Question 1

How do I calculate a gear ratio from tooth counts?

Accepted Answer

The ratio of a single gear pair is the driven tooth count divided by the driving tooth count: i = z_out / z_in. For example a 20-tooth pinion driving a 60-tooth gear gives i = 60 / 20 = 3, a 3:1 reduction.

Question 2

How do I find output speed from a gear ratio?

Accepted Answer

Output speed equals input speed divided by the ratio: N_out = N_in / i. A 3:1 reduction turning at 1500 rpm at the input gives 1500 / 3 = 500 rpm at the output.

Question 3

How does a gear train change torque?

Accepted Answer

Ignoring losses, torque is multiplied by the ratio: T_out = T_in × i. A 3:1 reduction with 10 N·m at the input gives 30 N·m at the output. Real gears lose a few percent, so multiply by an efficiency between 0 and 1.

Question 4

How do I combine multiple gear stages?

Accepted Answer

Multiply the stage ratios together: i_total = i_1 × i_2 × … For two stages of 3:1 and 2:1 the total is 6:1. Speed divides by the total ratio and torque is multiplied by it.

Question 5

What is efficiency and how does it affect the result?

Accepted Answer

Efficiency η (0 to 1) accounts for friction, churning and meshing losses. It scales output torque, T_out = T_in × i × η, but does not change the speed ratio. The default 1.0 is the ideal, lossless case; spur-gear stages are often around 0.97–0.99 each.

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