Am Gear Ratio Calculator: Compare Teeth and Ratios

An AM gear ratio calculator works out the ratio between two meshing gears from their tooth counts, and can also estimate the driven gear’s speed from the driver’s speed. Enter the driver and driven tooth counts plus the input speed; the results show the gear ratio and output speed.

Formula

For a pair of external gears, the driven-to-driver gear ratio is the driven gear’s tooth count divided by the driver gear’s tooth count. The ideal driven speed is the input speed divided by that ratio.

• N_driver = number of teeth on the driving gear (teeth).
• N_driven = number of teeth on the gear being driven (teeth).
• R = gear ratio, expressed here as driven:driver or a numerical ratio to 1.
• n_in = driver or input rotational speed (revolutions per minute, rpm).
• n_out = ideal driven or output speed (rpm).

R = N_driven / N_driver
n_out = n_in / R

These equations describe an ideal gear pair. They calculate speed relationship, not the actual torque available after losses, nor whether two gears physically fit together.

Worked Example

Using the calculator’s defaults: the driver has 20 teeth, the driven gear has 40 teeth, and input speed is 1,000 rpm.

1. Calculate the ratio: 40 ÷ 20 = 2, so the driven-to-driver ratio is 2:1.
2. Calculate ideal output speed: 1,000 rpm ÷ 2 = 500 rpm.

The calculator displays a ratio of 2.00:1 and an ideal output speed of 500.00 rpm. This is a speed reduction: the larger driven gear turns at half the driver’s speed.

How to Use an AM Gear Ratio Calculator

“AM gear ratio calculator” can refer to a calculator for an AM-branded part or setup, but the basic tooth-count calculation is the same for ordinary gear pairs. Confirm what “AM” means in the context you encountered it; do not assume that the calculator accounts for a particular product’s dimensions or specifications.

• Count the teeth on the gear receiving power from the input shaft. Enter this as the driver.
• Count the teeth on the gear it meshes with. Enter this as the driven gear.
• Enter the driver’s rotational speed in rpm. If you only want the ratio, the speed does not affect that result.
• Read the ratio and ideal output speed, then check the direction, gear arrangement, and other design constraints separately.

Tooth counts are whole numbers greater than zero. If you know a gear’s model or part number but not its tooth count, consult its reliable specification or count the teeth; an outside diameter alone is not enough to determine the ratio.

What the Ratio Tells You

A ratio greater than 1 in this calculator means the driven gear has more teeth than the driver, so output speed is lower and ideal output torque is higher. A ratio below 1 means the driven gear has fewer teeth, so output speed is higher and ideal torque is lower. A 1:1 ratio means equal tooth counts and equal ideal speeds.

For example, a 12-tooth driver turning a 36-tooth driven gear gives 36 ÷ 12 = 3, or 3:1. At 900 rpm input, the ideal output speed is 900 ÷ 3 = 300 rpm. In an ideal system, torque changes in the opposite direction to speed: the 3:1 reduction can multiply torque by three. Real torque is lower because gears and bearings have friction and other losses.

With a simple pair of external gears, the two gears rotate in opposite directions. The ratio calculation gives the speed magnitude, not the direction. An internal gear arrangement or an idler gear can alter direction relationships, but an idler between two external gears does not change the tooth-count ratio between the first and last gears.

Compound Trains and Important Limits

A gearbox may have multiple stages. For a simple series of stages, multiply each stage’s driven-to-driver ratio to find the overall reduction. For example, two stages of 2:1 and 3:1 give an overall reduction of 2 × 3 = 6:1. If the input is 1,200 rpm, the ideal final speed is 1,200 ÷ 6 = 200 rpm. The calculator above handles one pair at a time; for compound gears, calculate each stage and combine the ratios.

Tooth counts alone do not establish whether gears can mesh. Compatible tooth spacing (module in metric systems or diametral pitch in inch-based systems), pressure angle, gear type, center distance, shaft alignment, and clearance matter. A ratio calculator is not a gear-design or strength check.

Common Mistakes and Interpretation

• Reversing driver and driven: Swapping the tooth counts changes the ratio to its reciprocal. Label the gear connected to the power source as the driver.
• Mixing ratio conventions: Some sources state input:output, while this calculator labels driven:driver. A 2:1 reduction here means output speed is input speed divided by two.
• Confusing rpm with torque: The calculator estimates speed. It does not measure real torque, efficiency, or power.
• Rounding too early: Keep the full ratio during intermediate calculations and round only the displayed result. Tooth counts themselves should not be rounded.
• Assuming a nominal speed is exact: A motor’s loaded speed can differ from its rated or unloaded speed. Use the speed that applies to the actual operating condition for a better estimate.

For clarity, a ratio of 2.00:1 is dimensionless: it is not 2 rpm, 2 inches, or a gear diameter. Input and output speed use the same unit, so entering rpm produces output in rpm. If you enter another consistent speed unit, the same division works, though the displayed label would need to match that unit.

Frequently Asked Questions

How do I calculate a gear ratio from teeth?
For the convention used here, divide the driven gear’s tooth count by the driver gear’s tooth count. A 40-tooth driven gear with a 20-tooth driver gives 40 ÷ 20 = 2, or 2:1.

How do I calculate output rpm?
Divide input rpm by the driven-to-driver ratio. For a 2:1 reduction with a 1,000 rpm input, ideal output speed is 1,000 ÷ 2 = 500 rpm.

Does a bigger gear always make the system slower?
If the larger gear is the driven gear, it turns more slowly than the smaller driver. If the larger gear is driving a smaller gear, the smaller driven gear turns faster. The roles and tooth counts both matter.

Does an idler gear change the gear ratio?
An ordinary idler gear placed between a driver and a final driven gear changes the direction relationships, but not the overall speed ratio. The ratio is determined by the driver and final driven gear tooth counts, assuming a simple external gear train.

Can I use this calculator for a multi-speed gearbox?
Use it for each gear pair or stage, then multiply the stage ratios for a simple compound train. A gearbox with planetary gears or other complex arrangements may need a formula specific to its gear layout and which parts are held, driven, or measured.

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in driver_teeth | Driver gear teeth | - | 20 | 0
in driven_teeth | Driven gear teeth | - | 40 | 0
in input_rpm | Input speed | rpm | 1000 | 0
out ratio | Gear ratio (driven:driver) | :1 | driven_teeth / driver_teeth | 2
out output_rpm | Ideal output speed | rpm | input_rpm / ratio | 2