Gear Ratio Calculator
Gear Parameters
Gear 1 · Driver
Gear 2 · Driven
Calculated Results
How to Calculate a Gear Pair
Gear module and pitch diameter
The module describes the size of the teeth and must be the same for two standard metric gears that mesh. For a standard spur gear, the pitch diameter is the module multiplied by the number of teeth.
Here, d is the pitch diameter, m is the module and z is the number of teeth. Because the tooth count must be a whole number, a freely entered pitch diameter is adjusted to the nearest compatible tooth count for the selected module.
Center distance
The center distance is the distance between the rotational axes of two externally meshing gears. For standard gears without profile shift, it is half the sum of their pitch diameters.
Gear ratio and rotational speed
The tooth-count ratio determines the speed relationship. The larger gear rotates more slowly than the smaller gear. For two external gears, the gears rotate in opposite directions.
Torque, Power and Gear Efficiency
Output torque
For an ideal gear pair, torque increases in proportion to the driven gear’s tooth count. The calculator applies the entered efficiency to estimate the output torque for Gear 1 driving Gear 2.
The efficiency η is entered as a percentage and converted to a decimal for the calculation. The reverse calculation estimates the required input torque from the entered output torque.
Rotational power
Rotational power depends on torque and rotational speed. The output power shown by the calculator is the input power multiplied by the selected efficiency.
When n is in revolutions per minute and T is in newton metres, this expression gives power in kilowatts.
Pitch line velocity and tangential force
Pitch line velocity is the linear speed at the pitch circle. Tangential force is the force transmitted at the pitch circle and is calculated from the torque and pitch radius.
For these two expressions, d₁ must be in metres. The calculator converts the entered pitch diameter from millimetres where required.
Example Gear Pair Calculation
Example with a 2:1 ratio
Consider two external spur gears with a module of 2 mm. Gear 1 has 20 teeth and Gear 2 has 40 teeth. Their pitch diameters are 40 mm and 80 mm, respectively.
If Gear 1 rotates at 1,000 rpm, Gear 2 rotates at 500 rpm. With an input torque of 10 N·m and an efficiency of 95%, the estimated output torque is 19 N·m.
Assumptions and Limitations
This calculator models two external spur gears with a common metric module. It assumes standard geometry without profile shift, backlash, elastic deformation or detailed tooth-contact effects. The calculated efficiency is a user-supplied overall value rather than a prediction of actual losses.
The calculated tangential force is based on the input torque and the pitch diameter of Gear 1. For design verification, also consider tooth strength, material, lubrication, bearing loads, service factor, temperature and applicable gear-design standards.
Frequently Asked Questions
How do I calculate the center distance between two gears?
For two standard external gears without profile shift, add their pitch diameters and divide by two: a = (d₁ + d₂) / 2.
How does the module affect a gear pair?
The module defines the tooth size. For standard metric gears to mesh correctly, they need compatible tooth geometry and the same module. The pitch diameter is the module multiplied by the tooth count.
How do I calculate the gear ratio?
For this calculator, the ratio is defined as the driven gear tooth count divided by the driving gear tooth count: i = z₂ / z₁. A ratio of 2:1 means Gear 2 turns at half the speed of Gear 1.
Why does the rotational speed decrease when the driven gear is larger?
The pitch-line speeds of meshing gears are equal. Therefore, a gear with twice as many teeth rotates at half the speed of the smaller gear.
How does efficiency affect output torque?
The calculator multiplies the ideal output torque by the entered efficiency. For example, 20 N·m ideal output torque at 95% efficiency becomes an estimated 19 N·m.
Can I use this calculator for internal gears or helical gears?
The current model is intended for two external spur gears. Internal gears, helical gears, profile-shifted gears and more complex gear trains require additional geometric and design parameters.