How to Design a Gear & Sprocket

Determine the gear or sprocket reduction you need. The theory of gear reduction centers on using gears or sprockets of two different sizes to transfer power and increase or decrease RPM of the motor. Use the following formula to determine the gear reduction you need:

Gear reduction = Input RPM : Desired Output RPM

Example - If you have a motor that spins at 2,800 RPM and you'd like the output RPM to be 700 RPM, your formula would look like this.

Gear reduction = 2,800:700 or 4:1

Determine the circumference of your input gear or sprocket. Gear reduction works based on the geometry of the gears or sprockets utilized. Think of the circumference of your input gear or sprocket as the distance it travels in a straight line, for one revolution. To find the circumference of your gear or sprocket, measure the diameter of the gear or sprocket and use the following formula:

Circumference = π * Diameter

Example - A gear with a 10-inch diameter would have a circumference as follows:

Circumference = 3.14 * 10 = 31.40 inches

Determine the needed circumference of your output gear or sprocket. In a single-stage gear or sprocket reduction, you'll want the distance the output gear travels (the circumference) per revolution to be a multiple of the input distance. The formula for this is:

Gear reduction ratio = Output gear circumference : Input gear circumference

Example -
The desired gear reduction is 4:1
The input gear circumference is 31.4 inches
4:1 = Output : 31.4
4:1 = 125.6 : 31.4
The output gear circumference is 125.6 inches.

In this way, for every time the input gear rotates once, the output gear rotates a quarter of a turn, thereby reducing the number of revolutions per minute by a factor of four.

Determine the diameter of your gear or sprocket and transfer the cog size. Use the formula for circumference, again, to determine the needed output gear or sprocket diameter. As you recall:

Circumference = π * Diameter

Therefore,

Diameter = Circumference/π

With the previous example -

Diameter = 125.6 / 3.14
Diameter = 40 inches

Use the original input sprocket to transfer the size and shape of the teeth (cogs) to the larger output sprocket.