Calculate gear speed ratio or find input and output gear teeth from any two values for quick gear ratio calculations with teeth counts.
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Speed Ratio Formula
The speed ratio for a simple gear pair is calculated from the number of teeth on the output gear and the input gear.
SR = T_o / T_i
Rearranged forms used to solve for a missing value:
T_o = SR * T_i
T_i = T_o / SR
- SR = speed ratio
- To = number of teeth in the output gear
- Ti = number of teeth in the input gear
If you enter the output gear teeth and input gear teeth, the calculator finds the speed ratio. If you enter the speed ratio and input gear teeth, it finds the required output gear teeth. If you enter the output gear teeth and speed ratio, it finds the required input gear teeth.
Common Speed Ratio Interpretations
A gear speed ratio tells you how the output gear compares to the input gear based on tooth count.
| Speed Ratio | Tooth Count Relationship | General Meaning |
|---|---|---|
| Less than 1 | Output gear has fewer teeth than input gear | Output gear rotates faster than the input gear |
| 1 | Both gears have the same number of teeth | Input and output rotate at the same speed |
| Greater than 1 | Output gear has more teeth than input gear | Output gear rotates slower than the input gear |
Example Calculations
Example 1: Calculate speed ratio
You have an output gear with 60 teeth and an input gear with 20 teeth.
SR = T_o / T_i
SR = 60 / 20 = 3
The speed ratio is 3.
Example 2: Calculate output gear teeth
You need a speed ratio of 2.5, and the input gear has 24 teeth.
T_o = SR * T_i
T_o = 2.5 * 24 = 60
The output gear needs 60 teeth.
FAQ
What does a speed ratio of 2 mean?
A speed ratio of 2 means the output gear has twice as many teeth as the input gear. For example, a 40-tooth output gear and a 20-tooth input gear give a speed ratio of 2.
Can gear teeth be a decimal number?
In a real gear, the number of teeth must be a whole number. The calculator may show decimals when solving for a missing value, but you would need to round to a practical whole number and check whether the final ratio is still acceptable.
Why can the input gear teeth or speed ratio not be zero?
The formula divides by the input gear teeth or by the speed ratio when rearranged. Division by zero is undefined, so those values cannot be zero.
