Sprocket Calculator
Find the drive ratio and output RPM of any sprocket-and-chain system by entering the tooth counts for both sprockets and the input shaft speed.
Result
4:1
A 11-tooth driving sprocket and 44-tooth driven sprocket give a 4:1 ratio, 250 output RPM from 1,000 input RPM
Quick Answer
A sprocket calculator divides the driven sprocket's tooth count by the driving sprocket's tooth count to get the drive ratio, then divides input RPM by that ratio to get output RPM. For a 12-tooth drive sprocket, a 36-tooth driven sprocket, and 1,200 RPM input, the ratio is 36 ÷ 12 = 3 and the output speed is 1,200 ÷ 3 = 400 RPM.
Sprocket Calculator: What It Computes and Its Purpose
A sprocket calculator finds the speed and torque relationship between two sprockets connected by a chain drive. The driving sprocket is attached to the motor or power source; the driven sprocket is attached to the output shaft or load. The ratio of their tooth counts determines how much the chain drive multiplies or reduces speed between the two shafts. A drive ratio above 1 means the output shaft turns slower than the input with proportionally more torque. A drive ratio below 1 means the output shaft turns faster with less torque.
Sprocket Drive Ratio and Output RPM: The Full Formula
Drive ratio = driven teeth ÷ driving teeth Output RPM = input RPM × driving teeth ÷ driven teeth
- Drive ratio = driven teeth ÷ driving teeth
- Output RPM = input RPM × driving teeth ÷ driven teeth
- Output RPM = input RPM ÷ drive ratio
- Ideal output torque = input torque × drive ratio
Using the Sprocket Calculator: A Clear Step By Step
Inputs
- Driving sprocket teeth: count the teeth on the sprocket mounted to the motor or power source shaft
- Driven sprocket teeth: count the teeth on the sprocket on the output shaft
- Input speed (RPM): the rotational speed of the driving shaft, from the motor nameplate or a tachometer reading
Steps
- Count or read the tooth count on the driving sprocket.
- Count or read the tooth count on the driven sprocket.
- Record the driving shaft speed in RPM.
- Enter all three values and read drive ratio and output RPM from the results.
Sprocket Calculation: A Worked Example With Scenarios
A motor driving a 15-tooth sprocket at 1,800 RPM connected to a 45-tooth driven sprocket.
- Calculate drive ratio: 45 ÷ 15 = 3.00.
- Calculate output RPM: 1,800 ÷ 3.00 = 600 RPM.
The chain drive provides a 3:1 speed reduction, delivering 600 RPM at the output shaft.
Where a Sprocket Calculator Is Most Useful for Design
Use this calculator when selecting sprocket tooth counts to achieve a target output speed, when verifying the speed ratio of an existing drive, or when comparing multiple sprocket combinations during design. It also helps when checking whether a replacement sprocket changes the driven speed. This calculator assumes a single-stage chain drive with two sprockets. For two-stage or compound chain drives (three or more sprockets in series), calculate each stage separately and multiply the drive ratios.
Assumptions
- The chain has no slip; sprocket-and-chain drives are positive drives with fixed ratio.
- The calculation assumes a single-stage (two-sprocket) drive; compound drives require a separate calculation per stage.
- Drive efficiency (typically 97 to 99% per stage) is not included in the speed ratio; the formula gives the theoretical ratio.
- Input RPM is the steady-state shaft speed; startup or variable-speed conditions require a separate analysis.
Limitations
- Does not calculate chain length; use the chain length formula separately.
- Does not calculate pitch diameter; pitch diameter = (number of teeth × chain pitch) ÷ π.
- Does not account for chain drive efficiency; multiply output torque by 0.97 to 0.99 for a realistic estimate.
- Does not handle belt-and-pulley drives; those use pulley diameters, not tooth counts.
In Practice
The most common sprocket sizing mistake is choosing a tooth count combination that puts the chain under high polygon effect. A sprocket with fewer than 17 teeth produces a noticeable speed variation in the chain (the chordal action effect), which causes vibration and shortens chain life. Where output speed smoothness matters, use at least 17 teeth on the small sprocket, even if this requires a larger ratio on the driven side to achieve the target output speed.
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Frequently Asked Questions: Sprocket Calculator Tool
How do I calculate sprocket drive ratio?
Divide the number of teeth on the driven sprocket by the number of teeth on the driving sprocket. A driving sprocket with 15 teeth and a driven sprocket with 45 teeth gives a drive ratio of 45 ÷ 15 = 3. This means the output shaft turns 3 times slower than the input shaft.
What is the difference between drive ratio and gear ratio?
Drive ratio and gear ratio describe the same concept: the ratio of output speed to input speed. In sprocket-and-chain systems the preferred term is drive ratio. A ratio greater than 1 means the output turns slower (speed reduction, torque increase). A ratio less than 1 means the output turns faster (speed increase, torque reduction).
How does changing sprocket size affect torque?
Torque and speed are inversely related in an ideal drive. If the drive ratio is 3 (output 3× slower than input), the output torque is 3× the input torque, before chain friction losses. Increasing the driven sprocket size increases drive ratio, reduces output speed, and increases output torque. Decreasing the driven sprocket size does the opposite.
Can I use this calculator for bicycle gears?
Yes. Enter the chainring tooth count as the driving teeth, the rear cog tooth count as the driven teeth, and the cadence in RPM as the input speed. The output speed is the rear wheel RPM, which you multiply by the wheel circumference to get ground speed.
What is chordal action in chain drives?
Chordal action is the slight speed variation in the chain that occurs because the chain links engage the sprocket teeth as chords of a polygon rather than arcs of a circle. Sprockets with more teeth have a smaller polygon effect. Small sprockets (fewer than 17 teeth) show noticeable chordal action, which causes vibration and accelerated wear. Using 17 or more teeth on the smaller sprocket reduces this effect significantly.
Sources
Last updated: . Reviewed for accuracy against the formula shown above.