LEGO Gear Ratio Calculator and How to Use It

A LEGO gear ratio calculator works out how fast a driven axle turns compared with the axle driving it, using the tooth counts of the two gears. Enter the driver and driven gear teeth to get the ratio and the ideal output speed multiplier; this calculator uses a 1:1 input speed as its reference.

Formula

For a simple pair of external gears, the ratio is based on the number of teeth:

• Gear ratio (driven:driver) = driven gear teeth ÷ driver gear teeth.
• Output speed multiplier = driver gear teeth ÷ driven gear teeth.
• Ideal torque multiplier = driven gear teeth ÷ driver gear teeth.

Here, driver is the tooth count of the gear receiving input motion, and driven is the tooth count of the gear that receives motion from it. Tooth counts are unitless counts, so both gears must be counted in teeth. The calculator labels the ratio as driven:driver: a result of 3:1 means the driven gear has three times as many teeth as the driver. This convention makes a reduction easy to recognize.

Worked Example

Using the calculator’s defaults, the driver has 8 teeth and the driven gear has 24 teeth.

1. Gear ratio = 24 ÷ 8 = 3.00:1.
2. Output speed multiplier = 8 ÷ 24 = 0.33× (the unrounded value is one-third).
3. Ideal torque multiplier = 24 ÷ 8 = 3.00×.

Thus, if the driver turns at 90 revolutions per minute, the driven gear turns at 30 rpm in the opposite direction. In an ideal, lossless calculation, torque at the driven gear is three times the input torque. Real assemblies lose some energy through friction and other effects, so actual speed and torque will not match ideal values exactly.

How LEGO Gear Ratios Work

Meshing gears exchange rotational speed and torque. A smaller driver turns a larger driven gear more slowly, while a larger driver turns a smaller driven gear more quickly. For one pair of external gears, the two gears rotate in opposite directions. The tooth-count ratio describes the relative rates; it does not tell you an absolute speed unless you also know the input speed.

For example, a 20-tooth driver turning a 12-tooth driven gear gives a driven:driver ratio of 12 ÷ 20 = 0.60:1. The speed multiplier is 20 ÷ 12, or about 1.67×, so an input speed of 60 rpm ideally produces 100 rpm at the driven axle. The smaller gear spins faster, while its ideal torque is lower.

In a LEGO Technic model, gears may be used to trade speed for torque, change the direction of rotation, or route motion around a build. A reduction is useful when a mechanism needs slower movement and greater theoretical turning force; a speed increase can help a mechanism rotate faster but reduces available torque. The motor, battery or power source, friction, load, and construction all affect what the model actually does.

Compound Trains and Multiple Gear Stages

When several gears are connected in stages, calculate each stage and multiply the stage ratios. For speed multipliers, multiply driver teeth divided by driven teeth for every engaged pair. For reduction ratios expressed as driven:driver, multiply driven teeth divided by driver teeth at each stage.

Suppose an 8-tooth driver turns a 24-tooth gear, and that gear shares an axle with a 12-tooth driver that turns a 36-tooth gear. The first stage reduces speed by 3:1 and the second by 3:1, so the total reduction is 9:1. An input of 90 rpm would ideally produce 10 rpm at the final driven axle.

An idler gear placed between two gears changes the path and can affect rotation direction, but it does not change the overall tooth-count ratio when it is simply an intermediate gear. Count only the driver and driven gears at each actual stage. A gear sharing an axle with another gear does not mesh with it; those two gears rotate together at the same speed.

Choosing Gears and Avoiding Common Errors

Choose the ratio for the motion the mechanism needs, not just the largest or smallest gears available. A lower output speed can help a model move a load or operate a mechanism with more force, while a higher output speed can make a wheel or rotor turn faster. Check that the selected gears can physically mesh in the build and that axles and supports stay aligned.

• Keep the labels straight. The driver receives input; the driven gear is the output. Reversing them reciprocates the ratio.
• Do not confuse ratio with speed. A 3:1 reduction is a relationship, not 3 rpm. Multiply the input speed by the speed multiplier to estimate output rpm.
• Use tooth counts, not gear diameters. For standard meshing gears, tooth counts give the ratio directly. Mixing gear sizes from different systems or estimating by eye can lead to errors.
• Track each stage and shared axle. A compound train’s total ratio depends on all the meshing stages, but gears fixed to the same axle turn together.
• Remember direction and losses. One external gear mesh reverses rotation; friction, flex, and load mean real performance differs from the ideal calculation.

The calculator returns decimal values rounded to two places. The underlying ratio may be a repeating decimal, such as 1 ÷ 3 = 0.333…, so use the unrounded fraction when combining stages if you need a precise result. The tool assumes ordinary external gears and does not account for gear geometry, backlash, friction, motor limits, or mechanical strength.

Frequently Asked Questions

How do I calculate a LEGO gear ratio?
Count the teeth on the driver and driven gears, then divide driven teeth by driver teeth for the driven:driver ratio. Divide driver teeth by driven teeth to get the output speed multiplier.

Does a larger LEGO gear make a model faster?
Not by itself. A larger gear driven by a smaller gear turns more slowly and increases ideal torque. A larger driver turning a smaller driven gear increases output speed and reduces ideal torque.

Do idler gears change the ratio?
A simple idler gear between a driver and a driven gear changes the arrangement and rotation direction, but not the overall ratio. Its tooth count cancels from the overall speed relationship.

How do I calculate the ratio for two gear stages?
Calculate the speed multiplier for each stage as driver teeth divided by driven teeth, then multiply the stage multipliers. For reductions, multiply the driven-to-driver ratios instead.

Why is my model’s speed different from the calculator?
The calculator gives an ideal tooth-count relationship. Actual speed can vary because of friction, load, power-source performance, misalignment, flex, and other mechanical losses.

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in driver | Driver gear teeth | teeth | 8 | 1
in driven | Driven gear teeth | teeth | 24 | 1
out ratio | Gear ratio (driven:driver) | :1 | driven / driver | 2
out speed | Output speed multiplier | x | driver / driven | 2
out torque | Ideal torque multiplier | x | driven / driver | 2