Gear Ratio Calculator

How gear ratios work

Every turn of the crankshaft goes through two reductions before it reaches the pavement: the transmission gear you are in, and the rear end gear, the ring and pinion inside the differential. Multiply the two and you get the overall ratio, the number of times the engine turns for one turn of the tires. A 3.73 rear gear behind a 1:1 fourth gear means 3.73 engine revolutions per tire revolution; in a 0.73 overdrive the same axle gives 2.72.

The tire closes the loop. One turn of the tire moves the car roughly its circumference, π times the diameter, so a taller tire covers more road per turn and pulls engine speed down exactly like a numerically lower gear would. That is why a ratio means little on its own: always read it together with the diameter of the tire you actually run, which you can get from a size code with the tire size calculator.

Used as a gear ratio calculator for RPM, the first tab answers “how fast is the engine turning at this speed?” in every gear at once. Read the other way, as a gear ratio calculator for MPH, the chart shows how fast each gear will take the car before it hits the redline.

What to enter and where to find it

• Rear end gear ratio. It is usually on a tag under a cover bolt or in the axle code on the build paperwork. With the cover off, the ring gear is often stamped with both tooth counts, such as 41-11; enter those on the Ring & pinion tab.
• Transmission gear ratios. Take them from the transmission’s specification sheet or service information, first gear to top gear. Gearboxes that share a case can have very different ratios, so check the exact version.
• Tire diameter. Use the overall diameter from the tire maker’s data, or convert the size code. A loaded tire rolls slightly smaller than its nominal diameter, so real rpm runs a touch higher than calculated; the maker’s revolutions-per-mile figure is the most accurate number to work from. To use it here, enter 20,168 ÷ revolutions per mile as the tire diameter, in inches.
• Road speed and redline. The speed sets the highlighted row and the marker on the chart; the redline sets the top of the chart and greys out the speeds a gear can’t reach.

Final drive ratio and transmission ratios

On a rear-wheel-drive car, “final drive ratio” normally means the rear end gear, and that is how this calculator uses it. On front-wheel-drive and most all-wheel-drive cars the final drive sits inside the transaxle. A few transaxles even use two final drives for different gears; for those, enter one final drive as the rear end gear and, for each gear that runs through the other one, enter gear ratio × other final drive ÷ the final drive you entered.

The transmission ratios are fixed by the gearbox, so the rear gear is what most owners change: it moves every gear by the same proportion at once. A rear gear that is 10% shorter makes all of the gears 10% shorter, raises rpm at every speed by 10% and cuts the speed each gear reaches at the redline by about 9% (1 ÷ 1.1). That is the trade a gearing calculator lets you see before buying parts.

The gear ratio formula

The calculator uses four relationships. None of them is empirical, so the results are exact for the numbers you enter; the uncertainty is in the inputs, mainly the real rolling diameter of the tire.

1. Overall ratio = transmission gear ratio × rear end gear ratio
2. Engine rpm = mph × overall ratio × 336.14 ÷ tire diameter (in)
3. Road speed (mph) = rpm × tire diameter (in) ÷ (overall ratio × 336.14)
4. Ring and pinion ratio = ring gear teeth ÷ pinion teeth

The 336.14 is not a fudge factor. It is 63,360 inches in a mile divided by 60 minutes in an hour and by π, which turns road speed into tire revolutions per minute; old charts round it to 336. For a gear and tire swap the Gear swap tab adds two more: the effective ratio of the new gear, new ratio × old tire diameter ÷ new tire diameter, and the ratio that keeps today’s rpm on the new tires, old ratio × new tire diameter ÷ old tire diameter.

Worked example

Three typical questions, worked out with the same functions that run the calculator.

Typical rear end gear ratios

Rear end ratios are named by rounding the tooth-count ratio to two decimals. The table gives one tooth count that produces each common ratio, and the engine speed it gives at 65 mph with 26-inch tires, both in a 1:1 top gear and in a 0.70 overdrive. Tooth counts differ between axle designs, so treat that column as an example rather than a parts list.

Numerically higher ratios, from about 4.10 up, multiply torque more and help a car leave the line, at the cost of engine speed on the highway. Numerically lower ratios cruise quietly but feel soft off the line. An overdrive top gear is what lets a short, drag-friendly rear gear live with highway miles: compare the two rpm columns.

Common mistakes

• Changing the gear without the tire. Gears and tires move rpm in opposite directions. If both change, compare them together on the Gear swap tab, as the rear end gear ratio calculator alone will overstate the change.
• Mixing up “higher” and “lower”. A 4.10 is a numerically higher, or shorter, gear than a 3.73. It raises rpm at any speed; a taller gear is a smaller number.
• Reading the size code as the diameter. A 275/40R17 tire is not 27.5 inches tall: the 275 is the section width in millimeters. Convert the code with the tire size calculator first.
• Ignoring converter slip on an automatic. An unlocked torque converter lets the engine turn faster than the driveshaft, so the real cruise rpm reads above the calculated figure until the converter locks up. The rpm calculator takes slip into account.
• Losing count on the ring gear. If you count teeth by hand, mark the first tooth. Being one tooth out on a 41-tooth gear changes the ratio by 1/41, about 2.4%.