Gear Ratio Calculator

Background.

A gear ratio describes how many turns enter a gear pair for each turn that leaves it. This calculator handles four closely related jobs on one page. In tooth-count mode it divides the number of teeth on the driven gear by the teeth on the driving gear. Its gear-RPM mode applies that ratio to a known driving-gear speed. In vehicle RPM mode it estimates engine speed from road speed, transmission ratio, final-drive ratio, and tire diameter. In speed mode it rearranges the same driveline relationship to estimate 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 the user identifies 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. This calculator derives the unit conversion directly with 63,360 inches per mile, 60 minutes per hour, and pi rather than baking in the rounded 336 constant.

The direct derivation makes the relationship easier to audit: engine RPM = mph x 63,360 x overall ratio / (pi x tire diameter x 60). Solving for speed simply reverses it. The difference from a 336-based result is small because 63,360 / (pi x 60) is about 336.135, but the exact route avoids compounding an unexplained rounded constant when users compare close gearing options.

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.

Choose a tooth-count mode only for a single gear pair. For a vehicle RPM or speed calculation, use the exact ratio of the gear currently selected, not a model name or a guessed label such as 'top gear.' Transmission variants often use different ratio sets. Enter the differential or final-drive ratio separately. A transfer case, portal axle, or additional reduction stage must also be included in the overall ratio; if present, multiply it into one of the ratio inputs and record what you did.

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.

How to use this calculator.

1. 01Select tooth ratio, engine RPM, or vehicle speed.
2. 02For tooth ratio, enter the driving and driven tooth counts; the other fields are ignored.
3. 03For driven-gear RPM, also enter the driving gear's rotational speed.
4. 04For RPM, enter road speed, the selected transmission ratio, axle ratio, and loaded tire diameter.
5. 05For speed, enter engine RPM plus the same ratio and tire inputs.
6. 06Use specification-sheet ratios and a measured loaded diameter where possible.
7. 07Treat road-speed output as a theoretical relationship, not a safe operating limit.

The formula.

Tooth mode divides driven teeth by driver teeth. 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. Decimal arithmetic is retained until display rounding.

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.