratios will want a tire diameter (measured in inches). This formula is a quick way to get the tire diameter of those metric tires that are common on just about everything stock. For example a LT265/75R16 would be around 31.6 inches tall and 10 inches wide. Enter any three of the numbers into this form to solve for the fourth. "LT" means Light Truck and "P" means Passenger tire. The bigger number (on the left) is the Section Width. The number to the right of the slash ("/") is the Aspect Ratio (percent of width). The "R" means Radial tire and the last number, far right, is the rim diameter in inches.
Formula used :
-(Section Width x Aspect Ratio x 2) /25.4 + Rim Diameter = Tire Diameter
Width in inches = section width / 25.4
Section Height in inches = Width in inches X Aspect Ratio (%)
Finally...
GEAR RATIO CALCULATION
If your tires are bigger than stock you either guess at the actual MPH or do something like count the seconds between mile markers on the highway while maintaining 60 on the speedometer. If you know your gear ratios and tire size you can get a fairly close number using this calculating tool. Fill in all entries except the one you want an answer to in green section only. If you'd like to find your overall crawl ratio, enter the Diff/Trans/TransfCase ratios.
Formulas used :
-(RPM x Tire Diameter) / (Diff Ratio x Trans Ratio x Transf Case Ratio x 336) = MPH)
and
(Trans Ratio x Transf Case Ratio x Axle Ratio) = Crawl Ratio
Well, that's it...hope this helps someone, especially some of the new folks...enjoy!
