Gear Ratio Calculator

Background.

Swap a 3.73 rear axle for a 4.10 and the engine turns about 9.9% faster at every road speed, in every gear. Fit tires two inches taller than 26-inch originals and it turns about 7% slower. Both changes come down to gear ratio: how many turns enter a gear pair, or a whole driveline, for each turn that leaves it. Four related questions are answered here: the ratio from tooth counts, the speed of a driven gear, engine RPM from road speed, and road speed from engine RPM.

For a simple external gear pair, a 20-tooth driving gear turning a 60-tooth driven gear has a 60 / 20 = 3.00 ratio. The driven gear turns once for every three driver revolutions, ignoring losses and deformation; at 1,800 input rpm it turns at 600 rpm. KHK Gears states the same relationship as i = z2 / z1 = n1 / n2, where z is tooth count and n is rotational speed. This exact tooth-count calculation is useful for machine gears, chain sprockets, and other simple paired rotating elements, provided you identify which member drives and which is driven.

A vehicle adds stages. The selected transmission gear ratio and axle or final-drive ratio multiply to form the overall drivetrain ratio. A 0.68 overdrive gear with a 3.73 axle produces 2.5364 engine revolutions per tire revolution under the ideal no-slip model. Tire circumference is pi times diameter. Road speed determines tire revolutions per minute, and multiplying tire RPM by the overall ratio gives engine RPM. TREMEC publishes the familiar performance-industry shortcut RPM = mph x axle ratio x 336 x transmission ratio / tire diameter; here the unit conversion is derived directly from 63,360 inches per mile, 60 minutes per hour and pi rather than taken as the rounded 336.

These are kinematic estimates, not promises of tachometer or GPS readings. A tire's nominal size is not necessarily its loaded rolling diameter. Inflation, load, construction, tread wear, growth at speed, and manufacturer tolerances affect revolutions per mile. Torque-converter slip, clutch slip, wheelspin, and drivetrain compliance also separate real measurements from the ideal locked-driveline result. Automatic transmissions may unlock the converter or change ratio, and continuously variable transmissions do not have one fixed selected ratio. Use a measured tire circumference or manufacturer revolutions-per-mile value when precision matters.

The result helps compare rotational speed, cruising RPM, gearing changes, tire-size changes, and theoretical shift speeds. It does not determine whether a transmission, axle, tire, driveshaft, or engine is mechanically compatible or safe at that speed. Verify redline, tire speed and load ratings, component limits, calibration requirements, clearance, and manufacturer instructions before modifying a vehicle. Road-speed outputs are mathematical estimates, never a recommendation to drive at that speed.

What is gear ratio calculator?

A gear ratio is the quotient between linked input and output rotation. Tooth count supplies the exact ratio for a simple meshing pair. In a vehicle, transmission and final-drive stages multiply, while tire circumference converts rotational motion to road distance. The same equation can therefore solve engine RPM or theoretical vehicle speed when every other value is known. A ratio above 1 is a reduction: the output turns more slowly than the input but, losses aside, with proportionally more torque, which is why first gears and off-road crawl ratios are numerically large. A ratio below 1, such as a 0.68 overdrive, does the opposite: the transmission output shaft turns 1 / 0.68 ≈ 1.47 times for every engine revolution, trading torque for lower cruising RPM. Enthusiasts describe axle ratios by feel rather than number: a numerically lower ratio such as 3.08 is called taller gearing, a numerically higher one such as 4.10 shorter. In a chain of gears every stage multiplies, an idler gear between two others changes the direction of rotation but not the ratio, and two meshing external gears always turn in opposite directions, while a chain or belt keeps both sprockets turning the same way. Tooth counts are often chosen with no common factor, such as 41 and 11, so that every tooth meets every tooth on its partner in turn and wear spreads evenly; that is why axle ratios like 3.73 are rarely round numbers.

How to use this calculator.

1. 01Choose what to calculate: the ratio from tooth counts, the driven gear's RPM, engine RPM from road speed, or road speed from engine RPM.
2. 02For the two tooth-count modes, enter the driving and driven tooth counts, and for driven-gear RPM also the driving gear's speed; the vehicle fields are ignored.
3. 03For engine RPM, enter road speed, the ratio of the gear actually selected, the axle or final-drive ratio and the loaded tire diameter. For road speed, enter engine RPM with the same ratio and tire inputs.
4. 04Take ratios from the transmission and axle specification rather than a model name or 'top gear', since variants of one transmission often use different ratio sets. If a transfer case, portal axle or extra reduction stage is engaged, multiply it into one of the ratio fields and note what you did.
5. 05For the tire, a measured loaded diameter or the maker's revolutions-per-mile figure beats the nominal sidewall size; the diameter equivalent of a revolutions-per-mile figure is 63,360 ÷ (π × rev/mile).
6. 06Read the result as a theoretical, no-slip relationship, not a tachometer prediction or a safe operating limit.

The formula.

Tooth mode divides driven teeth by driver teeth, i = z_driven ÷ z_driver, and driven-gear RPM is the driving gear's RPM divided by that ratio. Vehicle modes multiply transmission and axle ratios, compute tire circumference as pi times diameter, and convert miles per hour to tire revolutions per minute using 63,360 inches per mile and 60 minutes per hour. Multiplying tire RPM by overall ratio gives engine RPM; algebraic inversion gives mph. Written out, engine RPM = mph × 63,360 × G_t × G_a ÷ (π × D × 60). The constant part, 63,360 ÷ (60π), is about 336.135, which is where the shortcut 336 comes from; using 336 instead reads about 0.04% low, under one rpm in the worked example, which matters only when comparing gearing options that are very close. Another way to see the same equation: a tire of diameter D turns 63,360 ÷ (πD) times per mile, about 775.7 times for a 26-inch tire, so engine revolutions per mile are that figure times the overall ratio, and RPM is revolutions per mile times mph ÷ 60. The model assumes a rigid, locked driveline and a tire that rolls without slip at a fixed effective diameter. Real tires roll on a radius slightly shorter than their unloaded size and grow a little at speed, torque converters slip until they lock, and a CVT has no single ratio to enter. Engine RPM is directly proportional to speed and to each ratio and inversely proportional to tire diameter, so a 10% change in any one of them moves the answer by about 10%. The same ratio scales torque in the opposite direction: engine torque times the overall ratio, less driveline losses, is the torque at the driven wheels, and dividing that by the tire's loaded radius gives the pushing force at the road. That is why a numerically higher ratio accelerates harder while it raises cruising RPM.

A worked example.

Frequently asked questions.

References& sources.

1. [1]KHK Gears. Calculation of Gear Dimensions and gear technical reference; defines speed ratio from reciprocal rotational speed and tooth-count ratio.
2. [2]TREMEC. Gear Ratio Calculator; manufacturer tool using engine RPM, axle ratio, transmission ratio, and tire height to determine speed.
3. [3]TREMEC. Performance Product Catalog; publishes RPM = mph x axle ratio x 336 / tire diameter x overdrive ratio.
4. [4]Bridgestone Commercial. Truck Tire Data Book; defines revolutions per mile and distinguishes overall diameter from loaded radius.
5. [5]NIST. SI Units — Length; official U.S. measurement reference for exact inch relationships used in the mile-to-inch conversion.