Gear Train Input
Enter one or more stages. Leave unused stages blank. Stage efficiency defaults to 100 if omitted.
Example Data Table
| Stage | Driver Teeth | Driven Teeth | Efficiency % | Stage Ratio |
|---|---|---|---|---|
| 1 | 12 | 36 | 98 | 3.0000 |
| 2 | 15 | 30 | 97 | 2.0000 |
| 3 | 18 | 27 | 99 | 1.5000 |
For this example, the overall ratio is 3 × 2 × 1.5 = 9. A 1500 RPM input gives about 166.67 RPM output.
Formula Used
Stage Ratio = Driven Gear Teeth ÷ Driver Gear Teeth
Overall Ratio = Ratio₁ × Ratio₂ × Ratio₃ × ... × Ratioₙ
Output RPM = Input RPM ÷ Overall Ratio
Total Efficiency = (Eff₁ × Eff₂ × Eff₃ × ... × Effₙ)
Output Torque = Input Torque × Overall Ratio × Total Efficiency
An odd number of external gear meshes reverses direction. An even number keeps the final direction the same.
How to Use This Calculator
- Enter the input speed if you want output RPM.
- Enter the input torque if you want output torque.
- Choose the torque unit that matches your value.
- For each active stage, enter driver and driven teeth.
- Set the stage efficiency. Keep 100 for ideal calculations.
- Leave unused stages empty.
- Press the calculate button.
- Review the overall ratio, stage table, and graph.
- Use CSV or PDF export to save the results.
About Multiple Gear Ratios
Why combined ratios matter
Multiple gear stages let designers reach large speed changes. One small gear pair may not give enough reduction. A compound train solves that problem. Each stage adds another ratio. The final ratio is the product of all stages. This makes planning easier. It also shows how speed and torque shift through the system. A high overall ratio lowers output speed. It also raises output torque when losses stay reasonable. That is why compound gearing appears in machines, tools, and vehicles.
What the calculator shows
This calculator reads each driver and driven gear pair. It computes the ratio for every stage. Then it multiplies them into one overall value. The stage table helps you inspect each step. The cumulative ratio column shows growth across the train. If input speed is entered, output speed is calculated. If input torque is entered, output torque is estimated. Efficiency is also included. That makes the result more practical. Real gear trains lose energy through friction, heat, and alignment effects.
How to read the output
A result of 1:9 means the output turns once while the input turns nine times. That is a reduction train. If the ratio is below one, the train increases speed. Direction also matters. Each external mesh flips rotation. An odd number of meshes reverses the final shaft. An even number keeps it aligned with the input direction. These details help when you model conveyors, reducers, and transmission systems. A quick check can prevent wrong part choices and costly redesigns later.
Best practice for accurate checks
Use correct tooth counts from actual parts. Add realistic efficiency values for each stage. Keep units consistent for torque inputs. Review whether the train is a speed reducer or a speed increaser. Compare the graph with the table. That makes unusual stage values easy to spot. When sharing results, export a CSV for spreadsheets or a PDF for reports. Clear records help during design review, maintenance planning, and classroom problem solving.
FAQs
1. What is a multiple gear ratio?
It is the combined ratio from two or more gear stages. You multiply each stage ratio to get the final ratio. This shows the total speed change across the full gear train.
2. How is one stage ratio calculated?
Divide driven gear teeth by driver gear teeth. For example, 36 driven teeth and 12 driver teeth give a stage ratio of 3. That means the driver turns three times for one output turn.
3. Why does output speed decrease with a large ratio?
A larger reduction ratio means the input shaft must spin more times to produce one output turn. That lowers output RPM. In return, torque usually rises when efficiency losses stay moderate.
4. Why is efficiency included?
Real gear systems lose energy through friction and heat. Efficiency helps estimate a more realistic output torque. It also shows why real systems perform below ideal mathematical predictions.
5. Can this calculator handle fewer than six stages?
Yes. Only fill the stages you need. Leave the rest empty. The calculator ignores blank stages and multiplies only the valid stages you entered.
6. Does the calculator show rotation direction?
Yes. Each external mesh reverses direction. An odd number of active stages gives the opposite final direction. An even number gives the same final direction as the input.
7. What if the ratio is less than one?
A ratio below one means the train increases speed instead of reducing it. In that case, output RPM rises and output torque drops when compared with the input, before losses.
8. When should I export CSV or PDF?
Use CSV when you want spreadsheet analysis or record keeping. Use PDF when you need a clean shareable report for classwork, clients, documentation, or maintenance review.