Calculator Form
Formula Used
Gear Ratio = Driven Teeth ÷ Driver Teeth
Output RPM = Input RPM × Driver Teeth ÷ Driven Teeth
Ideal Torque Multiplier = Driven Teeth ÷ Driver Teeth
Actual Torque Multiplier = Gear Ratio × Efficiency ÷ 100
Output Torque = Input Torque × Actual Torque Multiplier
For external gears, rotation direction reverses. For internal gears, the direction stays the same.
How to Use This Calculator
- Enter the driver gear teeth count.
- Enter the driven gear teeth count.
- Select external or internal gear pairing.
- Add input RPM if you need output speed.
- Add input torque if you need torque results.
- Enter efficiency to estimate real output torque.
- Optional diameter fields can verify the ratio.
- Press Calculate to view the result above the form.
- Use CSV or PDF buttons to export the result.
Example Data Table
The sample below uses 95% efficiency for output torque values.
| Driver Teeth | Driven Teeth | Input RPM | Gear Ratio | Output RPM | Input Torque | Output Torque |
|---|---|---|---|---|---|---|
| 20 | 40 | 1200 | 2:1 | 600 | 10 | 19 |
| 15 | 45 | 900 | 3:1 | 300 | 8 | 22.8 |
| 40 | 20 | 600 | 0.5:1 | 1200 | 12 | 5.7 |
About This Calculator
Gear ratio is one of the most useful mechanical values in mathematics and engineering. It compares the teeth on a driven gear with the teeth on a driver gear. This comparison shows how rotation changes through a gear set. A higher ratio usually lowers output speed. It also raises torque at the output shaft. That makes the calculator useful for students, technicians, hobby builders, and machine designers.
What The Ratio Means
A simple gear ratio tells you how many turns the input gear needs to move the output gear. When the driven gear has more teeth, the system creates speed reduction. When the driven gear has fewer teeth, the system creates speed increase. This is why gear ratio calculations matter in bicycles, conveyors, robotics, and automotive systems. Small changes in teeth count can change performance, force, and efficiency.
Why Extra Inputs Help
This calculator goes beyond the basic ratio. It can estimate output RPM from the input speed. It can also estimate output torque when efficiency is known. Optional pitch diameter fields help you compare size ratio with teeth ratio. That gives an extra check for consistency. The result section also shows simplified ratio form, direction change, torque multiplication, and speed change. These outputs save time during design checks and classroom work.
Accuracy Tips
Always enter correct teeth counts first. Teeth values should be whole numbers. Use RPM and torque only when you need motion or force results. Efficiency should stay realistic. Real systems lose power from friction, alignment error, heat, and wear. If your diameter ratio looks very different from the teeth ratio, review your gear dimensions. Matching values often suggest a more consistent setup.
Where People Use It
Simple gear ratio math appears in reduction drives, printer rollers, motor gearboxes, winches, and learning labs. It supports ratio analysis, rotational speed planning, and torque estimation. With export tools, example tables, and formula notes, this page is useful for quick calculations and repeatable records. It keeps the workflow clear, fast, and practical.
Learning Benefit
Because the calculator displays ratio, RPM, torque, and direction together, it helps users understand cause and effect. You can test several gear pairs quickly. That makes comparison easier during homework, prototyping, troubleshooting, and maintenance planning for small machines and daily teaching projects.
FAQs
1. What is a simple gear ratio?
A simple gear ratio compares the teeth on the driven gear with the teeth on the driver gear. It shows how output speed and torque change in a two gear system.
2. How do I calculate gear ratio by teeth?
Divide the driven gear teeth by the driver gear teeth. If the driver has 20 teeth and the driven gear has 40 teeth, the gear ratio is 2:1.
3. Why does output RPM become smaller?
Output RPM drops when the driven gear has more teeth than the driver gear. The larger driven gear needs more input turns to complete one full rotation.
4. Why does torque increase with a larger ratio?
A larger gear ratio trades speed for force. As output speed decreases, torque usually increases. Real systems lose some power, so efficiency affects the final torque value.
5. What does efficiency change in the result?
Efficiency reduces the ideal torque gain to a more realistic value. Friction, heat, and contact losses lower the actual torque that reaches the output gear.
6. Do pitch diameters matter in this calculator?
Pitch diameters are optional. They help verify whether the size relationship matches the teeth relationship. They are useful when checking design consistency or drafting gear dimensions.
7. What is the difference between external and internal gears?
External gears usually rotate in opposite directions. Internal gears rotate in the same direction. The ratio math still works, but the output direction result changes.
8. When should I export to CSV or PDF?
Use CSV for quick records, spreadsheets, or repeated comparisons. Use PDF when you want a printable summary for reports, homework, maintenance notes, or design reviews.