Where the 336 comes from
Every gear chart on the internet gives you this formula:
and almost none of them say where 336 came from, which makes it look like a fudge factor. It is not. It falls straight out of the units:
- One mile is 63,360 inches.
- An hour is 60 minutes, so 1 mph is 63,360 ÷ 60 = 1,056 inches a minute.
- A tyre travels π × diameter every turn.
- So wheel rpm per mph is 1,056 ÷ π ÷ diameter, and 1,056 ÷ π = 336.1352.
That is the whole of it. This page uses the exact 1,056 ÷ π rather than the rounded 336, which runs 0.04% low. That difference is far too small to matter next to the error in your tyre diameter, and saying so is the point: the arithmetic is not what makes these predictions wrong.
The tyre is where the error lives
A worn tyre can be half an inch shorter than a new one of the same size, and the rpm moves in proportion. On a 31 inch tyre at 65 mph with 3.73 gears:
| Tyre diameter | Engine rpm at 65 mph |
|---|---|
| 31.0 in (new) | 2,629 |
| 30.5 in (worn) | 2,672 |
| 33.0 in (upsized) | 2,470 |
| 35.0 in | 2,328 |
Half an inch of wear is worth 43 rpm. Going from 31s to 35s drops 300 rpm at the same road speed, which is why a tyre upgrade quietly changes your gearing, your speedometer reading and how often the transmission hunts on a hill. It is the same reason people re-gear after fitting bigger tyres: they are putting back the ratio the tyres took away.
Marked size is not real size
The number on the sidewall is not the diameter. A 265/70R17 is 265 mm wide, with a sidewall 70% of that, on a 17 inch wheel:
which gives 17 + 2 × (265 × 0.70) ÷ 25.4 = 31.6 inches. Enter that, not the 17. It is the single most common way this calculation goes wrong.
Belt drives run on one rule
Switch the mode above and the same page does pulleys. A belt cannot be in two places at once, so it travels at a single speed and:
A 6 inch pulley at 1,750 rpm driving a 3 inch pulley gives 3,500 rpm. Driving a 12 inch pulley gives 875. A smaller driven pulley always turns faster, and that is the entire trick behind compressors, drill presses and every machine with a stepped cone on it.
Two things worth knowing when you use it:
- Torque moves the other way. Whatever you gain in speed you give up in twist. Double the rpm and you have roughly half the torque at the other end, minus losses.
- Belt speed has a ceiling. Ordinary V belts are comfortable to around 5,000 feet per minute. Above that you are into proper drive design rather than a swap of pulleys, and the calculator prints your belt speed so you can see where you are.
What this cannot account for
The engine calculation assumes no tyre slip and a solid connection from engine to wheels, which means a manual gearbox or an automatic with the torque converter locked. An unlocked converter slips on purpose and the engine will read higher than this.
It also assumes your speedometer is honest. If you have changed tyre size and not recalibrated, the speedometer is reading the old diameter and will disagree with every number here. In that case the rpm from this page is right and the dashboard is wrong, which is a strange feeling the first time.
If you are working the other way and want road speed from a known rpm, leave the speed blank and fill in the rest. For the trade between speed and twist that the pulley section mentions, the torque calculator does the lever arithmetic, and speed, distance and time handles the plain journey side.