A spur gear set has 40 teeth on the driver gear and 20 teeth on the driven gear. What is the gear ratio and the output speed relative to input?

• A. Gear ratio is 2:1; output speed is half of the input
• B. Gear ratio is 1:2; output speed is double the input
• C. Gear ratio is 1:1; output speed equals input
• D. Gear ratio is 4:1; output speed is quarter of input

Answer: (A)

In a simple spur gear pair, the speed relationship comes from the gear teeth counts. The output speed is the input speed multiplied by the ratio of the driver’s teeth to the driven’s teeth. Here the driver has 40 teeth and the driven has 20, so the ratio is 40:20, which simplifies to 2:1. That means the output gear would rotate at twice the input speed (the pitch line speeds match as the gears mesh, so the smaller driven gear turns faster to keep up with the larger driver). The gear ratio is 2:1 in this setup. Be aware that some conventions express the ratio differently, which can lead to descriptions like a halved speed in other contexts, but the standard mechanical relation for these tooth counts yields a speed increase by a factor of two.