Gear Math

This page should help clarify the function of gears in the vehicle's drivetrain, by illustrating how engine speed is related to vehicle speed. The basic formula for determining the vehicle's speed at a given engine speed (in RPM) is:

In most cases, the transfer case ratio will be 1.0. A transfer case is used only in four wheel drive vehicles, and is not present in the vast majority of automobiles. In the original formula above, the constant 336 takes into account Pi, the number of inches in a mile, and the number of minutes in an hour. To see how this formula was derived, click here.

By substituting different numbers in the formula, one can see how the gears are helpful for matching the engine's speed to the vehicle's speed. The chart below illustrates the relationship of engine speed to vehicle speed for a typical vehicle. Each curve shows the car's speed in MPH versus the speed of the engine in RPM.

Here, we can see that each transmission gear results in a different speed for a given engine RPM. When we consider the effective power band of the engine (see torque and horsepower), it can be seen that gearing is important.

Torque Multiplication

Besides matching the speed of the vehicle to the engine's power band, reduction gearing also multiplies the output of the engine's torque. A gear ratio having an input to output ratio of 2 to 1 will also multiply the engine's output torque or twisting force by a factor of two. This is why a car accelerates much more briskly in first gear than it does in higher gears.

Some other Useful formulas

Since most passenger car tires and many light truck tires are sold in "P-metric" sizes, here is a simple formula for calculating the tire diameter in inches from the tire size. For example, suppose you have a tire size labeled "P-185/75-R14". This indicates that the tire's section width is 185 millimeters, and the tire's height from the rim to the tread is 75% of the section width or 138.75 mm. This formula not only serves to convert from millimeters to inches, but it also accounts for the size of the rim.

If a different size of tire is used on a car, there will be an error in the reading of the speedometer. This is due to the greater or smaller distance per revolution that a different sized tire might have. The speedometer is actually driven by a small gear off the transmission, or by the car's computer. Either way, it is predetermined to operate with a specific tire size. Any deviation from that size will introduce error, unless the car's speedometer gearing is changed or the computer is reprogrammed. This formula will help determine how much error will be present for a given change in tire size. Keep in mind that even with the proper sized tires, speedometer error is often up to 5%.

(New Tire Diameter Old Tire Diameter) Speedometer MPH = Actual MPH

Finally, here is a simple formula for determining the gear ratio of a ring and pinion gearset. The same formula holds true for other gear sets as well. Simply divide the number of teeth on the output gear by that of the input gear. For example, if a ring and pinion gearset has 41 teeth on the ring gear and 13 teeth on the pinion gear, its ratio is 3.15 to 1.

Ring Gear Teeth Count Pinion Gear Teeth = Gear Ratio

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