Gear ratio tells you how much a gearbox changes speed and torque. This Gear Ratio Calculator computes the gear ratio from tooth counts, then calculates output RPM and output torque using clear formulas and unit-safe inputs.
What Is Gear Ratio?
Gear ratio is the relationship between the rotation of an input gear and the rotation of the output gear. It is usually written as a ratio or as a number like 3:1, meaning the output turns once for every three input turns (depending on which direction you define).
In most gear-train problems, you can compute gear ratio using number of teeth because gear teeth act like proportional rotation markers.
Key Formulas (Teeth, RPM, and Torque)
For a simple two-gear mesh (one input gear driving one output gear), use these standard relationships.
- Gear ratio (GR) = Input teeth ÷ Output teeth
- Output RPM = Input RPM ÷ GR
- Output torque (ideal) = Input torque × GR
Variable meanings:
- Input teeth (Tin): number of teeth on the driving gear
- Output teeth (Tout): number of teeth on the driven gear
- Input RPM (RPMin): rotational speed of the driving gear
- Input torque (τin): twisting force applied to the input shaft
Direction Check: Does GR Increase or Decrease Speed?
Gear ratio and speed change are linked. If the output gear has more teeth than the input gear, the gearbox typically reduces speed and increases torque. If the output gear has fewer teeth, the gearbox typically increases speed and decreases torque.
Using the formula GR = Tin ÷ Tout:
- If GR > 1, output RPM is lower than input RPM.
- If GR < 1, output RPM is higher than input RPM.
- Ideal torque scales with GR (output torque = input torque × GR).
How to Use the Gear Ratio Calculator
The calculator is designed for the most common two-gear case. Enter the tooth counts and then choose what you want to compute: output RPM, output torque, or both.
- Enter Input gear teeth and Output gear teeth.
- Enter Input RPM if you want output speed.
- Enter Input torque if you want torque at the output.
- Pick your torque unit (N·m or ft·lbf) and let the calculator handle conversion.
- Click Calculate to get gear ratio, output RPM, and output torque.
Important note: Results assume an ideal gearbox with no losses. Real systems lose power to friction, gear meshing losses, bearing drag, and sometimes belt slip (for belts). If you need real-world accuracy, apply an efficiency factor.
Unit Handling: Torque Conversion
Torque is commonly expressed as newton-meters (N·m) or foot-pounds force (ft·lbf). A torque value in one unit can be converted to the other using a constant factor.
| Torque unit | Symbol | Conversion idea |
|---|---|---|
| Newtons·meters | N·m | Used in SI-based engineering |
| Foot-pounds force | ft·lbf | Common in US engineering |
This calculator uses the standard conversion between N·m and ft·lbf so you can enter values in the unit you already have.
Practical Examples
Example 1: Reduce Speed for Higher Torque
Suppose a motor spins at 3000 RPM and drives a gear train where the input gear has 12 teeth and the output gear has 36 teeth. Compute the gear ratio and the new speed.
- GR = 12 ÷ 36 = 0.333
- Output RPM = 3000 ÷ 0.333 ≈ 9000 RPM
This setup actually increases speed because the output gear has more teeth than the input gear only if you define the ratio the other way. Many people define “reduction” using a different GR convention. The calculator follows the formula GR = Tin ÷ Tout consistently, so the output speed result is always internally consistent.
Example 2: Estimate Output Torque for a Load
Imagine you have a gearbox where the input gear has 20 teeth, the output gear has 10 teeth, and the input torque is 5 N·m. Compute output torque under ideal assumptions.
- GR = 20 ÷ 10 = 2
- Output torque = 5 × 2 = 10 N·m
If you know the gearbox efficiency (for example 85%), you can multiply the ideal output torque by 0.85 to get a more realistic estimate.
Efficiency and Real-World Corrections
Gearboxes are not perfectly efficient. A typical approach is to apply efficiency η (eta) as a multiplier to torque output or as a divider to input power. For quick planning, you can adjust ideal torque:
- Real output torque ≈ Ideal output torque × η
Use manufacturer data when available. If you do not have it, efficiency can vary widely based on gear type, lubrication, load, and speed.
Limits and Safety Notes
Gear ratio math is straightforward, but mechanical design requires more than calculations. Check tooth strength, module/pitch compatibility, backlash needs, shaft ratings, and bearing load paths. Always verify that your gears are correctly matched and aligned.
- Use compatible gears (same pitch/module system).
- Confirm center distance and tooth engagement.
- Consider lubrication and wear over time.
- Account for shock loads and safety factors.
Frequently Asked Questions
How do I calculate gear ratio from gear teeth?
For a simple two-gear mesh, gear ratio equals input teeth divided by output teeth. If the input gear has T_in teeth and the output gear has T_out teeth, then GR = T_in / T_out. Use this GR consistently in speed and torque formulas.
Does a higher gear ratio mean more torque?
In an ideal gearbox, output torque equals input torque multiplied by gear ratio (output torque = τ_in × GR). So if GR is greater than 1, torque increases. If GR is less than 1, torque decreases. Real losses reduce the result by efficiency.
How do I find output RPM from input RPM?
For two gears, output RPM is input RPM divided by gear ratio. Using the same GR definition as above, RPM_out = RPM_in / GR. If GR is less than 1, the output RPM becomes higher than input RPM. Always keep units consistent.
What torque units should I use?
You can use either N·m or ft·lbf as long as you stay consistent. The calculator accepts your chosen input torque unit and converts internally. The gear ratio is unitless, so only torque requires conversion. Output torque will be shown in both the chosen unit and the computed standard.
Are these results accurate for real gearboxes?
The formulas assume ideal behavior with no friction or slippage. Real gearboxes lose power, so output torque is usually lower than the ideal value. If you have an efficiency rating η, multiply ideal output torque by η. That gives a better estimate for planning and sizing.
Next Steps
Use the Gear Ratio Calculator to get fast, consistent numbers for speed and torque. Then validate with gearbox efficiency, gear compatibility checks, and mechanical strength calculations before building or selecting hardware.