Gear Calculator
Geometry, ratio, speed, torque and force for spur and helical gear pairs, multi-stage gear trains and planetary gears. Calculated with standard relations and shown in a simulation with real involute profiles.
// Inputs
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// Simulation
Frequently asked questions
What is module and how does it relate to diametral pitch?
Module is the pitch diameter divided by the number of teeth: m = d / z (mm). Imperial practice uses its inverse, diametral pitch: DP = z / d (1/in). They relate as m = 25.4 / DP; for example DP 10 ≈ m 2.54.
What is the minimum number of teeth?
For a standard (x = 0) spur gear with a 20° pressure angle, the theoretical limit to avoid undercut is z = 2 / sin²20° ≈ 17. Fewer teeth need a positive profile shift; the tool calculates x_min for each gear and warns about undercut.
What should the contact ratio be?
The transverse contact ratio εα is the average number of tooth pairs in mesh. Below 1 there is no continuous mesh; at least 1.2 is recommended in practice. Helical gears have a total contact ratio εγ = εα + εβ, which is why they run more quietly.
Why use profile shift?
To avoid undercut on pinions with few teeth, to fit a non-standard center distance and to balance root strength between the two gears. The "from target center distance" option calculates the total shift needed for a given center distance.
How is the axial force of a helical gear calculated?
F_a = F_t · tan β. A larger helix angle increases contact ratio and quietness but also the axial load on the bearings, so β is usually chosen between 8° and 20°.
What are the assembly conditions for planetary gears?
There are three: coaxiality (z_r = z_s + 2·z_p), assembly (z_s + z_r divisible by the number of planets) and neighbour clearance ((z_s + z_p)·sin(π/N) > z_p + 2, planet tips must not touch). The tool checks all three; if assembly fails, the simulation shows the teeth overlapping.
How is the direction of rotation found in a gear train?
Each external mesh reverses the direction. An even number of stages turns in the input direction, an odd number in the opposite direction. An idler gear reverses direction without changing the ratio.
Which standard are the calculations based on?
Geometry and meshing follow ISO 21771 / DIN 3960 (basic rack: h_a* = 1, c* = 0.25). The tool does not calculate root and flank strength (ISO 6336); verify strength separately for critical applications.