Gears Calculators

These tools cover the gear math working engineers and gearheads actually need, from a quick ratio to full tooth geometry. The gear ratio calculator goes past the bare z₂/z₁ number: feed it an input RPM, torque and a drive-wheel diameter and it returns output shaft speed n₂ = n₁/i, torque rise T₂ = T₁·i, and road speed at that gear. The gear center distance calculator then turns module or diametral pitch and two tooth counts into a = m·(z₁+z₂)/2, with pitch diameters shown for layout.

The involute gear calculator builds standard full-depth ISO/AGMA geometry from module or diametral pitch and pressure angle and exports a real DXF tooth profile. When the job is tooth depth rather than a full involute profile, the addendum dedendum calculator isolates addendum a = m, dedendum b = 1.25m, whole depth, clearance, outside diameter and root diameter from module, DP or circular pitch. When the job is tooth clearance, the gear backlash calculator estimates module-based backlash allowance, angular backlash, the equal tooth-thickness split and the approximate center-distance equivalent while keeping production tolerance limits explicit. When the job is only the involute generating circle, the base circle diameter calculator isolates d_b = d·cos(alpha), base radius and base pitch from pitch diameter, module, DP or circular pitch. The gear contact ratio calculator adds the mesh-overlap screen: transverse contact ratio from path of contact and base pitch. The gear pitch-line velocity calculator then turns pitch diameter, module, DP or circular pitch plus RPM into pitch-line speed, pitch circumference and transmitted power when torque is entered. For angled teeth, the helical gear calculator converts normal module to transverse module with mt = mn/cos(beta), then returns pitch diameters, center distance, axial pitch and lead. The gear mesh force calculator converts torque, pitch diameter, pressure angle and helix angle into tangential, radial and axial loads for shaft and bearing checks. For right-angle layouts, the bevel gear calculator returns ratio, pitch cone angles, cone distance and face-width guide for straight bevel pairs. Pitch/module pages handle d = m·z, circular pitch and DP conversions.

Every result shows its formula and the governing standard — no quote gate, no shallow physics widget. New to ratios? Start with our how to calculate gear ratio guide. Metric and imperial throughout.