How do you work out a gear ratio?

Divide the number of teeth on the driven gear by the number on the driving gear. 41 driven by 12 is 3.417, which means the output shaft turns once for every 3.417 turns of the input. Multiplying that by the axle ratio gives the overall ratio, and that is the number road speed comes from — 3.417 × 3.55 = 12.129 for the same car.

What is the difference between gear ratio and axle ratio?

The gear ratio is the pair of gears inside the gearbox; the axle ratio, also called the final drive, is the pair inside the differential. They multiply: an overall ratio of 12.129 can come from a 3.417 gearbox ratio and a 3.55 axle, or equally from a 2.34 gearbox ratio and a 5.18 axle. Only the product decides how fast the car goes at a given engine speed, which is why it is worth looking at both numbers rather than the gearbox one alone.

Why does a high gear ratio mean a slow car?

Because a ratio above 1 is a reduction: the driven gear is bigger than the driving gear, so the output turns slower than the input and the torque is multiplied. First gear at 12.129 overall puts a 3,000 rpm engine at 19.1 mph. The ratio in a given gear and the road speed move in opposite directions, so a numerically large ratio always belongs to the slow, strong gear and a small one to the fast, weak gear.

Which tire diameter should I enter?

The overall diameter of the whole wheel — the rim plus the sidewall twice — not the rim diameter printed on the tire. A 205/55R16 has a 16 inch rim but a 24.9 inch diameter. Measure it on the car if you can rather than trusting the nominal size, and remember that a tire flattened under load rolls on a slightly smaller radius than its measured diameter, so the true speed is a little below this page's figure.

Does a lower ratio make the car faster?

It makes it faster to accelerate and slower at the top end, and the two effects come from the same change. A shorter ratio, numerically higher, multiplies torque more, so the car pulls harder out of a corner but runs out of rpm sooner and reaches a lower top speed. A taller ratio does the reverse. There is no ratio that is better in both directions, which is why a gearbox has several ratios rather than one.

Gear Ratio Calculator

Result

3.417

Gear ratio

Overall ratio: 12.129
Speed (mph): 19.1 mph
Speed in km/h: 30.8 km/h
Wheel speed (RPM): 247 rpm

Give this gear ratio calculator the two tooth counts, the axle ratio and the tire diameter, and it returns the gear ratio, the overall ratio and the road speed the car is actually doing at that engine speed. The gear ratio on its own is one division — driven teeth divided by drive teeth — and it is rarely the whole answer, because the number that decides road speed is that ratio multiplied by the final drive. 41 teeth driven by 12 is 3.417; multiply by a 3.55 axle ratio and the overall ratio is 12.129, which means the engine turns 12 times for every single turn of the wheel. That is why a first gear that feels enormous on paper puts the car at 19.1 mph at 3,000 rpm rather than the 40 or 50 a driver might guess. A ratio above 1 reduces speed and multiplies torque; a ratio below 1, an overdrive, does the opposite and lets the engine turn slowly at highway speed. The tire diameter is an input rather than a footnote because the same overall ratio covers more ground per revolution on a taller wheel.

Axle ratio chart

Axle ratio	Engine RPM at 60 mph	MPH per 1,000 RPM
2.73	2118	28.3
3.08	2389	25.1
3.23	2506	23.9
3.42	2653	22.6
3.55	2754	21.8
3.73	2893	20.7
4.1	3180	18.9
4.56	3537	17
4.88	3785	15.9

Every row is worked out for the same car: the gearbox in its 1:1 gear, so no gearbox reduction is included, and a 26 inch tire. Read the middle column to see what an axle swap does to cruising rpm — going from 3.55 to 4.10 raises the engine speed at 60 mph by about 15%. Read the last column to see how much speed 1,000 rpm buys, which is the quickest way to compare two candidates.

Formula

gear ratio = driven teeth ÷ drive teeth; overall ratio = gear ratio × axle ratio

driveTeeth: Teeth on the driving gear — the input side
drivenTeeth: Teeth on the driven gear — the output side
finalDrive: Axle or final drive ratio, for example 3.55
tireDiameter: Overall tire diameter, in inches
engineRpm: Engine speed, in rpm

Use it when you have two gears and want the ratio, or when you have a ratio and want to know what it does to road speed. The formula also runs backwards well enough to answer the question that follows: pick the speed you want at a given rpm and solve for the axle ratio that gets you there. If all you need is the ratio from two tooth counts, the first output is the whole answer and the rest of the page is about what that number means on the road.

Worked examples

A first gear: 12 teeth driving 41, with a 3.55 axle
1. Gear ratio: 41 ÷ 12 = 3.417, a reduction, because the driven gear has more teeth
2. Overall ratio: 3.417 × 3.55 = 12.129
3. Wheel speed: 3,000 ÷ 12.129 = 247 rpm
4. Distance per wheel revolution: π × 26 in = 81.68 in
5. Road speed: 247 × 81.68 = 20,197 in/min = 19.1 mph
6. In metric: 19.1 × 1.609344 = 30.8 km/h
19.1 mph at 3,000 rpm. This is a starting gear, not a cruising one, and the arithmetic is worth reading twice: an overall ratio of 12 means the engine must turn twelve times to move the car the distance of one wheel revolution. A 3.417 on the spec sheet sounds like a big number, and a big ratio in a given gear always means a slow car rather than a fast one.
A 1:1 gear with a 1:1 axle
1. Gear ratio: 20 ÷ 20 = 1.000, so the output turns exactly as fast as the input
2. Overall ratio: 1.000 × 1 = 1.000
3. Wheel speed: 3,000 ÷ 1 = 3,000 rpm — the wheel turns as fast as the engine
4. Road speed: 3,000 × π × 26 in = 245,044 in/min = 232 mph
No reduction anywhere in the drivetrain, so the only thing setting road speed is the tire. 232 mph is not a real car — it is the engine's rev limit multiplied by the circumference of the wheel — and that is the point: with both ratios at 1, nothing is left in the calculation but the rolling distance of one tire revolution.
An overdrive: 34 teeth driving 29, with a 3.08 axle
1. Gear ratio: 29 ÷ 34 = 0.853 — below 1, so the output turns faster than the input
2. Overall ratio: 0.853 × 3.08 = 2.627
3. Wheel speed: 2,200 ÷ 2.627 = 837 rpm
4. Road speed: 837 × π × 30.5 in = 80,237 in/min = 76 mph
5. In metric: 76.0 × 1.609344 = 122.3 km/h
The same car, in a different gear, at a lower engine speed and a much higher road speed. That is what the ratio below 1 buys: the driven gear is smaller than the driving gear, so the output spins faster and the engine can loaf at 2,200 rpm while the car sits at 76 mph. The taller 30.5 inch tire takes some of it back, which is why the two inputs have to be read together.

Limitations

The speed computed here assumes the tire rolls exactly its geometric diameter, and it does not. A loaded tire is flattened against the road, so its rolling radius is 1–3% smaller than half the nominal diameter, and the real road speed is lower than the figure on this page by about that much — the faster you go, the more it matters. The diameter also has to be the true one: a 26 inch tire measured on the car is usually 25.5, and two tires of the same nominal size from different makers differ. Torque converter slip on an automatic adds a few percent more at low speed, and no gear ratio calculation can see it. Nothing here models acceleration, grade, or whether the engine can actually pull that ratio at that rpm — a ratio that is arithmetically fine can be undrivable on a hill with a small engine. Road speed quoted at a given rpm assumes the clutch is fully engaged and the car is not wheelspinning.

Frequently asked questions

How do you work out a gear ratio?: Divide the number of teeth on the driven gear by the number on the driving gear. 41 driven by 12 is 3.417, which means the output shaft turns once for every 3.417 turns of the input. Multiplying that by the axle ratio gives the overall ratio, and that is the number road speed comes from — 3.417 × 3.55 = 12.129 for the same car.
What is the difference between gear ratio and axle ratio?: The gear ratio is the pair of gears inside the gearbox; the axle ratio, also called the final drive, is the pair inside the differential. They multiply: an overall ratio of 12.129 can come from a 3.417 gearbox ratio and a 3.55 axle, or equally from a 2.34 gearbox ratio and a 5.18 axle. Only the product decides how fast the car goes at a given engine speed, which is why it is worth looking at both numbers rather than the gearbox one alone.
Why does a high gear ratio mean a slow car?: Because a ratio above 1 is a reduction: the driven gear is bigger than the driving gear, so the output turns slower than the input and the torque is multiplied. First gear at 12.129 overall puts a 3,000 rpm engine at 19.1 mph. The ratio in a given gear and the road speed move in opposite directions, so a numerically large ratio always belongs to the slow, strong gear and a small one to the fast, weak gear.
Which tire diameter should I enter?: The overall diameter of the whole wheel — the rim plus the sidewall twice — not the rim diameter printed on the tire. A 205/55R16 has a 16 inch rim but a 24.9 inch diameter. Measure it on the car if you can rather than trusting the nominal size, and remember that a tire flattened under load rolls on a slightly smaller radius than its measured diameter, so the true speed is a little below this page's figure.
Does a lower ratio make the car faster?: It makes it faster to accelerate and slower at the top end, and the two effects come from the same change. A shorter ratio, numerically higher, multiplies torque more, so the car pulls harder out of a corner but runs out of rpm sooner and reaches a lower top speed. A taller ratio does the reverse. There is no ratio that is better in both directions, which is why a gearbox has several ratios rather than one.

References

NIST Guide to the SI, Special Publication 811 — US National Institute of Standards and Technology
The International System of Units (SI Brochure) — Bureau International des Poids et Mesures

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