Math Question

jpat30

Adventurer
Ok Guys and Gals I have a math question of sorts. I recently changed the tires on my 2003 WJ; went from a LT 245 75 16(31) to a LT 285 70 17(33) and as expected the speedo is off. According to my GPS, the speedo now reads 5mph slow. This of course means that my odometer is off as well. Question; how to calculate how much my odometer is off? ie if it says that I have traveled 300 miles, what have a I actually? I was a CJ Major in college :sombrero: so I appreciate any help that I can get. I will soon correct this problem by installing a Speedo DRD, but until then would really like to be able to keep up on my mileage. Thanks again.
Jeremy
 

Ducky's Dad

Explorer
I was a CJ Major in college
What's a CJ major? I have a guess, but not for polite company.

Go to the manufacturers' websites for your old and new tires, look up your specific sizes, and get the revolutions per mile for each size, usually stated at 60mph road speed. Once you have those numbers, it's easy to do the calcs to see how much your speedo and odo are off. In your case, divide the larger number by the smaller number, and you'll get an answer like 1.056. That means that, in this example, you are traveling 5.6% faster/farther than your speedo/odo are calibrated for. Using revs per mile for the two tires allows for differences between nominal and actual tire sizes, inflation pressures, and centrifugal expansion at speed. It does not allow for worn old tires vs larger new tires. Or you could just skip all this and use the 6% rule of thumb for a 2" difference in tire diameter, close enough for government work. Remember that your vehicle came from the factory with a speedo that reads high, because the manufacturer can be fined for speedos that read low. It's also a liability management tool for them to read a tad higher than actual.
 

jpat30

Adventurer
easy there junior; CJ Major= Criminal Justice. Thank you for your time in answering the question. This is the reason I come here for quick rock solid answers. Thanks again and have a great weekend
 

Airmapper

Inactive Member
If you have a GPS you can use it to record actual distance traveled and compare to the odometer or trip meter. Or compare GPS speed to vehicle speedometer.

What data you collect will determine how to make the calculation. If you use the trip meter, take the difference between GPS and odometer, and divide by actual miles.

For example, my personal numbers. I run stock tires but there is still a small variation.

GPS reading: 30 miles.
Odometer reading: 30.6 miles

30.6 - 30 = .6

.6 divided by 30 = .02

For every mile I travel my odometer reads .02 miles more than reality. So it is 2% fast.
 

Eaglefreek

Eagleless
Your speedometer will be off by a percentage not a set mph. Drive at 50 mph according to the GPS and then check what the speedometer is reading and subtract that from the GPS reading. Then multiply that by 2 and that will be the percentage your speedometer is off. So lets say it is reading 4 mph slow, that is 8%. So multiply your trip odometer reading by 1.08 to get your actual miles traveled. Odometer reading x 1.08= actual miles driven. If it was reading 8% faster, just subtract that from 100 and that will be your multiplier. Odometer reading x .92= actual miles driven.
 
Last edited:

rayra

Expedition Leader
to answer the 'math' part, divide the circumference of your new tires into that of your old factory tires to find out the percentage. Or the other way to find out what multiplier you need to apply to your speedo reading to get close to actual speed.

"went from a LT 245 75 16(31) to a LT 285 70 17(33)"

Old tire
245mm wide, tire height from rim to tread is 75% of the width. so the height is 183.75. x2 for both sides of the rim is 367.5mm. Divided by 25.4mm per inch is 15.7". Plus the rim dia is 17, so 32.7" diameter. Times Pi for circumference of old tire = 95.8"

New tire
285mm wide, tire height from rim to tread is 70% of the width. so the height is 199.5. x2 for both sides of the rim is 399mm. Divided by 25.4mm per inch is 15.7". Plus the rim dia is 17, so 32.7" diameter. Times Pi for circumference of old tire = 102.7"

So the new tire / wheel combo is 7.2% bigger around than the old one. So your speedo is off by that. roughly. 55mph indicated is 59mph
 

Ducky's Dad

Explorer
So the new tire / wheel combo is 7.2% bigger around than the old one. So your speedo is off by that. roughly. 55mph indicated is 59mph
Maybe yes, maybe no. Tire manufacturers are very inconsistent when it comes to actual dimensions vs nominal dimensions. The only thing that matters for OP's purposes is the OD or circumference of the tire, and that OD can vary by more than 1/2" from one manufacturer to another for the same nominal size tire. Can also vary from tire model to tire model within a given brand of tires. Does not sound like much, but a 1/2" difference in actual diameter vs nominal diameter on a 32" tire is a 1.6% error.
 

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