Mechanical Abilities · Free Study Guide
Gears & Gear Ratios
We teach the common gear rules: ratio, direction, and torque trade-off. Locals vary. Check your local's test format. Free to read; no signup.
How gears work
Meshing gears turn in opposite directions. The gear ratio tells you how much faster or slower the driven gear spins. Press play below to watch the rotation. Notice the larger gear turns slower.
Driver
12 teeth
Driven
18 teeth
Gear Ratio = Driven teeth ÷ Driver teeth = 18 ÷ 12 = 1.5 : 1
Adjacent meshing gears always rotate in opposite directions.
Worked example
Question
A driver gear has 15 teeth and meshes with a driven gear that has 45 teeth. If the driver turns at 120 RPM, how fast does the driven gear turn?
Find the gear ratio: Ratio = Driven ÷ Driver = 45 ÷ 15 = 3:1
Apply the ratio: Driven RPM = Driver RPM ÷ Ratio = 120 ÷ 3
Answer: 40 RPM
Tip: More teeth = slower rotation but more torque. The driven gear direction is always opposite the driver. Count the meshing points in a gear train, odd number of meshes means opposite direction, even means same.
The rules you need
| Concept | Formula | What to Remember |
|---|---|---|
| Gear Ratio | Ratio = Driven teeth ÷ Driver teeth | More teeth on driven = slower but more torque. |
| Gear Direction | Adjacent = opposite direction | Same shaft = same direction. Count meshes for direction. |
| Output RPM | RPMout = RPMin ÷ Ratio | Faster input doesn't help if the ratio slows it. |
| Torque Trade-off | More teeth = less speed, more torque | Same trade as every simple machine: force vs. distance. |
Try 18 free first
Try 18 questions free, then finish the Gears guide
Score high. Get called sooner. This test puts you on the Applicant Waiting List. Miss the cutoff and you typically wait 6 to 12 months. Eighteen questions. About 10 minutes. No card.
The other study guides (pulleys, levers, reading, figure visualization, etc.) are unlocked with a free account or a paid tier. Gears stays free for everyone.