Gear speed calculations look more intimidating than they are. The car does not care about opinions. It cares about engine RPM, gear ratio, diff ratio and tyre circumference.
The basic idea is simple. The engine spins at a certain RPM. The gearbox reduces that speed. The diff reduces it again. The tyre turns that wheel speed into distance travelled. Put those together and you can calculate road speed in any gear.
The imperial formula
The common imperial formula is:
mph = (RPM x tyre circumference in inches) / (gear ratio x final drive ratio x 1056)The 1056 is just the conversion factor that turns inches per minute into miles per hour. There are 63,360 inches in a mile and 60 minutes in an hour, and 63,360 divided by 60 is 1,056. The important bit is not memorising the number. The important bit is understanding the variables.
The metric formula
If you think in kilometres, this version skips the inches entirely:
km/h = (RPM x tyre circumference in metres x 60) / (gear ratio x final drive ratio x 1000)The 60 turns minutes into hours. The 1000 turns metres into kilometres. Same maths, fewer conversions.
A worked example
Take a simple example. A car has a 1.00 fourth gear, a 3.90 final drive, a tyre circumference of 78 inches and a 6,500 rpm redline.
mph = (6500 x 78) / (1.00 x 3.90 x 1056)
mph = 507000 / 4118.4
mph = 123.1So fourth gear theoretically reaches about 123 mph at 6,500 rpm. That does not mean the car has enough power to reach it. It means the gearing allows it.
Getting the tyre circumference
To work out tyre circumference, start with the tyre size. A 205/55R16 has a 205 mm section width. The sidewall is 55 percent of 205, so 112.75 mm. The wheel is 16 inches, or 406.4 mm. Overall diameter is the wheel plus two sidewalls:
406.4 + 112.75 + 112.75 = 631.9 mmCircumference is diameter x pi:
631.9 x 3.1416 = 1985 mmThat is about 78.1 inches, or 1.985 metres.
Running the whole gearbox
One gear is a sum. The whole box is a table. Here is an example five-speed with ratios of 3.14, 1.89, 1.33, 1.00 and 0.81, on that 205/55R16 tyre and a 3.90 diff, using the metric formula at 6,500 rpm:
| Gear | Ratio | Overall ratio | Speed at 6,500 rpm |
|---|---|---|---|
| 1st | 3.14 | 12.25 | 63 km/h |
| 2nd | 1.89 | 7.37 | 105 km/h |
| 3rd | 1.33 | 5.19 | 149 km/h |
| 4th | 1.00 | 3.90 | 199 km/h |
| 5th | 0.81 | 3.16 | 245 km/h |
The overall ratio column is just gear times diff. It is the single number that decides how each gear feels, which is why swapping the diff changes every row at once.
Turning it round: RPM at a given speed
Reverse the formula and you get the number that decides whether a road car is pleasant or tiring: cruising RPM.
RPM = (km/h x 1000 x gear ratio x final drive ratio) / (60 x circumference in metres)
At 110 km/h in fifth:
RPM = (110 x 1000 x 0.81 x 3.90) / (60 x 1.985)
RPM = 347,490 / 119.1
RPM = about 2,920About 2,900 rpm at 110 km/h, which is roughly 68 mph. Fine for most engines. Swap to a 4.30 diff and it goes past 3,200. Fit taller tyres and it drops again. Now you can see the trade before you pay for it.
What the numbers leave out
The calculation is theoretical. Real life adds a few small corrections, and it is worth knowing which way they push.
- Tyres squash under load. The rolling radius is a little smaller than the calculated one, so real speed at a given RPM is slightly lower than the sum says.
- Tyres wear. A worn tyre is a few millimetres shorter than a new one. Small effect, but it is there.
- Clutches and torque converters slip. An automatic with an unlocked converter will not match the numbers until the converter locks up.
- Power is a separate question. The gearing tells you the speed each gear allows. Drag and power decide whether you get there.
None of these makes the calculation wrong. They make it a comparison tool, which is exactly how to use it. Compare two setups with the same method and the difference between them is real.
4WD and the crawl ratio
Four-wheel-drive builds add one more multiplier: the transfer case. In low range, first gear, the low-range ratio and the diff multiply together into the crawl ratio. A 4.0 first gear, a 2.6 low range and a 4.10 diff give:
4.0 x 2.6 x 4.10 = 42.6:1A higher crawl ratio means slower, more controlled progress over rocks and steep descents. The same speed formula works for low range. Just include the transfer case ratio.
Questions this answers
Once you have this, you can calculate every gear at redline, or reverse the formula to find RPM at a given road speed. This is how you answer useful questions. What RPM will the engine sit at on the motorway? Will second gear cover the speed you need? Will a shorter diff make first useless? Will bigger tyres move the whole car out of its sweet spot?
BoxSelector does the repetitive part for you. Enter the gearbox ratios, tyre size, diff ratio and RPM, then compare the table. Change one variable at a time and the effect becomes obvious.
The calculation is theoretical, but it is still far better than guessing. Guessing is how people buy the wrong gearbox and then blame the engine.