Gear Ratio Calculator
Calculate gear ratios, output speed, and torque multiplication for single-stage, compound gear trains, and various gear types.
Add multiple gear stages for compound gear train calculations. Total ratio = product of individual stage ratios.
Calculate gear backlash for precision applications. Backlash is the play between mating gear teeth.
Results
Gear Mesh Diagram
How It Works
Gear Ratio Basics
The gear ratio is determined by the number of teeth (or pitch diameter) of the driven gear divided by the driver gear:
Gear Ratio = N2 / N1 = D2 / D1
Where N2 is driven gear teeth, N1 is driver gear teeth, D2 and D1 are the respective pitch diameters.
Speed Reduction
Output speed is inversely proportional to the gear ratio:
Output RPM = Input RPM / Gear Ratio
A ratio greater than 1:1 reduces speed (speed reducer). A ratio less than 1:1 increases speed (speed increaser).
Torque Multiplication
Torque is multiplied by the gear ratio, accounting for efficiency losses:
Output Torque = Input Torque x Ratio x Efficiency
This is the fundamental power transmission trade-off: reducing speed increases torque proportionally (minus efficiency losses).
Compound Gear Trains
Multiple gear stages multiply their individual ratios:
Total Ratio = Ratio1 x Ratio2 x Ratio3 x ...
Each stage also multiplies efficiency, so a 3-stage train at 97% per stage has 91.3% overall efficiency.
Gear Types and Efficiencies
- Spur Gears (98%): Straight teeth, parallel shafts. Simple, economical, but can be noisy at high speeds.
- Helical Gears (97%): Angled teeth for smoother, quieter operation. Creates axial thrust loads.
- Bevel Gears (96%): Conical gears for right-angle or other shaft angle applications.
- Worm Gears (50-90%): High ratios in single stage (up to 100:1). Self-locking at low efficiency. Efficiency varies with ratio - higher ratios have lower efficiency due to increased sliding contact.
Worm Gear Efficiency
Worm gear efficiency depends heavily on the lead angle and ratio:
- Low ratios (5:1): ~90% efficiency
- Medium ratios (20:1): ~70-80% efficiency
- High ratios (40:1+): ~50-60% efficiency
Below ~50% efficiency, worm gears become self-locking (cannot be back-driven).
Direction of Rotation
External spur and helical gears reverse rotation direction at each mesh. Internal gears maintain the same direction. Worm and bevel gear directions depend on helix hand and mounting orientation.
Gear Type Efficiency Reference
| Type | Efficiency | Max Ratio | Characteristics |
|---|---|---|---|
| Spur | 97-99% | ~6:1 | Simple, economical |
| Helical | 96-98% | ~10:1 | Smooth, quiet |
| Bevel | 93-97% | ~5:1 | Right-angle drives |
| Worm | 50-90% | ~100:1 | High ratio, self-locking |
| Planetary | 95-97% | ~12:1 | Compact, high torque |
Key Formulas
Gear Ratio:
i = N2 / N1 = RPM1 / RPM2
Output Torque:
T2 = T1 x i x eta
Power (constant):
P = T x omega = T x 2 x pi x n / 60
eta = efficiency, omega = angular velocity (rad/s), n = speed (RPM)