Calculator Inputs
Use gear teeth, a known ratio, or measured rotations. Then combine the ratio with transmission, transfer case, tire size, speed, torque, and efficiency.
Example Data Table
| Ring Teeth | Pinion Teeth | Gear Ratio | Transfer Ratio | Tire Diameter | Speed | Engine Torque | Efficiency | Differential Ratio | Engine RPM |
|---|---|---|---|---|---|---|---|---|---|
| 41 | 10 | 0.78 | 1.00 | 31 in | 65 mph | 250 lb-ft | 88% | 4.100:1 | 2253.9 rpm |
Formula Used
1. Differential ratio from teeth
Differential Ratio = Ring Gear Teeth / Pinion Gear Teeth
2. Differential ratio from measured rotations
Differential Ratio = Driveshaft Turns / Wheel Turns
3. Overall drive ratio
Overall Ratio = Differential Ratio × Transmission Ratio × Transfer Case Ratio
4. Wheel RPM from road speed
Wheel RPM = (Vehicle Speed × 1056) / (π × Tire Diameter)
5. Engine RPM
Engine RPM = Wheel RPM × Overall Ratio
6. Speed per 1000 RPM
Speed per 1000 RPM = (1000 / Overall Ratio) × (π × Tire Diameter / 1056)
7. Wheel torque
Wheel Torque = Engine Torque × Overall Ratio × Efficiency
8. Tractive force
Tractive Force = Wheel Torque / Tire Radius
These formulas assume steady-state rolling conditions, a fixed tire diameter, and no converter slip. Real vehicles may differ because of tire growth, clutch slip, or drivetrain losses.
How to Use This Calculator
- Select how you want to obtain the axle ratio: gear teeth, known ratio, or measured rotations.
- Enter transmission ratio, transfer case ratio, tire diameter, vehicle speed, engine torque, and efficiency.
- Optionally add a comparison ratio to see how cruising RPM changes at the same road speed.
- Press the calculate button to display the results above the form and generate the RPM graph.
- Use the CSV and PDF buttons to save the result summary for reports, tuning notes, or workshop records.
FAQs
1. What does a higher differential ratio do?
A higher ratio multiplies torque more aggressively. That improves launch, towing, and climbing, but it usually raises cruising RPM and can reduce highway efficiency.
2. What does a lower differential ratio do?
A lower ratio keeps engine RPM lower at the same road speed. It often helps highway comfort and economy, but it reduces torque multiplication at the wheels.
3. Why is tire diameter included?
Tire diameter changes wheel circumference. Larger tires travel farther per revolution, lowering engine RPM at a given speed. Smaller tires do the opposite.
4. Why use overall drive ratio instead of axle ratio alone?
Overall drive ratio includes transmission and transfer case effects. That gives a more realistic view of engine RPM, torque delivery, and crawl performance.
5. Is measured rotation ratio always exact?
No. Measurement errors, open-differential behavior, tire slip, and incomplete rotation counting can distort the estimate. Gear tooth counts remain the most direct method.
6. What does drivetrain efficiency affect?
Efficiency reduces theoretical wheel torque to a more realistic delivered value. Lower efficiency means more power lost through gears, bearings, shafts, and other components.
7. Can I use this for towing setup comparisons?
Yes. Compare axle ratios at the same speed, tire size, and transmission gear. The RPM and wheel torque changes quickly show towing tradeoffs.
8. Does this replace full vehicle simulation?
No. It is a practical engineering estimator. Real acceleration, gradeability, and fuel use also depend on mass, aerodynamics, shift strategy, and tire traction.