If you are researching how to calculate gear ratios, it can be confusing since there are several ways to come to the same answer. And once there were general practices that have gotten skewed by the years since. But math doesn't change, only the way you look at it does. Simple math is all that is needed to find the different ratios and information about the gear train. Simple formulas are used to achieve this. The trouble can be which formula to use for what purpose.

If you only have one gear splined to one shaft, you know how many turns they make based off the RPM of the gear shaft. So there is no need to find a ratio. When you add a second gear with teeth meshed to the first and both are different sizes, one will turn at a different speed than the other. Therefore, their respective shafts will also turn at different speeds.

Driver vs Driven Gear
When the teeth are meshed together on the 2 separate shafts, one gear drives the other. The gear making the other move is called the driver gear and the other gear is being driven (thus driven gear). The driver gear is closest the power source. The mainshaft receives power from the engine by way of the clutch. The countershaft receives power from the mainshaft by way of the gears selected.

In the (left) drawing below, there are only 2 gears that are splined to the transmission mainshaft (M1 and M2 gears). The other 3 gears on the mainshaft are sleeved over bearings on the shaft and have to be locked to the mainshaft by way of either M1 or M3 in order to turn the shaft. There are '+' signs above/below each gear in RED or BLACK. Such as M4 has a BLACK '+' and C4 has a RED '+' and M1 has a RED '+'. The BLACK '+' gears are SLEEVED over the shaft on which they are located. This means they can turn separately from the shaft unless otherwise engaged. The RED '+' gears are SPLINED to the shaft on which they are located. This means they always turn whenever that shaft turns. Both M1 and M3 are sliding gears (as is C3) and they are moved by way of the shift forks when you move the shifter pedal.
M1 and M2 (in Neutral) are the driving gears and they are both driving their respective counter gears (C1 and C2). Neither C1 nor C2 are splined to the countershaft, they just sit there and spin while the transmission is in Neutral. So power stops there and allows the bike to idle without being “in GEAR”

In the (right) drawing below, M1 and M2 are still moving and turning their respective gears but now the power from the engine is being used to turn the engine sprocket (to rear tire) so the emphasis is on that flow of power. M1 is (driving) and C1 is being (driven). C1, being sleeved on the shaft, is locked to the countershaft by C3 which makes the countershaft turn. Following the flow of power,C5 is splined to the countershaft and turns when the shaft turns. However, the mainshaft 5th gear (M5) is sleeved and can't turn on it's own. With C5's teeth in constant mesh with M5, C5 is (driving) and M5 is being (driven).

The standard gear ratio tells you how fast the second gear (driven gear) turns as opposed to how fast the first gear (driver gear) turns.
So you know how fast the first one is turning but now need a ratio of the two gears to find out how fast (or slow) the second gear is turning. Normally, to find that, you'll divide the teeth count of the first gear (driver gear) by the teeth count of the second gear (driven gear). Example: A 20 teeth gear is driving a 40 teeth gear. By dividing the first gear teeth by the second gear teeth, you get a number of 0.5 (20 / 40 = 0.5). That means the second gear will only turn at a rate of 0.5 (or 1/2) turns when the first gear has made 1 full turn on it's shaft. And if the RPM of the first gear is turning at 1000 RPM, the second gear is turning at 500 RPM (1000 x 0.5 = 500).

The inverse of the gear ratio tells you how fast the first gear (driving gear) turns as opposed to how fast the second gear (driven gear) turns.
Now if you divide backwards instead, teeth count of the second gear divided by the teeth count of the first gear, you'll get a number that represents how much faster the first gear is turning as opposed to the second gear. So now the formula changes and you do the math to get (40 / 20 = 2). That means the first gear is turning 2 times when the second gear has made 1 full turn on it's shaft. And the speeds are the same between them. The RPM of the first gear is still turning at 1000 RPM and the second gear is still turning at 500 RPM (1000 / 2 = 500).

These 2 different ratios above are generally not distinguished apart from each other or at least not enough.
As you can tell, each result points to one or the other's gear speed although the result is to the relationship between both gears. The difference is in the calculations and which gear or gearset is being referred to.

The inverse gear ratio is used to find a change in torque or speed when the second gear is either smaller or larger in teeth count.
The power from the source is what it is and can only be changed by more or less throttle (or engine RPM). However, that power can be manipulated to either achieve more torque or more speed (but not both) further down the gear train by changing the gear ratios. The total power stays the same, from the conservation of energy (the law of conservation of energy says that energy is neither created nor destroyed. When people use energy, it doesn't disappear. Energy changes from one form of energy into another form of energy.) ¹⁾

Torque vs Speed
The ratio shows the trade-off between torque and speed. Speed is RPM and Torque is PUSH. RPM is what is needed on the highway and Torque is the ability to move the bike faster from a stand still. Progressively through the upper gear changes, torque is lowered and speed is gained through gear ratio changes. As with the 2 gear train mentioned above;
If the driving gear is smaller than the driven gear, the result is the driven gear turns slower (less speed) but with (more torque) applied downstream of it.
If the driving gear is larger than the driven gear, the result is the driven gear turns faster (more speed) but with (less torque) downstream of it.

For our Sportster transmissions, the Gear Ratio is the ratio between the number of teeth on the two gears that are meshed together in the gearbox.

• It's important to distinguish between the input and output sources as these two conditions change during a ride.
  • The input source to the transmission with the clutch engaged (clutch lever released) is the engine.
    When you are on the throttle, the motor is driving the transmission and thus the rear tire.
    The motor is driving the mainshaft and it's gears, and the mainshaft gears are driving respective countershaft gears and thus the rear tire.
  • The input source to the transmission with the clutch disengaged (clutch lever pulled) is the rear tire.
    When you disengage the clutch, the motor is now not attached to the transmission but the transmission gears still turn.
    The rear tire is now driving the countershaft and it's gears which turn their respective mainshaft gears.
• When you let off the throttle with the clutch engaged (lever released), the rear tire is still trying to drive the transmission at the speed the motor was before pulling the clutch.
  So there is a push/pull going on inside the transmission while riding depending on throttle load.

• Final Drive Ratio:
  The final drive ratio is the last bit of gearing between the transmission and the rear wheel.
• Gear Ratios: Gear ratios represent the gears’ relation to each other in size. ²⁾
  When different sized gears mesh together, they can spin at different speeds and deliver different amounts of power.
  When the input gear rotates, it transfers its rotational energy to the output gear. The gear ratio determines the speed and torque of the output gear.
  Gear ratio is normally expressed as an ordered pair of numbers separated by a colon, for example, 3:1 (or 3 to 1).
  A Gear Ratio can increase the output torque or output speed of a mechanism, but not both. ³⁾
  • Gear Ratio:
    The ratio of a 2 gear train is the rate of the number of teeth on the driving gear to the number of teeth on the driven gear for our purposes. ⁴⁾
  • Final Drive Ratio: The ratio between the transmission sprocket and the rear wheel.
  • Internal Gear Ratio:
    Number of mainshaft revolutions required to drive the output sprocket 1 revolution. ⁵⁾
    This number includes all transmission gears in the selected power train but does not include the primary drive or rear wheel.
  • Speed Ratio: The speed ratio is the ratio of output speed to input speed (the inverse of the gear ratio). ⁶⁾
    It is calculated the same as the mechanical advantage but the results are used differently.
    If a 29T gear drives a 34T gear, the gear ratio is 0.85294, the driven gear turns 0.85294 turns to 1 full revolution of the driver gear.
    Using the inverse of that, the driven gear turns 1.1724 times slower than the driver gear.
  • Overall Gear Ratio:
    Number of engine revolutions required to drive the rear wheel 1 revolution. ⁷⁾ This number includes all gearing in the system (primary, transmission and final drive).
  • Primary Drive Ratio: The ratio between the crankshaft sprocket and the clutch sprocket.
• Drive and Driven Gears: Determining which is which is crucial in calculating the gear ratio.
  Example 1: A 20T gear drives a 40T gear at a ratio of 0.5:1 - driven gear turns 0.5 (or 1/2) revolution for every 1 full revolution of the driving gear.
  Example 2: A 40T gear drives a 20T gear at a ratio of 2:1 - driven gear turns 2 full revolutions for every 1 full revolution of the driving gear.
  • Driving Gear:
    (aka input gear), The driving gear is the gear that transmits power.
  • Driven Gear:
    (aka output gear), The driven gear is the gear that receives power.
• Gear Train :
  A Gear train consists of two or more gears in series. It's application is to increase or decrease the speed or torque of the output shaft. ⁸⁾
• Input Shaft:
  The input shaft is the shaft that is transmitting power (the mainshaft when clutch is engaged or the countershaft when clutch is disengaged).
  In 5th gear, the power is transferred entirely through the mainshaft at a 1:1 ratio. So in 5th gear, the mainshaft is the output shaft.
• Mechanical Advantage:
  A mechanical advantage refers to an increase (or decrease) in torque or force that a mechanism achieves through a power transmission element. Gear ratio is used to define the mechanical advantage. Mechanical advantage is a measure of the ratio of output force to input force in the gear train in this application. ⁹⁾ Despite changing the forces that are applied, the conservation of energy is still true and the output energy is still equal to the input energy.
• Torque Ratio:
  The torque ratio is the rate of the torque of the driving gear to the torque of the driven gear. ¹⁰⁾ It determines the torque of the system.
• Speed Ratio:
  The speed ratio is the ratio of the angular velocity of the driving gear to the angular velocity of the driven gear. ¹¹⁾ It determines the speed of the system.
• Speed (RPM):
  The rotational speed of the shaft generated by the motor, expressed in rpm (rotations per minute). ¹²⁾ The shaft speed in a gearmotor is proportional to the gear ratio. The output speed can be found by dividing the input speed by the gear ratio. Gear ratios above one will reduce speed, while those below one will increase speed. Another explanation: In a simple gear system, two gears with different numbers of teeth are meshed together. ¹³⁾ When the input gear rotates, it transfers its rotational energy to the output gear. The gear ratio determines the speed and torque of the output gear. A gear with fewer teeth than the input gear will rotate faster and provide less torque, while a gear with more teeth will rotate slower and provide more torque.
• Spur Gears:
  The spur gears used in Sportsters have straight cut teeth positioned with mated pairs on parallel axis.
• Output Shaft: The output shaft is the shaft that is receiving power (countershaft when clutch is engaged in 1st-4th gears) or (mainshaft in 5th gear).

• Gear Ratio for 2 gears = (number of teeth on driving gear) / (number of teeth on driven gear)
• Internal Gear Ratio for 4 gears: (driver gear teeth x driver gear teeth) / (driven gear teeth x driven gear teeth)
• Speed Ratio = (driven gear) / (driver gear)
• Output Speed = (input speed) x (gear ratio)
• Mechanical Advantage for 2 gears = (number of teeth on driven gear / number of teeth on driving gear)
• Mechanical Advantage for 4 gears = (number of driven gear teeth x number of driven gear teeth) / (number of driver gear teeth x number of driver gear teeth)
• Output Torque = (input torque) x (mechanical advantage).

The examples below all use transmission 2nd gear as a reference.
The drawing below shows how the gears are positioned while in second gear and can be used in reference to the examples.
The gears in the power flow:
M2 is splined to the mainshaft and is driving C2 which is sleeved over bearings on the countershaft.
C2 is locked to the countershaft by C3 and C5 is splined to the countershaft. C5 is driving M5 which is sleeved over bearings on the mainshaft.
With both C2 and C5 locked to the same shaft, the speed for both these gears are the same. M5 is splined to the transmission sprocket and their speeds are the same.

¹⁴⁾

The information below shows how to calculate the numbers for a gear train using only 2 gears.
Instead, you can find a gear ratio calculator online to do the math for you.
Click Here to link to one that gives you gear ratio, mechanical advantage, output speed and torque by inputting known values.

The examples below are using a MS-2 (29T) and a CS-2 (34T) gearset (or gear train). Engine RPM at constant 1000 and initial torque of 50 ft/lbs.
In this gearset, M2 is splined to the mainshaft, turns the same speed as the mainshaft and serves as the driving gear of the set.
C2 is sleeved over bearings on the countershaft, has to be coupled to the countershaft by the dogs on C3 gear and serves as the driven gear to M2.
These are arbitrary combinations just for example.

• Gear Ratio = (number of teeth on driving gear) / (number of teeth on driven gear)
  • Example: A 29 teeth gear is driving a 34 teeth gear at a ratio of 0.85:1
    Plug the numbers into the formula (29 / 34) = 0.85294 (or 0.853)
    The result is expressed in ratio as 0.853:1 (or 0.853 to 1).
    In this example, CS-2 turns (slower) and at 0.853 times for MS-2 to turn 1 full revolution.
    While this setup shows a gear reduction in terms of speed, it creates an output that has more torque when compared to the input torque between these 2 gears.
• Output Speed = (input speed) x (gear ratio)
  • Example: Given a mainshaft speed of 1000 rpm using the gear ratio above (0.853), the countershaft speed is 853rpm
    Plug the numbers in the formula (1000 x 0.853) = 853
    In this example and with a constant input rpm, the countershaft (by way of CS-2) has a speed of 853 rpm.
• Mechanical Advantage = (number of teeth on driven gear / number of teeth on driving gear)
  • Example: A 34 teeth gear is being driven by a 29 teeth gear at a mechanical advantage of 1.172:1
    Plug the numbers into the formula (34 / 29) = 1.172413793103448
    In this example, the result is expressed in ratio as 1.172:1 (or 1.172 to 1).
    This example gives 0.172 times more output torque as compared to the input torque between these 2 gears.
• Output Torque = (input torque) x (mechanical advantage).
  • Example: Given an input torque 50 ft/lbs, the output torque will increase to 58.6 ft/lbs @ 1000 RPM between the example gears
    Plug the numbers into the equation (50 x 1.172) = 58.6
    In this example, the torque from the mainshaft was increased on the countershaft by 8.6 ft/lbs (by way of CS-2).

The information below shows how to calculate the numbers for a gear train using 4 gears (2 drivers and 2 driven).
Instead, you can find a gear ratio calculator online to do the math for you.
Click Here to link to one that gives you internal gear ratio and output speed by inputting known values.

AKA, gearbox ratio, the internal ratio includes the mainshaft and countershaft gears that are in the power flow for the transmission GEAR selected.
Use the transmission illustration above for this example.
To find out what 2nd gear calculations from above did to the final drive sprocket speed, this example uses 4 gears, since the power flow for 2nd gear uses all 4 of these.
This example uses the M-2 (29T) and a C-2 (34T) gearset from the above example plus C-5 (25T) and M-5 (42T) and the transmission sprocket.
And still using engine RPM of a constant 1000 and initial torque of 50 ft/lbs.
M-2 gear is driving C2 gear and C5 gear is driving M5 gear.
M5 gear is a 1:1 relationship with the transmission drive sprocket which means they are traveling at the same speed.

• Internal Gear Ratio: (driver gear teeth x driver gear teeth) / (driven gear teeth x driven gear teeth)
  • Assemble gear teeth count for each gearset:
    • M-2 (29T) / C-2 (34T)
    • C-5 (25T) / M-5 (42T)
  • Calculate combined gear ratio:
    • Driver teeth: 29 x 25 = 725
    • Driven teeth: 34 x 42 = 1,428
    • Driver teeth (725) / Driven teeth (1,428) → 725/1,428 = 0.507703081232493 (or 0.508)
  • The internal gear ratio for this gear train in 2nd gear is (0.508:1)
• Output Speed: (input speed) x (gear ratio).
  • Input speed (1000 rpm) x gear ratio (0.508:1) → 1000 x 0.508 = 508 RPM for the example 2nd gear.
• Mechanical Advantage = (driven gear teeth x driven gear teeth) / (driver gear teeth x driver gear teeth)
  • Assemble gear teeth count for each gearset:
  • C-2 (34T) / M-2 (29T)
  • M-5 (42T / C-5 (25T)
  • Calculate combined mechanical advantage:
    • Driver teeth: 34 x 42 = 1,428
    • Driven teeth: 29 x 25 = 725
    • Driver teeth (1,428) / Driven teeth (725) → 1,428/725 = 1.969655172413793 (or 1.970)
  • The internal mechanical advantage is (1.970:1) for the example 2nd gear
• Output Torque = (input torque) x (mechanical advantage).
  • Given an input torque 50 ft/lbs, the output torque will increase to 98.5 ft/lbs @ 1000 RPM for the example 2nd gear.

The primary ratio is calculated between the engine's crankshaft sprocket and the transmission clutch sprocket.
This example uses an engine sprocket with 35 teeth and a clutch sprocket with 56 teeth.

• Gear Ratio: (driving gear) / (driven gear)
  • Engine sprocket (35T) / clutch sprocket (56T) → 35/56 = 0.625 (or 0.625:1)
• Mechanical Advantage: (driven gear) / (driving gear)
  • Clutch sprocket (56T) / engine sprocket (35T) → 56/35 = 1.60 (or 1.60:1)
  • The gear ratio IS NOT listed in the FSM.
    The mechanical advantage (or torque advantage) is listed, as calculated above, at 1:60:1 for a 1998 Sportster.

The final drive ratio is calculated between the transmission output sprocket and the rear wheel.
This example uses a transmission sprocket with 29 teeth and a rear wheel sprocket with 61 teeth on a 1998 XL1200 Sportster.

• Gear Ratio: (driving gear) / (driven gear)
  • Transmission sprocket (29T) / rear wheel sprocket (61) → 29/61 = 0.4754098360655738 (or 0.475:1)
• Mechanical Advantage: (driven gear) / (driving gear)
  • Rear wheel sprocket (61T) / transmission sprocket (29T) → 61/29 = 2.103448275862069 (or 2.103:1)
  • The gear ratio IS NOT listed in the FSM.
    The mechanical advantage (or torque advantage) is listed as 2.10:1 for a 1998 1200 Sportster.

The overall gear ratio is calculated for the entire gear train in the system including primary, transmission and final drive ratios.
This example uses the calculations above for each of those parts of the gear train.

• Overall Gear Ratio: (primary ratio) x (internal ratio) x (final drive ratio)
  • Primary gear ratio (0.625:1) x transmission 2nd gear internal ratio (0.508:1) x final drive ratio (0.475:1)
    → 0.625 x 0.508 x 0.475 = 0.1508125 (or 0.151:1)
• Mechanical Advantage: (primary ratio) x (internal ratio) x (final drive ratio)
  • Primary mechanical advantage (1.60:1) x transmission 2nd gear internal mechanical advantage (1.970:1) x final drive mechanical advantage (2.10:1)
    → 1.60 x 1.970 x 2.10 = 6.6192 (or 6.619:1)
  • The overall gear ratio IS NOT in the FSM.
    The overall mechanical advantage (or torque advantage) is listed as 6.62:1 for a 1998 1200 Sportster second gear.