Deriving the formula rather than memorising it
Every version of this calculation you will find online is the same chain of unit conversions with the constants pre-multiplied, which is why they all look different and none of them explain themselves. The chain is short enough to build from scratch.
Start at the engine. It turns at some rpm. Between the engine and the wheel there are two reductions in series: the transmission gear and the final drive. Multiply them and you have the overall drive ratio, the number of engine revolutions per single revolution of the wheel. A 0.70 top gear behind a 3.55 axle gives 0.70 × 3.55 = 2.485.
So the wheel turns at engine rpm divided by that ratio. At 3,000 rpm the wheel is doing 3,000 ÷ 2.485 = 1,207.2 rpm.
Each turn of the wheel moves the car forward by one tire circumference. A 25 inch tire has a circumference of π × 25 = 78.54 inches. So the car covers 1,207.2 × 78.54 = 94,816 inches per minute.
Now convert. There are 63,360 inches in a mile and 60 minutes in an hour, so inches per minute becomes miles per hour by multiplying by 60 and dividing by 63,360 — that is, dividing by 1,056. 94,816 ÷ 1,056 = 89.8 mph.
Written as one line:
mph = rpm × π × diameter_in × 60 ÷ (gear × final × 63,360)
Or equivalently, since revolutions per mile is 63,360 ÷ (π × diameter):
mph = rpm × 60 ÷ (gear × final × revs_per_mile)
Both give 89.8 mph for that combination. Running it backwards to find rpm at a target speed is the same equation rearranged, which is how the cruising-rpm figure above is produced.
The two ratios do different jobs
They multiply, so mathematically they are interchangeable — a 15 percent deeper axle and a 15 percent shorter gear produce identical road speed. Mechanically they are not interchangeable at all.
| Change | Affects | What you notice |
|---|---|---|
| Final drive ratio | Every gear, equally | All ratios shift together. Acceleration in every gear changes and so does cruising rpm. |
| One transmission ratio | That gear only | Changes the spacing between gears. Others are untouched. |
| Tire diameter | Every gear, equally | Acts exactly like a final drive change, plus it moves the speedometer. |
The tire row is the one people forget. Fitting a tire two inches taller on a truck lengthens the effective gearing by roughly eight percent in every gear at once, which is the same as going from a 4.10 axle to a 3.79. That is why a lift with oversize tires so often ends up paired with a re-gear: the tire undid the axle ratio the factory chose.
Where cruising rpm actually matters
The mph-per-1,000-rpm figure is the useful summary of a drivetrain, because the relationship is perfectly linear. If a combination gives 30 mph per 1,000 rpm in top, then 70 mph is 2,333 rpm and 80 is 2,667, no further calculation needed. Comparing two axle options is a matter of comparing two of these numbers.
Deeper gearing multiplies torque at the wheel, so it launches harder and pulls a load better, at the cost of higher rpm — and therefore more fuel and more noise — at any given cruise. Taller gearing does the reverse and can push the engine below the speed where it makes usable torque, which is why an over-tall combination feels lazy and downshifts constantly on hills. There is no formula for the right answer; it depends on the engine's torque curve, the vehicle's weight and what you actually do with it.
Why the real number differs
Everything above assumes a rigid tire rolling without slipping and a mechanical connection all the way to the engine. Three things break that in practice. A tire under load has a smaller loaded rolling radius than half its free diameter, so it covers slightly less ground per turn than the geometry says — and then, at speed, centrifugal force grows the tire back, which pushes the other way. An automatic transmission with an unlocked torque converter lets the engine turn faster than the input shaft, sometimes by several hundred rpm, and no gear-ratio calculation can see that; once the converter locks up, the arithmetic here becomes accurate again. And a continuously variable transmission has no fixed ratio to enter, so this page has nothing useful to say about one. Use these numbers for comparing options and sizing a gear change, then verify the result against a GPS speed rather than the speedometer, which has its own error.
Questions people ask
How do I calculate mph from rpm and gear ratio?
Multiply the transmission gear ratio by the final drive ratio to get the overall drive ratio, which is how many times the engine turns for one turn of the wheel. Divide engine rpm by that to get wheel rpm. Multiply wheel rpm by the tire circumference in inches — pi times the overall diameter — to get inches per minute. Then multiply by 60 and divide by 63,360 to convert to miles per hour, which is the same as dividing by 1,056. As one expression: mph equals rpm times pi times tire diameter times 60, divided by gear times final times 63,360. Worked example: 3,000 rpm through a 0.70 overdrive and a 3.55 axle on a 25 inch tire gives 3,000 divided by 2.485 equals 1,207 wheel rpm, times 78.54 inches equals 94,816 inches a minute, divided by 1,056 equals 89.8 mph.
Does a numerically higher axle ratio mean faster or slower?
Numerically higher means shorter gearing, which means more acceleration and lower top-gear speed for a given rpm. A 4.10 axle turns the driveshaft 4.10 times for each turn of the wheel, so at any road speed the engine is spinning faster than it would with a 3.55. The confusing part is the vocabulary: people say a 4.10 is a "higher" ratio and also that it makes the car "lower geared", and both are correct because the first refers to the number and the second to the gearing. Numerically higher multiplies torque at the wheel, so it launches harder and tows better, and it costs fuel and noise at cruise. Numerically lower does the reverse and can leave the engine below its usable torque range, which produces constant downshifting on hills.
What tire diameter should I use if I only know the tire size?
Set the tire input to size mode and type it in — this page computes the diameter from the size for you, using the standard definition of the metric format. If you would rather do it by hand: multiply section width in millimetres by the aspect ratio as a decimal to get sidewall height in millimetres, divide by 25.4 for inches, double it because the tire has a sidewall top and bottom, and add the rim diameter. Flotation sizes like 33x12.50R15 already state the nominal diameter as the first number, so no conversion is needed. Bear in mind that computed diameters are the definitional figures rather than measurements, and the manufacturer's published specification for the specific tire commonly sits a percent or two either side of them.
Why does my speedometer disagree with this calculation?
Several reasons stack up, and they do not all pull the same way. Speedometers are commonly calibrated to read slightly high from new, which is a deliberate choice by manufacturers rather than an error. If your tires are not the original size, the vehicle is still applying the factory distance-per-revolution and will be wrong by the ratio of the diameters. Worn tires are smaller than new ones by up to half an inch of diameter across their life. An automatic with an unlocked torque converter puts engine rpm above what the drivetrain ratio implies. And this calculation uses free diameter rather than loaded rolling radius. Compare against a GPS reading rather than the speedometer if you want to know which of these is biting; GPS ground speed is not perfect either, but it is not affected by any of the above.