Gear ratio
i = N_driven / N_driver
A ratio greater than one is a speed reduction for the configured driver and driven gears.
Gear Ratio Calculator
Calculate the kinematics of one external spur-gear mesh from driver and driven tooth counts. Output speed, direction, torque, pitch-line velocity, pitch diameters, center distance, and transmitted tangential force are shown.
Access: Free to use, no installation, and No account required.
Inputs
This is a kinematic/preliminary power-transmission calculation. Tooth bending, contact stress, backlash, lubrication, dynamics, and AGMA design checks require the full engineering workflow.
Results
Gear ratio formula
For one external mesh, i = Ndriven / Ndriver and ωout = ωin / i. External gears reverse rotation direction. With a simple scalar efficiency, output torque is approximated by Tout ≈ Tin · i · η.
What this calculator does not determine
Gear tooth capacity, root stress, Hertzian contact stress, minimum tooth count/undercut, dynamic factors, shaft/bearing loads, lubrication, thermal limits, and manufacturing tolerances are not certified by this page.
Engineering reference
Gear Ratio Calculator: background and worked detail
Use the Gear Ratio Calculator to estimate reduction or overdrive ratio, output speed, idealized output torque, input/output power, pitch-line velocity, tangential tooth force, and rotation reversal for a single external spur-gear mesh.
Ratio, speed, and torque relationships
Output speed
n_out = n_in / i
Speed changes inversely with tooth-count ratio.
Output torque
T_out ≈ T_in · i · η
A scalar efficiency reduces the ideal torque multiplication.
18-tooth driver and 72-tooth driven gear
Drive an 18-tooth gear at 1,750 rpm and 10 N·m into a 72-tooth gear with 97% efficiency and 2.5 mm module.
- The ratio is 72/18 = 4:1.
- Output speed is 1,750/4 = 437.5 rpm.
- Estimated output torque is 10 × 4 × 0.97 = 38.8 N·m.
Result: The external mesh reverses direction; the input power is about 1.83 kW and the efficiency-adjusted output power about 1.78 kW.
Reading a gear train as a chain of ratios
For one external gear mesh, tooth count sets the kinematic ratio. A larger driven gear reduces speed and increases ideal torque in proportion to the ratio; a scalar mesh efficiency reduces the predicted output torque and power.
The calculation is a kinematic and first-order load estimate. Tooth bending stress, contact stress, undercut, face width, material, quality grade, dynamic factors, lubrication, shafts, bearings, alignment, and fatigue life require a fuller machine-design analysis.
Validation checks
Equal tooth counts
Case: Set driver and driven teeth equal.
Expected: Ratio should be 1, output speed should match input speed, and an external mesh should still reverse direction.
Ideal efficiency
Case: Set efficiency to 100%.
Expected: Output power should equal input power apart from display rounding.
Assumptions and model boundaries
Assumptions
- Involute spur gears are represented by tooth count and module for this focused calculation.
- A single external mesh is assumed.
- Efficiency is a constant scalar rather than a speed/load-dependent loss model.
Limitations
- Does not perform AGMA/ISO tooth rating or fatigue calculations.
- Does not validate minimum tooth count, profile shift, backlash, face width, shaft deflection, bearing life, or lubrication.
Gear Ratio Calculator FAQ
Do external gears rotate in the same direction?
No. A single external gear mesh reverses rotation direction. Additional external meshes reverse direction again.
Does an idler gear change the ratio?
An ideal idler can change rotation direction and geometry without changing the magnitude of the ratio between the first driver and final driven gear.
Can this calculator size the gear teeth?
No. Use the full machine-design workflow for tooth stress, material, geometry, shaft, bearing, and life checks.
Where this calculation comes from
The ratio chain is evaluated by the Gear Train Simulator engine, which also animates the resulting motion.
Open the source workbench →Read calculation and source methodology →