How to Calculate Engine RPM vs. Gear Ratio - Roadkill Extra

It’s time for more math class with David Freiburger on this episode of Roadkill Extra. You’ll learn how to calculate the change in engine rpm at any given speed after you’ve changed rear-axle ratio, tire diameter, or transmission ratio.

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[Eratiik]

Love these kinds of videos where you teach us a bit every now and again. Thanks David, I enjoyed it.

[grobetog]

The conversion factor for metric units is 5305.

RPM = (km/h x gearbox ratio x rear axle ratio x 5305) / ((25.4 x rim size) + (2 x tire width x tire profile))

So the RPM for a '97 Camaro Z28 in 5th gear at 250 km/h with stock wheels would be:
(250 x 0.74 x 3.42 x 5305) / ((25.4 x 16) + (2 x 245 x 0.50)) = 5153 RPMs

[MrSlowestD]

Thanks for the insight.
So unless I'm mistaken in the original form this equation assumes the gear selected (in the transmission) is a 1:1 (roughly 4th gear on many cars) creating a gear ratio of 1.0. So if I wanted to account for the gear, to say take a small 4 cyl car at the top of 1st which is probably rocking a 3.25 1st gear and a 4.25 rear (like a civic) and let's just use a 185/60/R14 diameter it'd be something along the lines of:
(30mph*4.25*3.25*336)/22.7 = 6, 133 RPM

That sounds about right. Think this is a good equation to hold onto for sure!

[joedirt]

I wish this how I learned math in school

[pedrobergamaschi]

that calculation is for cars with a 1:1 fourth gear, or whatever the top gear is. In a 5-speed, just like in the overdrive, the fifth gear ratio has to be multiplied too.

[ziptiesnbiasplies]

DEBOSS AND ROADKILL need to do an episode together! Canada and the USA come together! Fuckin eh!

[unicornsteaks]

Solving this way gives you what gear ratio you want in order to be crossing the finish line with your engine in its max HP range. But most people don't drive a drag car. So then you need to decide what RPM you can live with at a particular speed, fill out all the other variables and solve for rear end gear ratio. For most people they would solve for whatever gear gives them the max allowable RPM at, say, 55 MPH, or maybe 65 MPH for freeway driving. But an overdrive allows for lower gearing on the street. This calculator is available lots of places on the Interweb.

[MaliciousSRT]

How to find out what gears your car has (if its limited slip)? Rotate drive shaft one turn and see how much the tire goes around. 4 total turns and bit = 4.10's, 3 and a half 3.55's etc.

[drkiishchris]

There's also awesome apps for people with manual transmissions that want to rev match perfectly for every gear. Down shifting to say 2nd or 3rd may wear the clutch a bit if you don't know exactly where the revs should be. The apps can get you into 2nd gear with no slipping the clutch perfectly for a corner. Given once you know a car you don't need to know what rpm to be at, but on a brand new car you may wanna figure those ratios out so the learning curve is a lot faster.

[mindthependulum]

I've been mostly bored by classic mustangs, but cougars are awesome. My mom had a 68 carmel colored one when I was a kid. I used to scalp myself getting into it since I was tall from a young age, but it was still a super cool car.

[rogerkimball]

Roadkill should do episodes with a Reliant Robin & Trabant. A little hard to come by here in the states, but overseas they are cheap and many are made before 1975 so California regulations would be a non issue. I imagine container shipping can't be too bad especially if they put multiples in one container. I would die laughing see two tall americans crammed inside those cars. Put a turbo Honda motor and OMG! The number of views would be insane.

[Iykykykb]

I'm new to all this, but where does he get "336" from?

[totrodder]

Dave actually made learning math fun, thanks Dave

[MrAlexwoolf]

If USA changed to SI units you could eliminate strange conversion factors like 336. Also why not rearrange the formula, you make gear ratio the answer, you know speed and the max revs you want to hit, it will then pop out ratio, this prevents iterations and hunting for the answer.

[Nissanzxshowcar]

BEST DEFINITION OF RPM AND MPH EQUATION!!!

[pescaderoray]

Thanks Friburger I am starting a build I have a 2002 ford E350 boxvan with a POS 5.4 triton motor ( when is ford going to learn how to build a motor ??? I will be putting a whole new drive train in it It will be a cummins 4bt with a ATS built 47 RH and a atlas transfer case it will be a frame off build and my question would have been at 65 MPH what would be the RPM so 65x4.10x .69 x336 /33.5 = 1844 I will be running BFG 35 12.50 16 which is right in the power band for the cummins thanks for the info and keep the videos coming more info it has already been converted to 4wd by Salem Kroger but I will put in unjointed off road parts it has a Dana 60 high pinion front axel and a Dana 70 HD rear end with 4.10 gears I will also be installing ARB lockers front and rear this will be my retirement expidition van goal is to drive to the tip on South America turn around and drive to the North Pole to see Santa

[CalaverasSpcl]

Good to know. My daily driver Jeep needs a regear, and with this I can play around with ratios.

[MrBigBucks]

I'm sure I'm not the first here to say but just in case, you fudged a bit there, Dave. You said the higher gear ratio (lower gearing) would lower the RPMs and conversely. Otherwise, interesting lesson and thanks!

[MidnightMechanic]

Now tell them how the number of gear teeth is in direct correlation to gear ratio; ie take the number of ring gear teeth and divide it by the number of pinion gear teeth, that'll give you your gear ratio. 41 ring gear teeth divided by 11 pinion gear teeth is 3.73, however, add just four more teeth to the pinion gear and you have 2.73. That is a significant difference in RPMs between a street/strip gear ratio and a sole highway cruiser, and the difference between a 2 and 3 series carrier!

[Darkeiser.]

Let's say I want to hit 200 miles per hour and I'm using an LS 5.3. How much power does it need? What transmission do I need? And what rear end do you suggest? With a car weighing 3000 lb