Previously I compiled a detailed list of 3000GT/Stealth gear ratios for reference, which prompted more than a few emails about how they can be used. Gearing looks complicated, but it is actually very simple. Any formula for calculating vehicle speed, engine speed, or gear ratio is a matter of simple math and unit conversion.
What information is needed? A gearbox has many individual gear ratios, but these alone are not enough to determine gearing. The individual gears act through the final drive gearing to give an overall gear ratio. What makes this seem so complicated is that power is traveling through not two, but four gears before they even turn the wheels! Calculating your speed at a given engine RPM or engine RPM at a given speed is actually quite simple if you know what numbers you need and how to use them.
Above is a simple formula for finding vehicle speed with a known engine speed, tire size, and gear ratio. Let’s look at where this formula comes from in more detail…
Individual Gear Ratios - A gearset is a pair of gears that mesh together at a ratio determined by their geometry — that is the diameter and number of teeth they have. So first gear on your car might have a gear with 30 teeth driving a gear with 10 teeth. The resulting 30:10 ratio can be simplified to 3:1. So this first gear has a ratio of 3:1 — for every 3 revolutions of the input gear, there is 1 revolution of the output gear. The engine turns first gear directly (after the clutch)
Usually gear ratios are irrational fractions - like 43:14, so if we divide 43/14 = 3.071428571428… it’s a bit cumbersome to work with. Typically, the number will be rounded to three decimal places, like 3.071 for the previous example. Many sources will say 3.071 : 1, but you can leave the “: 1″ out. If you asked for 12:1 donuts, people would look at you funny.
Final Drive Gear Ratios - After going through your individual gearset - first gear in our example above - torque travels through a final drive gearset. In a FWD or AWD transaxle, where the differential is in the same casing as the gearshafts, the connection is direct and immediate. In most RWD cars (except those with transaxles, like Corvettes) there is a driveshaft between the gearbox with its individual gear ratios, and the final drive gearing at the rear axle. Luckily, this does not change the calculation at all! A final drive gear might have a ratio of 40:10 or 4:1. We will express this as 4.000 so that it fits neatly with other gear ratios.
The Overall Ratio - Here we multiply the 3:1 (3.000) first gear ratio times the 4:1 final drive ratio (4:000) to get 12:1 (but remember to call it 12.000, so the guy at Dunkin Donuts doesn’t think you’re crazy). This means that for every twelve revolutions the engine makes, the drive wheel will rotate once.
Tire Size - The ratio that is too often forgotten is tire size. Most people think of tires as a certain number of inches tall — “38 inch tires”, for the truck guys out there — but there is a simpler and more accurate way to look at it. The most accurate and easiest figure to use is the manufacturer-specified tire revs per mile. The Tire Rack actually gives detailed specifications for any tire they sell (click “specs” when viewing a particular tire), and most manufacturers include revs/mile specs for every size tire in a particular model line.
Putting It All Together - To get wheel speed we need to look at engine speed as it travels through the drivetrain. The engine goes through the individual gear ratio and the final drive ratio before it turns the wheels. In our original example 3 engine revolutions = 1 final drive revolution. 4 final drive revolutions = 1 wheel revolution. 3 * 4 = 12. If we are looking to find out the vehicle speed at, say, 6000 rpm, we divide engine RPM by the gear ratio (12). So if 12 engine revs = 1 wheel rev, 6000 engine revs = 500 wheel revs (6000/12). These are wheel revolutions per MINUTE however, and we are looking to find out miles per HOUR, so we multiply by 60 (minutes per hour), which gives us 30,000 wheel revolutions per hour. Now the only thing missing is tire revolutions per mile. A number for average tires might be 800 revs/mile. We are dividing 30,000 revolutions per hour by 800 revolutions per mile, the revolutions cancel giving us miles per hour. How many? 30,000/800 = 37.5mph — simple as that.
 If you want to find engine RPM for a given road speed, just rearrange the equation to solve for RPM:
In a practical application with a list of ratios, spreadsheets are your friends. If you haven’t figured out how to use formulas in Microsoft Excel, now is a great time to learn. Just type “=” and an equation like 3*4 to get started. The magic happens when instead of 3 and 4, you click another cell in the spreadsheet, which then uses the contents of that cell as the input to the equation. Try it!
on December 29, 2008 at 7:52 pm Travis Gillespie wrote:
DUDE.
“there is a driveshaft between the gearbox with its individual gear ratios, and the final drive gearing at the rear axle. Luckily, this does not change the calculation at all!”
Are you mentally challenged? If you are I apologize for my next couple of comments. Can you logically explain to me how a FINAL RATIO has no effect on the output of the engine to the ground? If it has no effect on the overall of the car then why is it there? or why is it in the major calculations for MPH? or KPH if you are from the other side of the puddle. maybe a quick look at http://travisgillespie.com/?q=GearRatioFormula will allow you to become enlightened to just how important a final ratio is.
“Usually gear ratios are irrational fractions - like 43:14, so if we divide 43/14 = 3.071428571428… it’s a bit cumbersome to work with. Typically, the number will be rounded to three decimal places, like 3.071 for the previous example” A website is a place for practical information not for a convenient way for you to twist an old method. there is a reason that the gear is 3.0714285714285714285714285714286. For example; your gear is 3.0714285714285714285714285714286 and your final is 4.11 that then means that for every 12.623571428571428571428571428571 rotations the tire turns 1 time. even truncated the engine still moves 12.623 times before the tire moves one. and if you are going to tell me that .623 is unimportant to the torque and speed ratings at the wheels then your freaking nuts. if i give you $12.62 are you gonna chuck out the $0.62? if so were do you live I’m coming to collect your change. lmao. If someone read your site and was programming a speedometer from your calculations for a go kart, and they uses your fuck it let it ride attitude their speedometer would be 0.00134465575559670849729685241 MPH off. thus once the gokart elapsed 1000 miles its odometer (a function of the speedometer) would be 1.34465575559670849729685241 miles off. before its first oil change it would be a mile and a third off. over its life it would be 134.465575559670849729685241 miles off. do you see the point. numbers are there for a reason.
case example;
475.3013070785944661347818706502 wheel rotations per 6000 rpm
based on an 8″ diameter wheel would be 25.13274122871834590768″ per rotation so their actual Wheel distance per minute would be 11945.624756477910124173145476151″ or 995.46872970649251034776212301262′ per minute or
0.18853574426259327847495494754027 MPM (miles per minute)
thus giving you 11.312144655755596708497296852416 MPH @ 6000 RPM
VS Your Calculation which yields;
475.30 wheel rotations per 6000 rpm
based on an 8″ diameter wheel would be 25.13″ per rotation so their actual Wheel distance per minute would be 11944.289″ or 995.35′ per minute or
0.18851 MPM (miles per minute)
thus giving you 11.3108 MPH @ 6000 RPM
You need to be a bit more specific. If you are going to use and example of something you should not absolute a situation you need to make sure the situation is absolute.”(except those with transaxles, like Corvettes)” You need to put an example of just exactly what American GM Corvette uses a transaxle, because as many will argue I’ve only seen them with C5 and C6 TRANSMISSIONS. “Basically with the base C6 Corvette the buyer has the option of a 6-speed manual or 6-speed paddle-shift automatic transmission.” From :http://www.corvette.zorly.com/2008/09/transmissions-available-for-new-model.html, at the same time the older Vettes did have a trans axle. and if you look closely the transmission and rear differential are in different housings. thus still making it a transmission
on December 29, 2008 at 11:07 pm Chris wrote:
For someone who likes to go on tirades, you certainly don’t read material very carefully. You took my final drive comment out of context. The full quote reads:
“In a FWD or AWD transaxle, where the differential is in the same casing as the gearshafts, the connection is direct and immediate. In most RWD cars (except those with transaxles, like Corvettes) there is a driveshaft between the gearbox with its individual gear ratios, and the final drive gearing at the rear axle. Luckily, this does not change the calculation at all!”
In order, this block asserts:
Do you see any incorrect statements there? I sure don’t.
The next order of business is significant digits. If you had read the article clearly, you would see that I’m not advocating throwing out anything after the decimal, as you imply. I give an example of ratios with nice round fictitious gear ratio numbers to simplify the concept. Of course rounding is a good idea — 2-3 decimal places is all that is necessary to get a reasonably accurate value in this case.
Apparently you think 30 decimal digits is useful. Would you consider 1/100th of a mph to be significant? I hope not, because you don’t have precise enough measurements to get that information anyhow, no matter how precise your gear ratios are.
“..based on an 8? diameter wheel…”
How do you know the wheel is 8″ in diameter? Did you measure it? With what? Even assuming you use dial calipers, you’re not likely to get a measurement more precise than the hundred thousandth. Is the tire 8″, 8.001″ or 7.999″? Rubber is flexible and tires are imprecise, so good luck getting it even within .001 — I think +/- .01 is more precision than you can hope for.
How about when the tire is spinning at 1000rpm”? How big is it now?
You’re advocating precision you can’t even back up. Even if you knew the exact dimensions of the tire when it was new, how do you know what dimensions it will have when it’s underinflated, or overinflated, or slightly worn, or loaded by passengers, or acceleration, or cornering, or spinning quickly….
I could go on. Do you know EXACTLY how fast the engine is turning?
You berate me for rounding to three decimals, which in your own example (in which you round to TWO, not even three) only yields a difference of about .001 mph. So I’ll ask again, who really cares about .001 mph?
The Corvette transmission/transaxle is really nit-picking. I’ve seen the C5 unit referred to both ways, and when it’s assembled it certainly looks like one unit.